Design of Penstocks

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A WATER RESOURCES TECHNICAL PUBLICATION
ENGINEERING MONOGRAPH No. 3
Steel ,Pensthcksy-
,’
r ;
UNITED STATES DEPARTMENT ’
6F Tt-tE INTERIOR
BUREAU, OF RECL-AMATI-ON ’ .
,-

2. -. I
The lower ends of the penstocks at Shasta Dam emerge from conerefa nnckors and pbcnge into the pozus~ho~csc

3. A WATER RESOURCES TKZHNICAL PUBLICATION
hrginooring Monograph No. 3
United States Department of the Interior l
BUREAU OF RECLAMATION

4. As the Nation’s principal conservation agency, the Department of the
interior has responsibility for most of our nationally owned public
’ lands and natural resources. This includes fostering the wisest use of
our land and water resources, protecting our fish and wildlife, preserv-
ing the environmental and cultural values of our national parks and
historical places, and providing for the enjoyment of life through out-
door recreation. The Department essessei our energy and mineral
~ resources and works to assure that iheir development is in the best
~ interests of all our people. The Departmerit also has a major respon-
1 sibility for American Indian reservation communities and for people
who live in tsland Territories under U.S. Administration.
ENGINEERING MONOGRAPHS are prepared and used by the technical
staff of the Bureau of Reclamation. In the interest of dissemination of re-
search experience and knowledge, they are made available to other inter-
ested technical circles in Government and private agencies and to the
general public by sale through the Superintendent of Documents, Govern-
ment Printing Office, Washington, D.C.
First Printing: 1949
Revised: 1959
Revised: 1966
Reprinted: 1977
Reprinted: 1986
U.S. GOVERNMENT PRINTING OF’FICE
WASHINGTON : 197’7

5. Preface
THIS MONOCRAPH will assist designers in the This edition now represents the contributions
solution of problems in design and construc- of many individuals in the Penstocks and Steel
tion of safe penstocks which may be fabricated Pipe Section, Mechanical Branch, Division of
in accordance with modern manufacturing Design, on the staff of the Chief Engineer,
procedures. Certain rules relative to materials, Denver, Colo.
stresses, and tests might be considered un- This monograph is issued to assist designers
necessarily conservative. Safety is of para- in the solution of problems involved in the de-
mount importance, however, and penstocks sign and construction of safe and economical
designed and constructed according to these welded steel penstocks.
rules have given satisfactory service through Because of the many requests for informa-
years of operation. tion concerning Bureau of Reclamation de-
Welded Steel Penstocks presents information signed and built penstocks, a comprehensive
concerning modern design and construction bibliography has been added in the back.
methods for pressure vessels applied to pen- Included in this publication is an informa-
stocks for hydroelectric powerplants. The data tive abstract and list of descriptors, or key-
are based on some 40 years experience in pen- words, and “identifiers.” The abstract was
stock construction by the Bureau of Reclama- prepared as part of the Bureau of Reclamation’s
tion. During this period many of the largest program of indexing and retrieving the litera-
penstocks in service today were designed and ture of water resources development. The
constructed. descriptors were selected from the Thesauw
Welded Steel Pmstocks was first issued in of Descriptors, which is the Bureau’s standard
1949 under the authorship of P. J. Bier. Be- for listings of keywords.
cause of the continuing interest in penstock Other recently published Water Resources
design, the monograph has been revised and Technical Publications are listed on the inside
updated to incorporate present day practice. back cover of this monograph.
iii

7. Contents
PWC
...
111
Report on Welded Steel Penstocks
Introduction ______________ _______ -- -__---------------_-__________ 1
Location and Arrangement ____- _____--___--- ____- ____ --__-_- ____ 1
Economic Studies ___________________________ -__-__-- ____--___ - .___ 5
Head Losses in Penstocks ________________________________________- 5
Effect of Water Hammer _______ _____ _____-- ____-_-_-- ____-- ____
- - 11
Pressure Rise in Simple Conduits _____________________ - ______ 12
Pipe Shell __--_______-____-_______________________------- - _______ 14
Temperature Stresses ________________________________________ 17
Longitudinal Stresses Caused by Radial Strain __________-----_ 17
Beam Stresses _______________-________________________------- 17
supports -- ----------_--------_----------------------------------- 19
Expansion Joints ___________________ ____- _____________ ______
- - -- - 23
Bends, Branch Outlets, and Wyes _________________________________ 26
Pipe Bends ____________-_____-_____________________---------- 26
Branch Outlets and Wyes _____________________ _____________ 27
- -
Penstock Accessories _____-__________________________________----- 33
For Installation and Testing __________________________________ 33
For Operation and Maintenance ______________________________ 33
Design of Piers and Anchors ______________________________________ 34 z
General ___--_ ___________------------------------------------- 34
Support Piers __--_-----^------------------------------------ 34
Anchors ---------------------------^------------------------~-. 35

8. vi CONTENTS
Materials --____---__-_-_-_--_____________________~~~~-~-~~~~~~~~~ 35
Steel Plates ___---_-_-____--_-_--~-~-~~-~~---~--~~~~~~~~~~~~~~ 35
Flanges, Fittings, Valves, and Other Appurtenances _- ________ 37
Fabrication ____----__________-_____________________-------------- 37
Structure and Arrangement _- ____- ____- _____ ----------__-__-_ 37
Nondestructive Inspection of Welds ___---_-_-_--_-__--_______ 39
Preheating and Postweld Heat Treatment _______ __________-_- 42
Installation -_-__-__---_--__________________________-~~~-~--~~~~~~ 42
Handling __-_----_-__--___-______________________~~~-----~~-~ 42
Placing and Welding --__--__--_--_--___--------- _____________ 43
Hydrostatic Test -_-_-_-_--_--_----______________________---- 44
Specifications and Welding Control _____ -__-_-_-__-__-_---_-______ 45
Specifications -___-___--_-____________________________-------- 45
Welding Control _- ______ ___________________________-_______
- - 45
Weld Tests ____-__---_-__----______________________-~~~~~~-~~ 45
Corrosion Control for Penstocks ____--___- ______ ____-___-_-_---_-_
- 45
A Selected Bibliography
rnd References _____-________-_________________________-------- 47
Coder and Standards _________________ -- ____ -- ______ -__-_----_ 47
Appendix -_----_---_-_------- _______-__----__-_-___- _______ -_-- 48
Absract _---___-------_- _________________________________ -- ____ 51
LIST OF FIGURES
Number PSLW
1. The 30-foot-diameter lower Arizona and Nevada penstock and
outlet headers were installed in two of the diversion tun-
nels at Hoover Dam. The upper headers were installed in
special penstock tunnels. The tunnels were not backfilled
with the exception of the inclined portions leading from the
intake towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. At Anderson Ranch Dam, the 15-foot-diameter penstock and
outlet header were installed in the diversion tunnel, which
was not backfilled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. General plan and typical profile of 15’-O’-diameter penstocks at
Glen Canyon Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4. Mass concrete of Kortes Dam encased the g-foot-diameter pen-
stocks, which were installed as the concrete was placed . . . 4
5. The 15-foot-diameter penstocks at Shasta Dam were embedded
in the concrete of the dam at the upstream ends and were
exposed above ground between dam and powerplant . . . . . 4

