Use the Hazen-Williams equation to compute friction loss with C-120- A.docx

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The document provides the steps to calculate flow rate (Q in cfs) through a 6-inch diameter pipe network using the Hazen-Williams equation. It accounts for minor losses in fittings. Given a head loss (Hf) of 100 feet across a 700 foot long pipe, the calculations determine Hf is approximately 90.5 feet and the flow rate (Q) is about 2.775 cfs.

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Use the Hazen-Williams equation to compute friction loss with C=120. Account for minor
losses. All pipes and fittings are 6-in diameter. Determine the flow (cfs) from A to B.
Solution
V=KC(D/4)^0.63 * S^0.54â€¦â€¦â€¦.(1) - hazen-william equation
Where S=Hf/L and Q=V*A , A=(/4)D^2
From bernouliâ€™s equation,
100+100=V^2/2g+Hf+(0.4*V^2/2g)+(0.8*V^2/2g)+(0.8*V^2/2g)+
(1* V^2/2g)
200= V^2/2g(1+0.4+0.8+0.8+1+Hf)
200*2*32.2= V^2(4+Hf)â€¦â€¦â€¦.(2)
Given, C=120, D=6in=0.5ft
L=700ft and take K=1.318
Substituting above values in (1), we get
V=1.318*120*(0.5/4)^0.63 * (Hf/700) ^0.54
V=1.241*(Hf)^0.54
Squaring above equation,
V^2=1.54*(Hf)^1.08
Approximating the power of Hf in above equation from 1.08 to 1.00, inorder to reduce the
complexity in calculations,

V^2=1.54*Hf.............(3)
Put (3) in (2), we get 12880=1.54*Hf(4+Hf)=6.16Hf+1.54Hf^2
On solving above quadratic equation, we have Hf=89.4747ft, therefore V=11.738ft/sec
Q=A*V=( /4)0.5^2*11.738=2.30cfs
If Hf is calculated by trial and error method, it is found to be, 90.5ft, and V=14.136ft/sec
Q becomes 2.775cfs

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