QUESTIONS
Practice
 Water flows through a 2-inch
diameter pipe at 200 lbm/min. Its
temperature is 60oF. Find the velocity
of water flow (fps).
Practice
 Water from a pipe line is diverted into
weigh tank for exactly 9 minutes.
Tank weight increases 4765 lbf.
Water temperature is 60oF. Find the
flow rate (gpm).
Practice
 Steady flow of gas through a pipe
whose diameter decreases from 1.0
meter to 60cm. The gas density
decreases from 2 kg/m3 to 1.6 kg/m3.
The entering velocity is 25 m/s.
What is exit velocity (m/s)?
Example
How long
will it take
for level to
drop from
h = 3m to
h = 30cm?
60 cm diameter
3 cm diameter
Energy equation
 Comparable to First Law of
Thermodynamics – conservation of
energy
 Bernoulli Equation limited by
assumptions & missing terms
 General energy equation – expanded
factors
General energy equation
 Terms: energy per weight of flowing
fluid
 Units: length
 Convention: head
General energy equation
 Equations:
 Pump head: hp = [(V22 – V12)/ 2g] + ( z2 – z1)
+ hf + ( P2 – P1)/
 hT omitted from this equation
 Power added to water: Ẃp = hp  Q
Where Q represents the volumetric flow rate of
the water
 Pump efficiency p = [(power added to water)/
(power supplied to motor)] 100
Example
 Water flows from a large reservoir at
the rate of 1.20 ft3/s through a pipe
system. See Figure. Calculate the
friction losses.
Homework
 At the maximum rate of power
generation, this hydroelectric plant
takes a discharge of 141 m3/s. The
head loss through the penstock and
outlet is 1.52 m. What is the power
generation (MW)?
Elevation = 610m
Penstock
Powerhouse
Elevation = 0
Turbine
Homework
 The pump supplies energy to the flow
causing the upstream pressure in the
12 in. pipe to be 10psi. The
downstream pressure in the 6 in. pipe
is 30psi. The water flow rate is 3.92
cfs. What horsepower is delivered to
the flow?
PB
PA
PUMP
Fluid flow


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No-slip concept
Reynolds Number (Re)
Dye experiment
Laminar flow
Turbulent flow
Dimensional analysis – dimensionless
parameter
Head loss
General energy equation
Pipe friction
Hagen-Poisuelle – laminar flow
Darcy-Weisbach – laminar & turbulent
flows
• f : friction factor
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References
Images & examples
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•
Applied Fluid Mechanics, 6th Edition, Mott, Prentice Hall
Engineering Fluid Mechanics, 5th Edition Crowe, &
Roberson, Wiley
Which of the examples
were helpful?
Why?