839CHAPTER 14
* Problems designated by a C are concept questions, and
studentsare encouraged to answer them all. Problems designated by
an Eare in English units, and the SI users can ignore them.
Problemswith the icon are solved using EES, and complete
solutionstogether with parametric studies are included on the
Online LearningCenter. Problems with the icon are comprehensive in
nature andare intended to be solved with a computer, preferably
using theEES software that accompanies this text. Problems with
the
icon are solved using the FlowLab CFD program.
PROBLEMS*
General Problems
141C What is the more common term for an energy-producing
turbomachine? How about an energy-absorbingturbomachine? Explain
this terminology. In particular, fromwhich frame of reference are
these terms definedthat of thefluid or that of the
surroundings?142C What are the primary differences between
fans,blowers, and compressors? Discuss in terms of pressure riseand
volume flow rate.143C List at least two common examples of fans, of
blow-ers, and of compressors.144C Discuss the primary difference
between a positive-displacement turbomachine and a dynamic
turbomachine.Give an example of each for both pumps and
turbines.145C For a pump, discuss the difference between
brakehorsepower and water horsepower, and also define
pumpefficiency in terms of these quantities.146C For a turbine,
discuss the difference between brakehorsepower and water
horsepower, and also define turbineefficiency in terms of these
quantities.147C Explain why there is an extra term in theBernoulli
equation in a rotating reference frame.148 A water pump increases
the pressure of the waterpassing through it (Fig. P148). The flow
is assumed to beincompressible. For each of the three cases listed
below, howdoes average water speed change across the pump? In
partic-ular, is Vout less than, equal to, or greater than Vin? Show
yourequations, and explain.
(a) Outlet diameter is less than inlet diameter (Dout Din)(b)
Outlet and inlet diameters are equal (Dout Din)(c) Outlet diameter
is greater than inlet diameter (Dout Din)149 An air compressor
increases the pressure (Pout Pin)and the density (rout rin) of the
air passing through it (Fig.P149). For the case in which the outlet
and inlet diametersare equal (Dout Din), how does average air speed
changeacross the compressor? In particular, is Vout less than,
equalto, or greater than Vin? Explain. Answer: less than
Pump Pout
Vout
Pin
Vin
Din
Dout
FIGURE P148
1410 Air flows through a 1-m-diameter roundpipe that has an
in-line turbomachine. Run FlowLab with template
Pump_turbine_incompressible. This template approxi-mates the pump
or turbine by specifying a sudden increase(pump) or decrease
(turbine) in pressure halfway through thepipe. The flow is
incompressible. Vary the pressure changefrom 10,000 to 10,000 Pa,
and write the results to the tablefor each case. For each case,
calculate the upstream and down-stream mass flow rate using the
values of density and averagevelocity calculated by FlowLab.
Compare to the calculatedmass flow rate. Also compare upstream and
downstream massflow rates. Discuss your results.1411 Air flows
through a 1-m-diameter roundpipe that has an in-line turbomachine.
Run FlowLab with thetemplate Pump_turbine_compressible. This
template approxi-mates the pump or turbine by specifying a sudden
increase(pump) or decrease (turbine) in pressure halfway through
thepipe. The flow is compressible, with the air treated as anideal
gas. Vary the pressure change from 10,000 to 10,000Pa, and write
the results to the table for each case. For eachcase, calculate the
upstream and downstream mass flow rateusing the values of density
and average velocity calculated byFlowLab. Compare to the
calculated mass flow rate. Alsocompare upstream and downstream mass
flow rates. Discussyour results.
Pumps
1412C There are three main categories of dynamic pumps.List and
define them.