9. CONTENTS vii
Numbo Pans
6. The full length of the %foot-diameter penstock at Marys Lake
Powerplant lies above ground . . . . . . . . . . . . . . . . . . . . . . . . ,
7. Economic diameter of steel penstocks when plate thickness is a
function of the head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8. Economic diameter of steel penstocks when plate thickness is a
function of the head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,
9. Friction losses in welded steel pipe based on Scobey’s formula
for 6-year-old pipe and nonaggressive waters . . . . . . . . . . .
10. Losses for various values of 5 ratios and deflection angles up
to900 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
11. Head losses in 90° pipe bends as determined for various
R ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5
12. Loss coefficients for divided flow through small tees and branch
outlets as determined for various flow ratios &a. . . . . . . . . 11
Q
13. Water-hammer values for uniform gate motion and complete
closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
14. Equivalent stress diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
15. A graphical illustration of heads and stresses determined for
the hydrostatic testing of the Shasta penstocks . . . . . . . . . 18
16. The Shoshone River siphon crosses the river on a 150-foot span 20
17. Moments and deflections developed in a pipe precisely full, using
various types of supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
18. Formulae and coefficients for the computation of stresses in ring
girders as developed for stiffener ring analyses . . . . . . . . . 22
19. Formulae and coefficients for the computation of stresses in ring
girders due to earthquake loads . . . . . . . . . . . . . . . . . . . . . . . 23
20. Typical ring girder and column support . . . . . . . . . . . . . . . . . . . . 24
21. Typical rocker support. The angle yoke is used only for aline-
ment during grouting . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
22. Typical sleeve-type expansion joint . . . . . . . . . . . . . . . . . . . . . . . . 25
23. Flexible sleeve-type expansion joint with two stuffing boxes used
to permit longitudinal temperature movement and trans-
verse deflection . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
24. Constant diameter bend with the radius of the bend five times
the diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
25. Bend reducing in diameter from 9 feet to 8 feet, the radius equal
to four times the smaller diameter . . . . . . . . . . . . . . . . . . . . 27
26. Computation method for determining true pipe angle in a com-
poundpipebend ... ....... ...... ...... .. .... ...... .. 28
27. Loading diagrams for the development of reinforcement of
branch outlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
28. Loading diagrams for the development of reinforcement of wye
branchesinpenstocks................................ 30
29. Typical internal and external reinforcement for a branch outlet 32
30. Installation of a piezometer connection in shell of penstock for
turbine performance tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

10. Vsii CONTENTS
Nwllbw
31. Typical manhole designed for inspection and maintenance . . . . .
32. Typical monolithic pier construction for rocker supports . . , . . 34
33. Resolution of forces on pipe anchors . . . . . . . . . . . . . . . . . . . . . . . 36
34. Typical concrete anchor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
36. Shop fabrication of large diameter penstock . . . . . . . . . . . . . , . . 38
36. Shop joints are welded with automatic equipment . . . . . . . . . . . 39
37. Radiographic inspection of welds is performed using portable
X-ray equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
38. Postweld heat treatment is accomplished by heating in an en-
closed furnace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
39. Transporting large wye-branch into place . . . . . . . . . . . . . . . . . . 43
4G. Penstocks being placed, showing temporary support . . . . . . . . . 43
41. Penstocks installed in Flaming Gorge Dam are encased in mass
concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
LIST OF TABLES
Number
1. Basic conditions for including the effects of water hammer in
the design of turbine penstocks . . . . . . . . . . . . . . . . . . . , . . 13
2. Testing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

11. Report on Welded Steel Penstocks
construction, and inspection of pressure vessels.
Introduction Present design standards and construction
A penstock is the pressure conduit between practices were developed gradually, following
the turbine scrollcase and the first open water the advent of welded construction, and are the
upstream from the turbine. The open water result of improvements in the manufacture of
can be a surge tank, river, canal, free-flow welding-quality steels, in welding processes
tunnel, or a reservoir. Penstocks should be as and procedures, and in inspection and testing
hydraulically efficient as practical to conserve of welds.
available head, and structurally safe to prevent
failure which would result in loss of life and
property. Penstocks can be fabricated of LOCATION AND ARRANGEMENT
many materials, but the strength and flexibil-
ity of steel make it best suited for the range of The location and arrangement of penstocks
pressure fluctuations met in turbine operation. will be determined by the type of dam, location
The design and construction of pressure of intake and outlet works, relative location of
vessels, such as penstocks, are governed by ap- dam and powerplant, and method of river
propriate codes which prescribe safe rules and diversion used during construction. At dams
practices to be followed. Until a special pen- requiring tunnels for diversion of the river flow
stock code is formulated, steel penstocks should during construction, the penstocks may be
be constructed in accordance with the ASME placed in the tunnels after diversion has been
Boiler and Pressure Vessel Code, Section VIII, discontinued and the intake of the tunnel has
Unfired Pressure Vessels, issued by the Ameri- been plugged. This arrangement was used for
can Society of Mechanical Engineers, herein- the 30-foot lower Arizona and Nevada penstock
after referred to as the ASME code. This code and outlet headers at Hoover Dam as shown
is subject to periodic revision to keep it abreast in figure 1, and for the l&foot penstock header
of new developments in the design, materials, at Anderson Ranch Dam as shown in figure 2.
1

12. POWER PLANT
FXGUXE l.-The SO-fooGdia?neter &now Arieona and Nevada penstock and outlet keadem were in&u&d in two of the diversion tunnels at Hoover
Dam. The upper headere were installed in special penstock tunnels. The tunnels were not backfilled with the exception of the inclined portion
leading from the intuke tower.

