CHE 311 (Fall 2000)
__________________
LAST NAME, FIRST
Quiz #1 (30 minutes, closed notes and closed book)
I.
A. When a fluid is subjected to a steady shear stress, it will reach a state of equilibrium in
which no further motion occurs.
B. Pressure and shear stress are two examples of a force per unit area.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
II.
A. Absolute pressures and temperatures must be employed when using the ideal gas law.
B. To convert from psia to psig, add 14.7, approximately.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
III. (8 pts) The U-tube shown in Fig. 1 has legs of
unequal internal diameters d1 = 10 mm and d2 = 5
mm, which are partly filled with immiscible liquids
of density 1 = 1,800 kg/m3 and 2 = 1,200 kg/m3,
respectively, and are open to the atmosphere at the
top.
1. If an additional 1.2 cm3 of the second
liquid is added to the right-hand leg, hA will change
by an amount .
 (cm) = 6.11 cm
hB
Fig. 1. U-tube with immiscible liquids
2. If the level hB falls by 0.6 cm, the level hC will rise by a distance
3. If hC = 3 cm and hA = 2 cm, then
hA
hC
(cm) = 0.15 cm
hB =
1.667 cm
IV. Determine the elevation where p = 200 Pa absolute assuming an isothermal atmosphere with T =
273oK. At sea level p = 101 kPa, gas constant R = 8.314 kJ/kmol.oK, molecular weigth of air = 28.97.
49,700 m
V. Water flows steadily through a 2-in.-inside diameter pipe at the rate of 170 gal/min. The 2in. pipe branches into two 1-in.- inside diameter pipes. Water viscosity is 1.2210-5 ft2/s. (1 ft3 =
7.48 gal)
1) If the average velocity in one of the 1-in. pipes is 25 ft/s,
the average velocity in the other 1-in. pipe is
44.45 ft
2)
The Reynolds number in the 2-in. pipe is
2.37105
VI. A two-lane highway carries cars traveling at an average speed of 60 mph. In a construction
zone, where the cars have merged into one lane, the average speed is 20 mph and the average
distance between front bumpers of successive cars is 25 ft. (1 mile = 5280 ft)
The average distance between front bumpers in each lane of the two-lane section is 150 ft
VII. A. According to the course syllabus you need a minimum of 12 hours per week to study
for CHE 311.
B. The course syllabus instructs you to put a box around each homework answer.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
CHE31101
MOMENTUM TRANSFER
Fall ‘2000
QUIZ #2
I.
A. In the energy balance or Bernoulli’s equation, the term p/ has the same units as the square
of a velocity.
B. As fluid flows through an orifice plate to the location of the vena contracta, its pressure will
rise, because it is going faster there.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
II. As shown, a pipe of cross-sectional area A = 0.002 m2
and a total length 10.0 m is used for siphoning water from a
tank. The discharge from the siphon is 1.5 m below the
level of water in the tank. At its highest point, the pipe rises
3.0 m above the level in the tank. Neglect pipe friction.
Atmospheric pressure is 1.013105 Pa. Water density is
1000 kg/m3.
a) The water velocity (m/s) in the pipe is 5.42 m/s
Siphon
b) The (gage) pressure in the
pipe at the same level of water in the tank is – 14,715 Pa
c) The lowest (gage) pressure in the pipe is – 44,145 Pa
III.
A horizontal 4-cm-diameter jet of water strikes a vertical plate. Determine the velocity issuing
from the jet if a force of 700 N is needed to
1) Hold the plate stationary
23.6 m
2) Move the plate away from the jet at 8 m/s
31.6 m
IV. Water flows in a 8-cm-diameter pipe with an
average velocity of 10 m/s. It turns a 90o angle and
flows radially between two parallel disks. The
distance between the disks is 0.4 cm,
The velocity at a radius of 50 cm is 4 m/s
disk
V. As shown, a 90o reducing elbow is located in a
horizontal plane (gravitational effects are unimportant),
through which water is flowing. The retaining force Fx and
Fy are required to keep the elbow in place. Neglecting
frictional loss, D1 = 0.20 m, D2 = 0.15 m, p1 = 1.5 bar
(gage), u1 = 6.0 m/s. 1 bar = 105 Pa. Water density is 1000
kg/m3.
