1. MET 306
Fluid Mechanics
Lecture # 3
11/5/2012

2. Objective
Discuss the application of Newton’s second
law to fluid flows.
Explain the development, uses, and limitations
of the Bernoulli equation.
Use the Bernoulli equation (stand-alone or in
combination with the continuity equation) to
solve simple flow problems.
Apply the concepts of
static, stagnation, dynamic, and total pressures.
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3. Newton’s Second Law
As a fluid particle moves from one location to another, it
usually experiences an acceleration or deceleration. According
to Newton’s second law of motion, the net force acting on the
fluid particle under consideration must equal its mass times its
acceleration
F ma
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4. Bernoulli Equation
1
p V2 z constant along streamline
2
Apply Bernoulli Equ between two points
1 2 1 2
p1 V1 z1 p2 V2 z2
2 2
This is the celebrated Bernoulli equation—a very powerful tool in
fluid mechanics. In 1738. To use it correctly we must constantly
remember the basic assumptions used in its derivation:
1. Viscous effects are assumed negligible
2. The flow is assumed to be steady
3. The flow is assumed to be incompressible
4. The equation is applicable along a streamline.
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5. Bernoulli Equation
 Example 1
Consider the flow of air around a bicyclist moving through still air with velocity as
is shown in Fig. Determine the difference in the pressure between points 1 and 2.
1 2 1 2
p1 V1 z1 p2 V2 z2
2 2
1
sloution : p2 p1 V12
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6. Bernoulli Equation
Example  2
 A stream of water of diameter d =0.1 m flows steadily from a tank of diameter
D=1.0 m as shown in Fig. Determine the flowrate, Q, needed from the inflow pipe
if the water depth remains constant, h = 2.0 m.
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7. Bernoulli Equation
Example  3
Air flows steadily from a tank, through a hose of diameter D = 0.03 m and exits to
the atmosphere from a nozzle of diameter d = 0.01 m as shown in Fig. The pressure
in the tank remains constant at 3.0 kPa (gage) and the atmospheric conditions are
standard temperature and pressure. Determine the flowrate and the pressure in the
hose. T1=15o
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8. Bernoulli Equation
• Example  4
Water is flowing from a hose attached to a water main at 400 kPa gage (Fig. below). A child
places his thumb to cover most of the hose outlet, causing a thin jet of of high speed water as
can be seen from Fig. If the hose held upward what is the maxmuinm height that the jet could
achieve?
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9. Flowrate Measurement
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10. Pitot Tube
V 2 g (h)
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