13. WELDED STEELPENSTOCKS 3
Outlet pipe
No S----. used to provide the required watertightness in
the concrete and at the contraction joints.
Figure 4 shows the g-foot penstocks which are
embedded in Kortes Dam.
Penstocks embedded in concrete dams, en-
cased in concrete, or installed in tunnels back-
SECTION filled with concrete may be designed to transmit
some of the radial thrust due to internal water
pressure to the surrounding concrete. More
P. I. Horimtol bend---’
Sta 1sto6.03 - El. 3810
generally, such penstocks are designed to with-
stand the full internal pressure. In either case,
PLAN
the shell should be of sufficient thickness to
FIWRE 2.-At Anderson Ranch Dam, the l&foot-d&am- provide the rigidity required during fabrica-
eter penstock and outlet header were installed in the tion and handling, and to serve as a form for
diversion tunnel, which wae not backwed. the concrete. Embedded or buried penstock
For low-head concrete dams, penstocks may be shells also should be provided with adequate
formed in the concrete of the dam. However, stiffeners or otherwise designed to withstand
a steel lining is desirable to assure watertight- any anticipated external hydrostatic or grout-
ness. In large concrete dams which have both ing pressures. At Shasta Dam the upstream
transverse and longitudinal contraction joints, portions of the 15-foot penstocks are embedded
such as Glen Canyon Dam, steel penstocks are in the dam, while the downstream portions are
3. Outlet popes
“-% Penstocks
PLAN
Fxeuav s.-G’ener~Jplan and typical pro@ of I s’-

14. 4 ENGINEERING MONOGRAPH NO. 3
-18’ Dia. air vent
FIGURE 4.-Mass concrete of Kortes Dam
encased the g-foot-diameter penstocks,
which were installed as the concrete
was placed.
,-Main unit trashrack
‘--Penstock oir inlet
,-15-o” Dia. main FIGURE S.-The 15-foot-diameter pen-
I unit pensfocks
stocks at Shasta Dam were embedded
in the concrete of the dam at the up-
:Concrete anchor stream end8 and were exposed above
ground between dam and powerplant.
‘-Line of excavation --I’
exposed above ground, between the dam and Considering only the economics of the penstock,
the powerplant, as shown in figure 5. At other the single penstock with a header system will
plants, the entire length of the penstock may usually be preferable; however, the cost of this
be situated above ground, as in figure 6, which item alone should not dictate the design.
shows the %foot-diameter penstock at Marys Flexibility of operation should be given con-
Lake Powerplant. sideration because with a single penstock sys-
When a powerplant has two or more turbines tem the inspection or repair of the penstock
the question arises whether to use an individ- will require shutting down the entire plant. A
ual penstock for each turbine or a single pen- single penstock with a header system requires
stock with a header system to serve all units. complicated branch connections and a valve

15. WELDED STEELPENSTOCKS 5
ECONOMIC STUDIES
A penstock is designed to carry water to a
turbine with the least possible loss of head
consistent with the overall economy of installa-
tion. An economic study will size a penstock
from a monetary standpoint, but the final di-
ameter should be determined from combined
engineering and monetary considerations. An
example would be an installation where the
economic diameter would require the use of a
surge tank for regulation, but a more economi-
cal overall installation might be obtained by
using a penstock considerably larger than the
TYPICAL SECTION AT SUPPORT
economic diameter, resulting in the elimination
FIGURH B.-The full length of the d-foot-diameter pen- of the surge tank.
stock at Marys Lake Poweqdant lies above ground. Voetsch and Fresen (1) l present a method of
determining the economic diameter of a pen-
stock. Figure 7 was derived from their
to isolate each turbine. Also, the trashracks method, and figure 8 is an example of its use.
and bulkhead gates will be larger, resulting in Doolittle (2) presents a method for determining
heavier handling equipment. In concrete the economic diameters of long penstocks
dams it is desirable to have all openings as where it is economical to construct a penstock
small as possible. The decision as to the pen- of varying diameters. This “step by step”
stock arrangement must be made considering method requires considerable time but should
all factors of operation, design, and overall cost be considered for final design for long pen-
of the entire installation. stocks.
Proper location of the penstock intake is im- All the variables used in an economic study
portant. In most cases the intake is located must be obtained from the most reliable source
at the upstream face of the dam, which available, keeping in mind that an attempt is
provides short penstocks and facilitates opera- being made to predict the average values of all
tion of the intake gates. In some cases variables for the life of the project. Special
the penstock intake may be situated in an in- attention must be given to the “plant factor”,
dependent structure located in the reservoir, as figure 7, as this item materially affects the cal-
at Hoover and Green Mountain Dams, where culations.
diversion tunnels or topographic conditions
influenced the arrangement. Regardless of
arrangement, the intake should be placed at an
elevation sufficiently below low reservoir level HEAD LOSSES IN PENSTOCKS
and above the anticipated silt level to allow an
uninterrupted flow of water under all condi- Hydraulic losses in a penstock reduce the
tions. Each intake opening is protected effective head in proportion to the length of
against floating matter by means of a trash- the penstock and approximately as the square
rack structure and is controlled by suitable of the water velocity. Accurate determination
gates. of these losses is not possible, but estimates can
be made on the basis of data obtained from
To prevent the development of a partial pipe flow tests in laboratories and full-scale
vacuum during certain operating conditions, installations.
penstock profiles from intake to turbine should,
‘Numbers in parentheses refer to literature cited in mxtlon, “A
whenever possible, be laid on a continuous Selected Bibliography and References”. at the end of thla mono-
slope. mwh.

16. ENGINEERING MONOGRAPH NO. 3

17. NOTATION
a : Cost of pipe per lb., instolled, dollars. Ii = Weighted overage heod including woter
8 = Diometer multiplier from Groph 6. hommer. (based an design head )
b = Volue of lost power in dollorr per k wh. KS = Friction coefficient in Scobey’s formula (0.34).
D = Economic diometer in feet. n = Ratio of overweight to weight of pope shell.
e = Overall plant efficiency. Cl = Flow in cubic feet per second. (ot design head of turbine)
eJ = Joint efficiency. r z Ratio of onnuol cost ta”a”( see explanotion)
f = Loss factor from Groph A. sg = Allowable tension, p.s.i
t = Weighted overage plate thickness(ot design head) for total length,
t, 2 Averoge plote thickness for length L,.
EXPLANATION AND EXAMPLE
Example for penstock Q = I28 CFS
ASSUME L,:22$ L,= 150; L,=(50’, L,ZlOO’
Dia.: 5’-0” Avg. plate =f H,=fJO’; H,=l20’, Hs=l70, H,= 2301i H,=240’
Value of power per kwh:‘0.005- b
” I ~~lL,t(~~Lz+~~)L,tlH~~L, _
Cost of steel pipe mstolled=sO.27/Ib =a 156.4’
L, t Lx + L, + L,
Plont factor (see GraphA):0.75(f~0.510)
0,8M,~u225x15.71)~~4wx 15.71x2)10.02 z)o,5,
Interest =3% n= 0.15 625 5
Depreciation = 0.005135
0.8 M.=‘0.02 per sq.ft. Weight/ foot=l57lx lO.2= 160.24 Ibs.
L
Gast/foot=l6a24x0.27=*43.26
r = 0.03 t0.005135+0.0119=0.0470 % 0.8 M.= sz o.ollg
L,t,+L*t2+LJts’...+Lntn
Kz -I
%efsgejb 0.34x095x 0.510x15.000x0.90x0.00~~ 690
t= or( I+n) 0.27x 0.0470 x I.15
L,+ Let Ls+...+ Ln t4 9: 1.285 (from GmphB);D’=3.7(from GmphG); Economic dia.: I.285 x3.7= 4.75 ( use 4’-10”dia.)
NOTE: Calculated economic diameter should be very close to ossumed diameter as it
is in this exomple. The problem should be reworked until this condition exists
% o a M, ~ 0. 8 M. per foot Depreciation is bosed on the accumulation of on onnual smkrng fund eorning 3%
Cast per foot of pipe
interest required to replace 50% of the pipe in 45 years, The annuol
0.8 M = Cost of mointainmg interior ond exterior surface poyment required is equal to 0.005135 times the first cost.
Oreo of pipe( inside surface oreo for embedded pipe,
inside ond outside surface areo for exposed pipe )
per year.
Depreciation = See Reclamation Monual, Vol. PI Fewer, page 2,4,llD.
r : Interest t Depreciation l % 0. 8 M.
FIGUREI 8.-Economic diameter of steel penstocks when plate thickness is a function of the head.

