8.72. CHAPTER 8, PROBLEM 72
1165
8.72 Chapter 8, Problem 72
Problem: A Laval nozzle has a normal shock as shown and the Mach number downstream of the shock
is M2 = 0.5956. The gas flowing through the nozzle is air.
(a) Compute A/A , the ratio of the cross

98
CHAPTER 11. POTENTIAL FLOW
11.70 Chapter 11, Problem 70
Problem: Consider the potential-flow solution for uniform flow past a rotating cylinder whose angular
velocity, (t) = (t)/(2R2 ), varies with time, t.
(a) State the velocity potential, (r, , t). V

70
CHAPTER 11. POTENTIAL FLOW
11.54 Chapter 11, Problem 54
Problem: An arctic hut in the shape of a half-circular cylinder has radius R. A wind of velocity U
is blowing and creates a substantial aerodynamic force on the hut. This force is due to the diffe

860
CHAPTER 6. CONTROL-VOLUME METHOD
6.118 Chapter 6, Problem 118
Problem: Consider steady, incompressible, viscous flow above a flat plate of length L with surface mass
removal, which is referred to as suction. The velocity above the plate is given by u(

7.8. CHAPTER 7, PROBLEM 8
907
7.8 Chapter 7, Problem 8
Problem: Beginning with Gibbs equation, viz., T ds = de + pd(1/), determine entropy as a function
of temperature in an isobaric flow of a perfect, calorically-perfect gas.
Solution: For an isobaric fl

962
CHAPTER 7. ENERGY PRINCIPLE
7.46 Chapter 7, Problem 46
Problem: What head, hp , must be supplied by the pump in order to pump water of density at a rate
m from the lower to the upper reservoir? Assume 1 = 2 = 1 and that the head loss in a pipe of
leng

1002
CHAPTER 7. ENERGY PRINCIPLE
7.70 Chapter 7, Problem 70
Problem: Water of density flows from a swimming pool skimmer near the surface, through a pump
and a filter, and then reenters the pool at its bottom as shown. All pipes in the figure have constan

7.32. CHAPTER 7, PROBLEM 32
945
7.32 Chapter 7, Problem 32
Problem: Consider a pipe of diameter D = 10 in and length L = 300 ft. Carbon tetrachloride at
68o F flows through the pipe with average velocity u = 39 ft/sec. Determine the friction factor, f , a

8.4. CHAPTER 8, PROBLEM 4
1087
8.4 Chapter 8, Problem 4
Problem: Determine the Mach numbers and corresponding flow classification for the following. Use
Table A.1 to determine appropriate gas properties.
(a) Air at 50o F flowing with a velocity of 2000 ft

8.32. CHAPTER 8, PROBLEM 32
1119
8.32 Chapter 8, Problem 32
Problem: Helium flows through a normal shock wave. In terms of standard shock notation, conditions
ahead of the shock are u1 = 2000 m/sec, p1 = 100 kPa and T1 = 320 K.
(a) Compute the velocity be

1112
CHAPTER 8. ONE-DIMENSIONAL COMPRESSIBLE FLOW
8.26 Chapter 8, Problem 26
Problem: Hypersonic experiments are proposed for a wind tunnel with a reservoir temperature of 400o C.
If the test-section Mach number is 10, determine the temperature in the tes

1172
CHAPTER 8. ONE-DIMENSIONAL COMPRESSIBLE FLOW
8.78 Chapter 8, Problem 78
Problem: A space vehicle is reentering Earths atmosphere. At an altitude of 12 mi, it is moving at
Mach 7. The stagnation-point temperature on the nosetip of the vehicle is given

11.6. CHAPTER 11, PROBLEM 6
7
11.6 Chapter 11, Problem 6
Problem: The streamfunction is (r, ) = Qr3 sin 3, where Q is a constant of dimensions 1/(LT ).
(a) Compute the velocity components and locate all stagnation points.
(b) If = 1 when x = y = 1, what i

7.18. CHAPTER 7, PROBLEM 18
923
7.18 Chapter 7, Problem 18
Problem: A centrifugal water pump is sufficiently insulated to prevent any heat transfer from the
surroundings. The power required to drive the pump is Ws , and the mass-flow rate through the pump

940
CHAPTER 7. ENERGY PRINCIPLE
7.28 Chapter 7, Problem 28
Problem: Consider steady, laminar flow of an incompressible fluid with density through the circular
pipe of radius R shown below. At the inlet, the velocity is uniform and equal to U . At the outl