Determine:
1) The gage pressure p2.
1.11105 Pa
2) The retaining force Fx.
Pipe
- 5,843 N
3) If p1 is not known and p2 = 0.5 bar (gage),
Fy = 2,894 N
CHE31101
MOMENTUM TRANSFER
Fall 2000
QUIZ #3
I.
A. A hydraulic jump is irreversible, and can only occur when a relative deep stream of
liquid suddenly becomes a relative shallow stream.
B. If two centrifugal pumps are placed in parallel, the overall pressure increase for a given
total flow rate Q will be twice what it is for a single pump with the same flow rate Q.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
II.
A. A friction factor is a dimensionless wall shear stress.
B. Rotational speed N is related to the angular velocity of rotation by the equation N = 2.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
III. The pump shown on the right adds 20 kW of power
to the flowing water (0.05 m3/s) that is then discharged to
the atmosphere. The only loss is that which occurs across
the filter at the inlet of the pump.
1) The pump head is
40.8 m
Use a pump head of 35 m for questions 2 and 3.
2) The head loss for this filter is
1.98 m
3) If there is no filter at the pump inlet, the inlet pressure
is (instead of –20 kPa) -3.94104 Pa
IV. Water at 0.1 m3/s and alcohol (SG = 0.8) at 0.3 m3/s
are mixed in a y-duct as shown on the right. The average
density of the mixture of alcohol and water is
850 kg/m3
V. What pressure increase (Pa, p u22) could be expected
across centrifugal pumps of .1 m impeller diameter when
pumping water. The impellers run at 1,200 rpm.
1.579105 Pa
If the swirl velocity is 5 m/s and the volumetric flow rate is
0.05 m3/s, the angular momentum leaving the impellers is
12.5 kg/m3
VI. As shown, a 90o reducing elbow is located in a
horizontal plane (gravitational effects are unimportant),
through which water is flowing. The retaining force Fx and
Fy are required to keep the elbow in place. Neglecting
frictional loss, D1 = 0.20 m, D2 = 0.15 m, p1 = 1.2 bar
(gage), u1 = 8.0 m/s. 1 bar = 105 Pa. Water density is 1000
kg/m3. Determine:
1) The gage pressure p2.
5.086104 Pa
2) If p1 is not known and p2 = 0.5 bar (gage),
Fy = 4,458 N
CHE31101
MOMENTUM TRANSFER
QUIZ #4
Fall 2000
I.
A. The drag coefficient is a dimensionless force per unit area.
B. For flow around a sphere, there is a transition region from laminar to turbulent flow in
which the value of the drag coefficient is quite uncertain.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
II.
A. When a descending sphere has reached its terminal velocity, Stokes’ law is always satisfied.
B. The sphericity of a cube is greater than that of a sphere of the same volume because the cube
has more surface area.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
III. A sphere is held in a small wind tunnel where air at 37.8oC and velocity of 2.3 cm/s is forced
on the sphere having a diameter of 0.042m. Density of air is 1.137 kg/m3 and viscosity of air is
1.910-5 Pa.s. Density of the sphere is 950 kg/m3.
1) If CD = 24/Re, the drag coefficient on the sphere is
0.4152
2) If CD = .44, the drag force on the sphere is
1.8310-7 N
3) If this sphere is falling in air at 37.8oC, the buoyancy force on the sphere is
4.3310-4 N
VI. As shown, the velocity of the water jet is 18 m/s. Water
density is 1000 kg/m3. Determine the force needed to
1) Hold the cone stationary
218.2 N
2) Move the cone away from the jet at 5 m/s 113.8 N
V. A balloon is being inflated with a water supply of 1.2 m3/s. Find the rate of growth of the
radius R at the instant when R = 0.5 m.