18. 8 ENGINEERING MONOGRAPH NO. 3
The various head losses which occur between V =velocity of flow in feet per second
reservoir and turbine are as follows: D =diameter of pipe in feet.
1. Trashrack losses Values for I& vary for different types of pipe.
2. Entrance losses For new continuous interior pipe unmarred by
3. Losses due to pipe friction projections on the inside (as for butt-welded
4. Bend losses pipe) a value of 0.32 may be used. Scobey
5. Losses in valve and fittings. gives values of Ks for old pipe allowing for
Losses through trashracks at the intake vary deterioration of the interior surface. To allow
according to the velocity of flow and may be for deterioration a value of Ks=0.34 is usually
taken as 0.1, 0.3, and 0.5 foot, respectively, for assumed in design for pipes whose interior is
velocities of 1.0, 1.5, and 2.0 feet per second. accessible for inspection and maintenance.
The magnitude of entrance losses depends Friction losses for this value of KS, for pipes
upon the shape of the intake opening. A cir- up to 10 feet in diameter, can be read from the
cular bellmouth entrance is considered to be chart, figure 9. For pipes too small to permit
the most efficient form of intake if its shape is access for maintaining the interior coating a
properly proportioned. It may be formed in value of Ks=0.40 is usually assumed.
the concrete with or without a metal lining at Bend losses vary according to the shape of
the entrance. The most desirable entrance the bend and the condition of the inside sur-
curve was determined experimentally from face. Mitered bends constructed from plate
the shape formed by the contraction of a jet steel no doubt cause greater losses than smooth
(vena contracta) flowing through a sharp- curvature bends formed in castings or concrete ;
edged orifice. For a circular orifice, maximum however, there is no way to evaluate such
contraction occurs at a distance of approxi- effects since data on actual installations are
mately one-half the diameter of the orifice. very meager. Laboratory experiments on very
Losses in circular bellmouth entrances are small size bends with low Reynolds numbers
estimated to be 0.05 to 0.1 of the velocity head. are not applicable to large size bends with high
For square bellmouth entrances, the losses are Reynolds numbers. When water flows around
estimated to be 0.2 of the velocity head. a bend, eddies and secondary vortices result,
and the effects continue for a considerable
Head losses in pipes because of friction
distance downstream from the bend. In sharp
vary considerably, depending upon velocity of
angle bends the secondary vortex motion may
flow, viscosity of the fluid, and condition of the
be reduced by guide vanes built into the bend.
inside surface of the pipe. Among the con-
Thoma’s (4) formula is based on experiments
ventional pipe flow formulae used for the
made at the Munich Hydraulic Institute with
computation of head losses, the Scobey, Man-
1.7-inch-diameter smooth brass bends having
ning, and Hazen-Williams formulae are the
Reynolds numbers up to 225,000, as shown on
most popular. For large steel pipe the Scobey
the chart in figure 10, and is expressed as:
formula is favored ; for concrete pipe, the
Manning formula ; and for cast-iron pipe in Ha=CL...................... (2)
waterworks, the Hazen-Williams formula. 2g
The Scobey formula(3), derived from ex- where
periments on numerous steel pipe installations, H,, = bend loss in feet
is expressed as follows: C =experimental loss coefficient, for bend
H*=K+. . . . ..,.............. loss
(1)
V =velocity of flow in feet per second.
in which The losses shown in figure 10 vary according
HP= head loss due to friction in feet per to the R/D ratio and the deflection angle of
1,000 feet of pipe the bend. An R/D ratio of six results in the
Ks = loss coefficient, determined experimen- lowest head loss, although only a slight de-
tally crease is indicated for R/D ratios greater than

19. WELDED STEEL PENSTOCKS
FRICTION LOSS - FEET PER 1000 FEET
,URE 9-Fmktion losses in welded steel pipe based on Scobey’s formula for &year-old pipe and nonaggressive
wat em.

20. IO ENGINEERING MONOGRAPH NO. 3
.26
.24
; .I6
W
i?
E .I4
g
o .I2
:
2 .I0
.06
.02
0’ 5” IO” 15“ 20” 25* 30” 35O 40=’ 45.’ 50” 55’ 60’ 65’ 70’ 75=’ 80’ 65’
DEFLECTION ANGLE A0
Fxoum lo.-LO88e8 for vari5248 value8 of g ratios and d43flection andes UP to 90'.
four. This relationship is also indicated by plished by the wicket gates of the turbines),
the curves of figure 11, which were plotted only the loss which occurs at the full open
from experiments with 90” bends, As the condition needs to be considered. According
fabrication cost of a bend increases with in- to experiments made at the University of
creasing radius and length, there appears to be Wisconsin (5) on gate valves of l- to Z-inch
no economic advantage in using R/D ratios diameter, the coefficient K in Equation (3)
greater than five. varies from 0.22 for the l-inch valve to 0.065
Head losses in gates and valves vary accord-
for the 12-inch valve for full openings. For
ing to their design, being expressed as:
large gate valves an average value of 0.10 is
H,=K-& . . . . . . . . . . . . . . . . . . . . . . (3) recommended ; for needle valves, 0.20 ; and
in which K is an experimental loss coefficient for medium size butterfly valves with a ratio of
whose magnitude depends upon the type and leaf thickness to diameter of 0.2, a value of 0.26
size of gate or valve and upon the percentage may be used. For sphere valves having the
of opening. As gates or valves placed in pen- same opening as the pipe there is no reduction
stocks are not throttled (this being accom- in area, and the head loss is negligible.