6.32. CHAPTER 6, PROBLEM 32
681
6.32 Chapter 6, Problem 32
Problem: A spherical ball of diameter d falls in a tank with square cross section of width h as shown
below. The tank is filled with an incompressible fluid of density . Determine the ratio d/h if

6.54. CHAPTER 6, PROBLEM 54
717
6.54 Chapter 6, Problem 54
Problem: A hemisphere of diameter 2d advances to the left at speed U into a tube of diameter 3d. An
incompressible fluid of density flows to the right at speed 2U . Flow speed and pressure across

6.40. CHAPTER 6, PROBLEM 40
695
6.40 Chapter 6, Problem 40
Problem: The velocity profile in a channel of half height h changes from u1 (y ) to u2 (y ), where
u1 (y ) = U y (h y ) and u2 (y ) = U y (2h y ) for 0 y h
Also, the profiles are symmetric about t

6.48. CHAPTER 6, PROBLEM 48
705
6.48 Chapter 6, Problem 48
Problem: A two-dimensional channel of width H has two slots of width h as shown. Fluid is injected
at the indicated velocities through the lower slot at an angle to the horizontal and normal to th

760
CHAPTER 6. CONTROL-VOLUME METHOD
6.74 Chapter 6, Problem 74
Problem: Incompressible fluid of density enters a channel of constant cross-sectional area A at the
left inlet with velocity U and leaves at the right outlet with velocity uo . The channel ha

6.82. CHAPTER 6, PROBLEM 82
777
6.82 Chapter 6, Problem 82
Problem: A really cheap faucet made of tin springs a leak so that an extra horizontal spray makes its
use practical only when the user is wearing a raincoat. Assuming the flow to be rotational, wh

790
CHAPTER 6. CONTROL-VOLUME METHOD
6.88 Chapter 6, Problem 88
Problem: Water of density flows through a shower head. The lower supply pipe has diameter d,
velocity upstream of the junction u1 = U i and velocity downstream of the junction u2 = 1 U i.
2
1

6.104. CHAPTER 6, PROBLEM 104
829
6.104 Chapter 6, Problem 104
Problem: The figure shows flow past a two-dimensional object in a water channel of height h and
width w out of the page. The density of the water is . The upstream pressure, po , is so low tha

876
CHAPTER 6. CONTROL-VOLUME METHOD
6.126 Chapter 6, Problem 126
Problem: A cylindrical container of diameter D filled with an incompressible fluid of density rests on
a frictionless horizontal surface. The mass of the container can be neglected relative

11.22. CHAPTER 11, PROBLEM 22
25
11.22 Chapter 11, Problem 22
Problem: The streamfunction for a two-dimensional flow is (x, y ) = exy , where , x and y are all
dimensionless. Plot the streamlines in the upper half plane, and find any stagnation points. Be

11.26. CHAPTER 11, PROBLEM 26
29
11.26 Chapter 11, Problem 26
Problem: The Cartesian velocity components for stagnation-point flow are u(x, y ) = Ax and
v (x, y ) = Ay , where A is a constant of dimensions 1/T .
(a) Determine the streamfunction, (x, y ).

720
CHAPTER 6. CONTROL-VOLUME METHOD
6.34 Chapter 6, Problem 34
Problem: The mass-flow rate through a nozzle is m = 0.65pc At / RTc , where pc and
Tc are pressure and temperature in the rocket chamber, respectively, and R is the gas
constant of the gases

6.50. CHAPTER 6, PROBLEM 50
749
6.50 Chapter 6, Problem 50
Problem: A water jet of cross-sectional area A with velocity Uj and density causes
a cart to move at a constant velocity U = 1 Uj . Use a Galilean transformation and a
5
stationary control volume

6.74. CHAPTER 6, PROBLEM 74
809
6.74 Chapter 6, Problem 74
Problem: Sand of density is being loaded onto a barge as shown. The velocity of
the sand is U , the cross-sectional area of the pipe is A, and the mass-flow rate through
the pipe is m = U A.
(a) I

6.98. CHAPTER 6, PROBLEM 98
865
6.98 Chapter 6, Problem 98
Problem: A water jet of density with initial velocity W and diameter do issues
vertically from a wall and supports a cone of half angle that rises to height h as
shown. You can assume the flow is