1413C For each statement about centrifugal pumps,choose whether
the statement is true or false, and discussyour answer briefly:
CompressorPout
rout, VoutPin
rin, Vin
Din Dout
FIGURE P149
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849CHAPTER 14
1491 Air (r 1.225 kg/m3 and m 1.789 105 kg/ms) flows through the
stator blades of an axial flow turbine. The inlet-air mass flow
rate is 3.0 kg/s. Weapproximate the flow as a 2-D cascade of stator
blades at a radius of 0.20 m. Run FlowLab with template
Axial_turbine_spacing.(a) Vary the stator blade spacing s from
0.050 m to 0.150 m,and write the results to the table for each
case. Also, for fourcases (0.075, 0.100, 0.125, and 0.150 m),
generate a pressurecontour plot combined with streamlines as
follows: The pres-sure contour plot is generated by default when
the run is complete. To superimpose streamlines,
Post-Streamlines-Activate. To save the image, File-Print Graphics,
pick the filetype, enter a file name, and Accept. Click on Phys to
returnto the main screen. At which of these four values of s
doesmassive flow separation appear to be imminent?(b) Using a
protractor, measure the angle at which the flowdownstream of the
stator is turned as a function of s. Discusswhat happens to this
turning angle as s increases. Explain.1492 Air (r 1.225 kg/m3, and
r 1.789 105 kg/ms) flows through the rotor of an axial flow
tur-bine. The inlet air mass flow rate is 2.0 kg/s, and the
rotorspins at 100 rad/s. We approximate the flow as a 2-D cascadeat
a radius of 0.20 m. Run FlowLab with template
Axial_turbine_angle.(a) Vary the rotor angle of attack for four
cases (0, 20, 40,and 60), and write the results to the table for
each case.Also, for these same four cases, generate a pressure
contourplot combined with streamlines as follows: The pressure
con-tour plot is generated by default when the run is complete.
Tosuperimpose streamlines, Post-Streamlines-Activate. To savethe
image, File-Print Graphics, pick the file type, enter a filename,
and Accept. Click on Phys to return to the mainscreen. At which
angle of attack is there the least amount offlow separation?(b)
Which angle of attack provides the most torque? Tabulatenet
pressure drop across the turbine (Pinlet Poutlet). At whichof the
four angles do you get the highest pressure drop? Dis-cuss your
results.
1493 Air (r 1.225 kg/m3, and m 1.789 105 kg/ms) flows through an
axial flow turbine consist-ing of a stator and a rotor. The inlet
air mass flow rate is 2.0kg/s, and the rotor spins at 100 rad/s. We
approximate theflow as a 2-D cascade at a radius of 0.20 m. Run
FlowLabwith template Axial_turbine_rotorstator. (a) Vary the rotor
angle of attack for four cases (0, 20, 40,and 60), and write the
results to the table for each case.Also, for these same four cases,
generate a pressure contourplot combined with streamlines as
follows: The pressure con-tour plot is generated by default when
the run is complete. Tosuperimpose streamlines,
Post-Streamlines-Activate. To savethe image, File-Print Graphics,
pick the file type, enter a filename, and Accept. Click on Phys to
return to the mainscreen. At which angle of attack is there the
least amount offlow separation? (b) Which angle of attack provides
the most torque? Tabulatenet pressure drop across the turbine
(Pinlet Poutlet). At whichof the four angles do you get the highest
pressure drop? Dis-cuss your results.1494 In the section on wind
turbines, an expression wasderived for the ideal power coefficient
of a wind turbine,CP 4a(1 a)2. Prove that the maximum possible
powercoefficient occurs when a 1/3.1495 Wind (r 1.204 kg/m3) blows
through a HAWTwind turbine. The turbine diameter is 22.5 m. The
combinedefficiency of the gearbox and generator is 88 percent. (a)
Fora realistic power coefficient of 0.42, estimate the
electricalpower production when the wind blows at 10.0 m/s.
(b)Repeat and compare using the Betz limit, assuming the
samegearbox and generator. 1496 The average wind speed at a
proposed HAWT windfarm site is 12.5 m/s. The power coefficient of
each wind tur-bine is predicted to be 0.41, and the combined
efficiency ofthe gearbox and generator is 92 percent. Each wind
turbinemust produce 2.5 MW of electrical power when the windblows
at 12.5 m/s. (a) Calculate the required diameter of eachturbine
disk. Take the average air density to be r 1.2kg/m3. (b) If 30 such
turbines are built on the site and anaverage home in the area
consumes approximately 1.5 kW ofelectrical power, estimate how many
homes can be poweredby this wind farm, assuming an additional
efficiency of 96percent to account for the powerline losses.
Pump and Turbine Scaling Laws
1497C Look up the word affinity in a dictionary. Why doyou
suppose some engineers refer to the turbomachineryscaling laws as
affinity laws?1498C For each statement, choose whether the
statementis true or false, and discuss your answer briefly:(a) If
the rpm of a pump is doubled, all else staying the same,the
capacity of the pump goes up by a factor of about 2.
Rotor
v
Stator
VoutVin
Hub and Generator
r
vr
? ? ?bst
FIGURE P1490
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