21. WELDED STEEL PENSTOCKS II
Fittings should be designed with smooth
and streamlined interiors since these result in
the least loss in head. Data available on losses
in large fittings are meager. For smaller fit-
tings, as used in municipal water systems, the
American Water Works Association recom-
mends the following values for loss coefficients,
K; for reducers, 0.25 (using velocity at smaller
end) ; for increasers, 0.25 of the change in
-Rough pipe velocity head ; for right angle tees, 1.25; and
for wyes, 1.00. These coefficients are average
values and are subject to wide variation for
-Smooth pipe different ratios between flow in main line and
branch outlet. They also vary with different
tapers, deflection angles, and streamlining.
0
012345670 9 IO
Model tests made on small tees and branch out-
lets at the Munich Hydraulic Institute show
that, for fittings with tapered outlets and de-
FRIES ll.-Head bsoea in so0 pipe benda as &to+ flection angles smaller than 90” with rounded
minsd fm uariuu.9 ratios.
E corners, losses are less than in fittings having
cylindrical outlets, 90” deflections, and sharp
corners. (See figure 12.) These tests served
as a basis for the design of the branch connec-
tions for the Hoover Dam penstocks.
EFFECT OF WATER HAMMER
Rapid opening or closing of the turbine
gates produce a pressure wave in the penstock
called water hammer, the intensity of which is
proportional to the speed of propagation of the
pressure wave produced and the velocity of
flow destroyed. Joukovsky’s fundamental
equation gives the maximum increase in head
for closures in time less than 2L/a seconds:
AH=-!% . . . . . . ..F*!. . . . . . . . . . . . . . . (4)
8
in which
AH =maximum increase in head
a =velocity of pressure wave
L=length of penstock from forebay to
turbine gate
v =velocity of flow destroyed
g =acceleration due to gravity.
From this formula, which is based on the
elastic water-hammer theory, Allievi, Gibson,
Fxoua~m-LO88 CO&i8Td8 for dbidd &HO thmwh Durand, Quick, and others developed inde-
amall tees and breach tnd8t8 a.8 da- fW d pendent equations for the solution of water-
0488 jtOl8 Vf3tiO80". hammer problems (6).
Q

22. ENGINEERING MONOGRAPH NO. 3
In his notes published in 1903 and 1913, in turbine speed regulatipn. A surge tank may
Alhevi introduced the mathematical analysis be considered as a branch pipe designed to ab-
of water hammer, while M. L. Bergeron, R. S. sorb a portion of the pressure .wave while the
Quick, and R. W. Angus developed graphical remainder travels upstream toward the fore-
solutions of water-hammer problems which are bay. When located near the powerhouse, it
more convenient to use than the analytical provides a reserve volume of water to meet
methods. A comprehensive account of methods sudden load demands until the water column in
for the solution of water-hammer phenomena the upper portion of the penstock has time to
occurring in water conduits, including graphi- accelerate.
cal methods, was published by Parmakian (7). When the length, diameter, and profile of
For individual penstocks of varying the penstock have all been determined, con-
diameter, the pressure reflections at points of sidering local conditions and economic factors,
change in diameter complicate the problem. the selection of a minimum closure time for the
However, if the varying diameter is reduced turbine gates will require a compromise be-
to a penstock of equivalent uniform diameter, tween the allowable pressure variation in the
a close estimate can be made of the maximum penstock, the flywheel effect, and the permis-
pressure rise. For penstocks with branch sible speed variation for given load changes on
pipes, it is necessary to consider the reflection the unit.
of pressure waves from the branch pipes and With reaction turbines, synchronous relief
dead ends in order to determine the true pres- valves, which open as the turbine gates close,
sure rise due to velocity changes. may be used to reduce the pressure rise in the
As the investment in penstocks is often con- penstock. Reduction of pressure rise is
siderable, they must be safeguarded against proportional to the quantity of water released.
surges, accidental or otherwise. Surges of the As relief valves are usually designed to dis-
instantaneous type may develop through charge only a portion of the flow, this portion
resonance caused by rhythmic gate movements, is deducted from the total flow in computing
or when the governor relief or stop valve is the reduced velocity and the corresponding
improperly adjusted. A parting and rejoining pressure rise.
of the water column in the draft tube or a
hasty priming at the headgate may also cause
surge waves of the instantaneous or rapid type. Pressure Rise in Simple Conduits
Adjustments iw the profile of a penstock may
be necessary to prevent the development of a With instantaneous gate closure, maximum
vacuum and water column separation during pressure rise in penstocks of uniform diameter
negative pressure surges. As water-hammer and plate thickness occurs at the gate ; from
surges occurring under emergency conditions there, it travels undiminished up the conduit
could jeopardize the safety of a penstock if they to the intake or point of relief. For slower
are not considered in the design, their magni- closures which take less than 2L/a seconds
tude should be determined and the shell thick- (L = length of penstock ; a = velocity of pressure
ness designed for the resultant total head. wave), the maximum pressure rise is trans-
Stresses approaching yield-point values may be mitted undiminished along the conduit to a
allowed. By using ductile materials in the point where the remainder of the distance to
penstock, excessive surge stresses may be ab- the intake is equal to Ta/2 (T=time for full
sorbed by yielding without rupture of plates gate stroke), from which point to the intake
or welds. Design criteria for including the the pressure rise diminishes uniformly to zero.
effects of water hammer in penstock and pump With uniform gate closure equal to or greater
discharge line installations, as used by the than the critical time, ZL/a, the maximum
Bureau of Reclamation, is shown in table 1. pressure rise occurs at the gate, from which
Surge tanks are used for reduction of water point it diminishes uniformly along the length
hammer, regulation of flow, and improvement of the penstock to zero at the intake. An anal-

