Transcript Thermodynamics I

Test 1A
Same material
 Voluntary
 Outside regular class
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General energy equation
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Equations:
Pump head: hp = [(V22 – V12)/ 2g] + ( z2 – z1)
+ hf + ( P2 – P1)/ + ht
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
Homework
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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)?
Mechanical power of pump
Ẃm = 2 (rad/rev) (N/60s) T
• N = rpm of motor
• 60 s converts rpm to rev/sec
• T is torque; ft lbf
 Ẃm to “hp” or “kW”
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Efficiency
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p= Ẃp/ Ẃm
Fluid flow
No-slip concept
 Reynolds Number (Re)
• Dye experiment
• Laminar flow
• Turbulent flow
• Dimensional analysis – dimensionless
parameter
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Head loss
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General energy equation
Pipe friction
Hagen-Poisuelle – laminar flow
Darcy-Weisbach – laminar & turbulent
flows
f : friction factor
Example
An oil has a SG = 0.85 and a =6x10-4
m2/s.The oil flows through a 15cm
diameter pipe at 0.02 m3/s.
 Find the friction loss per 100m of pipe.
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Absolute Roughness, e
Pipe Material
x 10-6 feet
micron
(unless noted)
drawn brass
5
1.5
drawn copper
5
1.5
commercial steel
150
45
wrought iron
150
45
asphalted cast iron
400
120
galvanized iron
500
150
cast iron
850
260
600 to 3000
0.2 to 0.9 mm
concrete
1000 to 10,000
0.3 to 3 mm
riveted steel
3000 to 30,000
0.9 to 9 mm
wood stave
Example
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Water at 20oC flows at a rate of 0.05m3/s
in a 20cm asphalted cast iron pipe. What
is the head loss per kilometer of pipe?
Example
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The pump of a water distribution system has a
motor with a 90% efficiency. Flow through the
pump is 50 L/s. Steady flow occurs through the
pump with no change in flow velocity; the inlet
and outlet elevations are essentially the same.
Inlet and outlet absolute pressures are 100kPa
and 300kPa respectively.
What is the mechanical efficiency and the
temperature rise of the water due to friction?
Homework
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Water is pumped at a rate of 15 m3/s from
the reservoir through a pipe having a
diameter of 1.50m. What power must be
added to the water to achieve this flow?
Homework - Group
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What power must the pump supply to the
system to pump oil from the lower
reservoir to the upper reservoir at a rate of
0.2 m3/s?
References
 Images
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& examples
Fluid Mechanics Fundamentals & Applications, 6th Edition,
Cengel & Cimbala, McGraw Hill
Applied Fluid Mechanics, 6th Edition, Mott, Prentice Hall
Engineering Fluid Mechanics, 5th Edition Crowe, & Roberson,
Wiley
Which
of the examples
were helpful?
Why?