23. TABLE l.-Basic conditions for including the effects of loater hummer in the design of turbine penstocks.
The basic conditions for ineludIng the &acts of water hammer in the design of turbine Denstock instaIlat.ions are
divided into normal and emergency conditions with s&able factors of safety assigned to each type of oDeratIon.
Nomad conditions of omwation Emergsncu conditiona of operation Emarmncu wnditious +wt to be comideed
as a basis for design
I. In those instances where. due to a The bssic conditions to be considered as 1. Other Doesible emereency conditions of
higher reservoir elevation. it is necessary WlergeneJT ODeration are as foIIows: operation are those during which certain
to set the st.,DS on tbe main relay valve pieces of control equipment are assumed to
1. The turbine Denstock installation may for a slower rate of gate movement. the 1. The turbine gates may be closed at malfunction in the most unfavorable man-
be werated at any head between the maxi- water hammer elTen3.a will be computed ner. The most severe emergency condition
mum and minimum values of the forebay foe this slower rata of gate movement any time by the action of the governor
head. manual control knob with the main of o~aration which wiII yield the maximum
water surface elevation. relay valve. or the emergency solenoid head rise in a turbine Denstock installation
device. will oeeur from either of the two following
2. The turbine eaten may be moved at 8. The reduction in head at various conditions of operation:
any rate of steed by the action of the BOV- points along the penstock will be corn-
emor head UD to a Dredatermined rate. or puted for the rate of gate opening which 2. The cushioning stroke will be as-
sumed t.0 be inoperative. (a) Rapid &sure of the turbine
at a slower rate by maneal control through is adually set in the governor in those gatesinIessthan2&seconds, (Lbthe
the aorili relay vaIve. cases where it aDDears that the u,mfiIe of
tbe Denstock is unfavorable. This mjni- a. If a relief valve is Dresent it, will be
length of the Denatik and a is the
2. The turbine may be operating at any mum Dressure will then be used as a bqsis assumed to be inoperative.
wte Dosition and be required to add or for normaI design of the pentik to in- wave velocity). when t& flow of water
drop any or ail of its load. sure that subatmospheric Dressures will in the Denstock is a maximum. (The
4. The Bate traversing time will be maximum head rise in feet due to this
not cause a penstock failure due to col- taken as the minimum time for which the
4. If tbe turbine penstock installation is IaDse. wndition of oDeration is 100 to 126
eanipDed with any of the following Dres- governor is designed. times the water velocity in feet per sac-
sure control devices it will be assumed that 9. If a surge tank is Drasent in the and. )
these devices are properly adjusted and penstock system the upsurge in the surge 6. The maximum head including water
function in tbe manner for which the tank will be computed for the maximum hammer at the turbine and along the (b) Rhythmic opening and closing of
equipment is designed: length of the panstock will be computed the turbine gates when a complete cy-
reservoir level condition for the rejection cle of gate owration is performed in
of the turbine flow which correspondb to for the maximum reservoir head condi-
(a) Surge tenks the rated output of the generator during tion for 5naI DWt gate closure to the -4L seconds. (Under extreme condIt,icms
the gate transversing time which is ac- zero-gate position at the -imum gover-
(b) Relief valves tually set on the governor. Unless an nor rate in 2& seconds. tie maximum head rise due to this con-
(e) Governor control SDParatus overflow sDiIlway is provided the top d- a ft$) of OD-tiOn is twice the static
(d) Cushioning stroke device evation of the surge tank will be deter-
mined by adding a freeboard of 20 Dar 6. If a surge tank is present in the
(e) Any other pressure control device. cent of the com~utd upsurge to the max- Since these conditions of operation re-
Denstock system the upsurge in the surge mire a complete malfunctioning of the
imum height of water at the highest tank wiII be eOmDUted for the maximum
6. Unless the actual turbine character- IlDSnrge. reservoir head condition for the rejection gowrnor control apDaratus at the most un-
istics are known. the efieetive area of fnil gate turbine flow at the maximum favorable moment. the DrobabiIIty of obtain-
through the turbine gates during the 10. The downsurge in the surge tank rate for which the governor Is designed. ing this t4pe of. oDeration is exceedingIy
mruimum rate of gate. movement will be will be e0m~ut.d for the minImum reser- The downsurge in the surge tank will be remote. Hence. these wnditioM will not. be
Upk as * linear relation wxth resDect to voir level condition for a load addition computed for the minimum r-air head used as a basis for design. However. after
from sDeed-no-load to the full Bate Do& condition for a fuI1 gate oDening from Se design has been eatabIiied from other
tion during the sate traversing iime the speed-n*Ioad position at tbe maxi- considerations. it is desimbIe that the
6. The water hammer &ecta will be which is actually set on the governor. The mum rate for which the governor is de- stresses in the turbine scrdl case. ~enstock.
computed on the basis of governor head bottom of the surge tank will be Iocatsd sign+. In determining the tom and bottom Bnd Dressme contrd devices be not in ax-
action for the governor rate which is BE- at a distance of 20 per cent of the com- elevatmns of the surge tank, nothing will :ess of the ultimate bursting strength of
anally set on the turbine for speed regal& DUti downsurge b&w the lowest down- be added to the UPsurgea and downsurges ;he structures for these emergene~ con%-
tion. If the r&w valve stoos are adinsted surm in the tank to safeguard against air for this -‘3EZX,CY eO&it&X, Of OD-- tiOns Of ODeratiOn.
to Bive a slower governor setting than wtering the Denstock. tion.
that for which the governor is designed,
this rate shall be determined DriOr to 11. The turbine, pens&k. surge tank. 7. The turbine. Denstuck. surge tank.
Droceeding with the design of turbine and other DRaWre control devices will be relief valve. or other control devices will
penstock installation and later adhered to designed to withstand the conditions of be designed to withstand the above emer-
at the Dower plant so that an economical normaI operation which are given above BemY wndltions of operation with a min-
basis for designing the penstoek. sclDu with a minImum factor of safety of 4 to imumfa+rofsafetqof2288an
WE=% etc.. Under ma-maI ODersting wndi- 5 based on the ultimata bursting or col- thgeh~mIbte bmxtmg or C0Sapaing
tions can be established. laDsing strenpth.
-
w

24. 14 ENGINEERING MONOGRAPH NO. 3
Ysis of pressure time curves shows that the static and water-hammer heads. Working
maximum pressure rise is determined by the stresses which will assure safety under all ex-
rate of change of velocity with respect to time. pected operating conditions should be used.
Maximum pressure rise will develop in a pen- However, stresses approaching the yield point
stock when closure starts from some relatively may be used in designing for emergency con-
small percentage of full stroke so that some ditions. For penstocks supported on piers in
finite velocity is cut off in a time equal to 2L/a open tunnels or above the ground, allowance
seconds. should be made for temperature and beam
The governor traversing time is considered stresses in addition to the stresses due to in-
to be the time required for the governor to ternal pressure. The diagram shown in figure
move the turbine gates from the rated capacity 14 permits a quick determination of equivalent
position to the speed-no-load position. As the stresses if principal stresses are known. The
rate of governor time is adjustable, it is im- diagram is based on the Hen&y-Mises theory
portant that a minimum permissible rate be of failure, sometimes called the shear-distor-
specified if maximum pressure rise in the pen- tion or shear-energy theory. The plate thick-
stock is to be kept within design limits. ness should be proportioned on the basis of an
Water-hammer conditions should be deter- allowable equivalent stress, which varies with
mined for the unit operating at rated head and the type of steel used. The ASME code gives
under maximum static head. The highest total maximum allowable tensile stresses for various
head, consisting of static and water-hammer types of steels.
heads, should be used for computing plate The hoop tension, S, in a thin shell pipe, due
thickness of the penstock. to internal pressure is expressed as:
R. S. Quick (6) simplified water-hammer
computations by using a pipeline constant, K,
s=* . .... .... . . . . . . . . . . . . . . . (5)
and a time constant, N, in the equations in which
(similar to Allievi’s) which determine pressure D=inside diameter of pipe in inches
rise, or water hammer, resulting from instan- p=internal pressure in psi
taneous closure. The chart in figure 13 shows t =plate thickness in inches
the relative values of K and P (equal to e =efficiency of joint.
h) for various values of N. Also in- Regardless of pressure, a minimum plate
h ..I thickness is recommended for all large steel
eluded is a chart which shows the velocity, a, pipes to provide the rigidity required during
of the pressure wave in an elastic water column fabrication and handling. For penstocks the
for various ratios of penstock diameter to desired minimum thickness for diameter, D,
thickness. Figure 14 gives only the maximum may be computed from the formula:
values of P for uniform gate motion and com-
plete closure. It covers a range of closures &in= D+zo.. . . . . . . . . . . . . . . . . . . . . (6)
400
from instantaneous to 50 intervals, and a range A thinner shell may in some cases be used if
of values of K from 0.07 to 40, which includes the penstock is provided with adequate stiff-
the majority of practical cases. The nearly eners to prevent deformation during fabrica-
vertical curve shows the limiting value for tion, handling, and installation.
maximum pressure rise at the end of the first Joint efficiencies for arc-welded pipe depend
time interval, 2L/a. Values of pressure rises on the type of joint and the degree of examina-
to the left of this line attain their maximum tion of the longitudinal and circumferential
values at the end of the first interval. joints. The ASME code stipulates a maximum
allowable joint efficiency of 100 percent for
double-welded butt joints completely radie-
PIPE SHELL graphed, and of 70 percent if radiographic
As has been stated, penstocks should be examination is omitted. Corresponding joint
c designed to resist the total head consisting of efficiencies for single-welded butt joints with

25. EXPLANATION
Cu. Ft. per sec.
0.6
0.5
Ok
0.3
0.2
0.10
0.09
E!
0.06
0.05
0.04
0.03 CHART SHOWING VELOCITY OF TRAVEL OF
PRESSURE WAVE IN ELASTIC WATER COLUMN
0.02
Formula : a - -
*=vyfTgb
O.OlW - 7L- -NJ l-+-J- ’ ’
007 0.1 0.2 0.5 IO 2 3 45
Values of Pipe - Line Constant K- $$ Where o - Velocity of Tmvel of. Pressure Wave. Ft. per Sec.
0
k- Bulk Modulus of Elasticity of Water- 294.000
CHART SHOWING MAXIMUM PRESSURE RISE WITH UNIFORM GATE MOTION Lbs. per Sq. In.
AND COMPLETE CLOSURE : BASED ON ELASTIC-WATER-COLUMN THEORY E = Younq’s Modulus for Pipe Walls = 29.400.000
Lbs. per Sq. In. approx. for Steel.
NOTE:Ratio of Pressure Rise’h” to Initial Steady HeadrH~determined from relation 2 Kp~b~, b = Thickness of Pips Walls, Inches.
d = Inside Diameter of Pipe, Inches.
FIGURE 13.-Water-hamm.er values for uniform gate motion and complete closure.
VI

26. I6 ENGINEERING MONOGRAPH NO. 3
NENCKY-YISES THEORY
FIGURE 14.-Equivalent stress diagram

27. WELDED STEEL PENSTOCKS 17
backing strips are 90 and 65 percent, respec- Steel on concrete (cradle supports) .0.60
tively. If radiographic spot examination is Steel on steel-rusty plates . . . . . . . . .0.50
used, allowable joint efficiencies are 15 percent Steel on steel-greased plates . . . . . . .0.25
higher than for nonradiographed joints. Steel on steel-with two layers
Postweld heat treatment of welds is required of graphited asbestos sheets
if the wall thickness exceeds a specified mini- between . . . . . . . . . . . . . . . . . . . . . . . .0.25
mum thickness. Joint efficiencies and radio- Rocker supports-deteriorated. . . . . .0.15
graphic inspection procedures used by the For expansion joints a frictional resistance
Bureau of Reclamation conform to the require- of 500 pounds per linear foot of circumference
ments of the ASME code. was determined by test and may be used for
Specifications issued by the Bureau of the computation of longitudinal forces in a
Reclamation for construction of penstocks pipeline.
usually require that they be welded by a
rigidly controlled procedure using automatic
welding machines, that the longitudinal and
circumferential joints be radiographed, and Longitudinal Stresses Caused by
that either the individual pipe sections or the Radial Strain
entire installation be tested hydrostatically.
Since the head varies along the profile of a
penstock in accordance with its elevation and Radial expansion of a steel pipe caused by
pressure wave diagram, it is customary to plot internal pressure tends to cause longitudinal
the heads and stresses as shown in figure 15. contraction (Poisson’s ratio), with a corre-
The total head at each point along the profile sponding longitudinal tensile stress equal to
can then be scaled off and the plate thickness 0.303 of the hoop tension. This is true, pro-
computed accordingly. vided the pipe is restrained longitudinally. This
Other stresses which must be considered in stress should be combined algebraically with
addition to hoop stresses are as follows: other longitudinal stresses in order to deter-
Temperature stresses mine the total longitudinal stress.
Longitudinal stresses which accompany
radial strain (related to Poisson’s ratio)
Beam stresses. Beam Stresses
When a pipe rests on supports it acts as a
Temperature Stresses beam. The beam load consists of the weight
of the pipe itself plus the contained water.
For a steel pipe fully restrained against Beam stresses at points of support, particu-
movement, the unit stress per degree of tem- larly for longer spans, require special consider-
perature change is equal to the coefficient of ation. This matter is discussed in the section
expansion of the steel multiplied by its on design of supports.
modulus of elasticity, or 0.0000065 X 30 X lo6 = Based on a preliminary design, various
195 psi per degree of temperature change. For combinations of beam, temperature, and other
a pipe having expansion joints and being free stresses should be studied so as to determine
to move on supports, the longitudinal tempera- the critical combination which will govern
ture stress is equal to the frictional resistance the final design. It may be necessary or
between supports and pipe plus the frictional desirable to reduce the distance between an-
resistance in the expansion joint. The resist- chors for pipes without expansion joints to
ance at supports varies according to the type reduce the temperature stresses or to shorten
of support and its condition. The following the span between supports ti reduce beam
average values of coefficients of friction have stresses. For penstocks buried in the ground,
been determined by tests: and for all other installations where the

28. m
t---Test pressureline - El. 1460
5-
)-
i-
)-
I-
)-
I ‘I
32-k i&t----...s
19”Byposicowi.:- -
1; f ” +---uownsrreom mce bI uWn
IntOk-El. bl!j-:
2’
n.1
Plate thicknessesvary from i’to 2b’
I Efficiency of joints : 99 X
-.-.
FIG- 16.-A graphical illustration of heada and stresses de temnined for the hydrostatic testing of the Shasta pen&o&.

29. WELDED STEELPENSTOCKS 19
temperature variation in the steel corresponds elastic theory of thin cylindrical shells (9).
to the small temperature range of the water, The shell will be mainly subjected to direct
expansion joints may be eliminated and all beam and hoop stresses, with loads being
temperature stresses carried by the pipe shell. transmitted to support rings by shear. Be-
For a pipe without expansion joints and an- cause of the restraint imposed by a rigid ring
chored at both ends in which the beam stresses girder or concrete anchor, secondary bending
are negligible, the longitudinal stresses may stresses occur in the pipe shell adjacent to the
be kept within allowable limits by welding the ring girder or anchor. Although this is only a
last girth joint in the pipe at the mean temper- local stress in the shell, which decreases
ature of the steel. A procedure similar to this rapidly with increasing distance from the
was used for the penstock and outlet headers stiffener, it should be added to the other longi-
at Hoover Dam where expansion joints for the tudinal stresses. For a pipe fully restrained,
30-foot pipe were not considered to be feasible. the maximum secondary bending stress is:
In this case it was desired to eliminate all
longitudinal tension in the penstock because %=1.82+. . . . . . . . . . . . . . . . . . . . . (7)
the pinned girth joints had an efficiency of in which
only 60 percent in tension but 100 percent in p =pressure in psi
compression. The lowest anticipated service r= radius of pipe in inches
temperature was.46” F. In order to reduce the t=plate thickness in inches.
length of a penstock section between anchors This secondary bending stress decreases with
to that corresponding to a temperature of 45” any decrease in restraint.
F, mechanical prestressing by means of jacks If use of Equation (7) results in excessive
applied at the periphery of the pipe was re- longitudinal stresses, it may be necessary to
sorted to. A compressive force corresponding increase the pipe shell thickness on each side
to the difference between the erection tempera- of the stiffener ring for a minimum length of
ture and the lowest service temperature was 3/q, in which q=1.236/lx At this distance
applied. After welding the final closing joint from the stiffener ring, the magnitude of the
the jacks were removed, leaving the penstock in secondary stresses becomes negligible. Sec-
compression. At 46O F. the longitudinal stress ondary bending stresses at edges or corners
is then zero, and at higher temperatures the of concrete anchors may be reduced by cover-
penstock is in compression. ing the pipe at these points with a plastic
material, such as asbestos -or cork sheeting,
prior to concrete placement. This will also
SUPPORTS protect the edges or corners of the concrete
against cracking or spalling.
Modern trend in design requires that steel Pipes designed in accordance with the pre-
pipes located in tunnels, above ground, or ceding principles may be supported on long
across gullies or streams be self-supporting. spans without intermediate stiffener rings.
This is possible in most cases without an in- Figure 16 shows the lo-foot S-inch Shoshone
crease in plate thickness except adjacent to River siphon, which has a 150-foot span. The
the supports of the longer spans. If the pipe length of the span to be used on any particular
is to function satisfactorily as a beam, defor- job is usually a matter of economy. Very long
mation of the shell at the supports must be spans, such as shown in figure 16, are econom-
limited by use of properly designed stiffener ical only under certain conditions, as in the
rings or ring girders. A long pipeline with a crossing of rivers or canyons where the con-
number of supports forms a continuous beam struction of additional piers, which shorter
except at the expansion joints, where its con- spans would require, is not feasible.
tinuity is lost. Ring girders prevent large de- If continuous pipelines with or without ex-
formation of the pipe shell at the supports. pansion joints are supported at a number of
Stresses may therefore be analyzed by the points, the bending moments at any point

30. 20 ENGINEERING MONOGRAPH NO.3
FIGURE 16.-Tke Shoshone River siphon cro8ses the river on a 150-foot span.
along the pipe may be computed as in an 4. By stiffener rings which carry the load
ordinary continuous beam by using applicable to concrete piers by means of support
beam formulae. Spans containing expansion columns.
joints should be made short enough that their
As the static pressure within a pipe varies
bending moments will correspond to those of
from top to bottom, it tends to distort the
the other spans. Expansion joints should be
circular shape of the shell. This is especially
placed at midspan where deflections of the two
pronounced for thin-shelled large-diameter
cantilevered portions of pipe are equal, thus
pipes under low head or partially filled. The
preventing a twisting action in the joint.
weight of the pipe itself and the weight of
A pipe can be designed to resist safely the backfill, if the pipe is covered, also cause dis-
bending and shear forces acting in a cross- tortion of the shell.
sectional plane by several methods, as follows: Depending on the method of support,
1. By sufficient stiffness in the shell itself stresses and deformations around the circum-
2. By continuous embedment of part of the ference of a filled pipe will assume various
periphery of the pipe patterns as shown in figure 17. These dia-
3. By individual support cradles or saddles grams indicate the best location for longitudinal

31. WELDED STEEL PENSTOCKS 21
S, in the ring section. By adding the direct,
bending, and tensile stresses in the ring due
to internal pressure in the pipe, the total unit
stress in the inner and outer fibers of the ring
may be determined.
Moments Deflrct,onr
In installations subject to seismic disturb-
ances, the severity of the earthquake shocks
should be ascertained from local records and
considered in the design of the supports. Un-
saddle wpport Moments
less the project is located close to a fault zone,
a horizontal seismic coefficient of 0.1 to 0.2 of
the gravity load is adequate for most areas in
the United States. Stresses due to earthquake
loads for various points along the periphery
of the ring girder may be computed from the
Rmg Girder and Poor Support Moments Deflectwns
equations and stress coefficients given in figure
FIGURE 17.-Momenta and deflections developed in a 19. In determining the required section for a
pipe precisely full, using various types of supports. ring girder, stresses so computed should be
added to the stresses caused by static loads.
A typical ring girder and column support
joints in pipe shell and joints in stiffeners to designed for an S-foot penstock with a span
avoid points of highest stress or largest defor- of 60 feet is shown in figure 20. The girder
mation. The saddle and the ring girder with consists of two stiffener rings continuously
column supports are widely used. The one-point welded to the pipe on both sides and tied
support should not be used for a permanent in- together with diaphragm plates welded be-
stallation. It is included merely to illustrate its tween the two rings. Two short columns
flattening effect on an unstiffened pipe. consisting of wide-flange l-beams are welded
For the ring girder and column-type support, between the rings to carry the load to the
the support columns are attached to the ring rockers by means of cast-steel bearing shoes.
girders eccentrically with respect to the cen- A typical rocker assembly is shown in figure
troidal axis of the ring section so as to reduce 21. It consists of an Winch cast-steel rocker, a
the maximum bending moment in the ring sec- 3-l/2-inch steel pin with bronze bushings, and a
tion. In computing the section modulus of the cast-steel pin bearing. The rockers are kept in
ring girder, a portion of the adjacent shell may alinement by means of a steel tooth bolted to the
be considered as acting with the girder. The side of each rocker and guided between two
total length of the shell thus acting is: studs threaded into the bearing shoe of the sup-
l=b+1.56ds . . . . . . . . . . . . . . . . . . . . (8) port. The two pin bearings transmit the load to
in which b is the width of the ring girder (see the concrete pier. After being positioned in
figure 18) and r and t are as defined in Equa- accordance with a temperature chart so as to
tion (7). Essential formulae and coefficients provide effective support for the range of
for the computation of stresses in ring girders temperature anticipated, they are grouted into
are given in figure 18. These formulae and the top of the pier as shown in figure 21. The
coefficients were developed from the stiffener adjustable steel angle yoke shown in figure 21
ring analysis for the Hoover Dam penstocks. is used only during erection and grouting,
The table gives stress coefficients, Kl to K6, after which time it is removed.
inclusive, for various points around the cir- Thin-shelled pipes, when restrained longi-
cumference of the ring. These coefWents tudinally, are subjected to buckling stresses
are to be inserted in the appropriate equations because of axial compression. The permis-
shown for the determination of direct stress, sible span between supports is limited by the
T, bending moment, M, and radial shear stress, stress at which buckling or wrinkling will