0.382 m/s
VI. Consider the manometer system shown on the
right. S is the specific gravity.
C
1) If the pressure of water is 2 kPa, the pressure
at A is 3,472 Pa (water density is 1000 kg/m3)
2) If the pressure at A is 50 kPa, the pressure at C
is 3.53104 Pa
B
A
CHE31101
I.
MOMENTUM TRANSFER
QUIZ #5
Fall ‘2000
A. The Ergun equation applies for both laminar and turbulent flow.
B. Turbulent flow through a packed bed can be modeled as flow through a noncircular
duct.
a. A and B are true b. Only A is true
c. Only B is true
d. A and B are false
II.
A. After a frictional dissipation term F has been established for flow in a packed bed, it may be
used in an energy balance for flow in either horizontal, vertical, or inclined directions, provided the flow
rate is not changed.
B. For flow through a porous material, the pressure drop is usually proportional to the square of
the flow rate.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
III. Find the horizontal force required to hold the
water nozzle shown in Fig. P11.3 in place. Assume
that the pressure at the entrance to the converging
section is 500 kPa (gage), and the exit velocity of
the water jet is 50 m/s.
Force = 44.72 N
IV. Water is being pumped from a reservoir to a site 50 m above the reservoir surface. The pump
is rated at 150 kW, but it is only 65% efficient. (This means that 35% of the power is lost in
overcoming frictional losses within the pump.) The total piping system is equivalent to 1000 m
of 500 mm diameter smooth pipe. Velocity of water in the pipe is 1.0 m/s. Friction factor can be
estimated from fF = 0.079Re-1/4, and the friction dissipation per unit mass is given as F =
L
2fF u 2m . Water density is 1000 kg/m3, and water viscosity is 0.008 g/cm-sec.
D
1) Pump head is 50.62 m
2) fF = 0.00281
3) If fF = 0.002, the total piping head loss is
196.4 kg/s
4) The discharge rate of water in kg/s is
0.8155 m
V. As shown in Fig. 1, a pipe of cross-sectional area A =
0.0002 m2 and a total length 8.0 m is used for siphoning
water from a tank. The discharge from the siphon is 2.0 m
below the level of water in the tank. At its highest point, the
pipe rises 1.0 m above the level in the tank. Neglect pipe
friction.
1) The lowest gage pressure in the pipe is –29,430 Pa
Siphon
2) (4 pts) Determine the time for the water level in the
tank to drop by 1.5 m. The cross-sectional area of
the tank is 0.60 m2. g = 9.81 m/s2. Show all your
work for this question. (958 s)
Fig. 1 Siphon for draining tank.
CHE 311 (Fall 2000)
________________________
LAST NAME, FIRST (10 pts)
Final Exam (Closed notes and closed book)
This test is given under the Honor System and by signing here ________________ you have
agreed that the work submitted is your work alone and that you neither sought nor received
help from others.
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I.
The figure on the right shows the horizontal cross
section of a well of radius r1 in a bed of fine sand that
produces water at a volumetric flow rate Q per unit depth
and at a pressure p1. The water flows radially inwards from
the outlying region, with symmetry about the axis of the
well. A pressure transducer enables the pressure p2 to be
monitored at a radial distance r2.
The following data were obtained for r1 = 3 in. and r2 =
30 in:
Q (gpm):
p2 - p1 (psi):
100
20
r1
r2
200
50
The pressure in the bed is related to the flow rate by the Ergun equation
dp
Q
Q2
=a +b 2
dr
r
r
1) a (with the proper unit) = 0.06514 psiin/gpm
Use a = 0.04 psi.ft/gpm and b = 0.0002 psi.ft2/gpm2 for questions (2) and (3)
2) For Q = 300 gpm, p2 – p1 = 92.43 psi
3) For Q = 100 gpm and p1 = 0 psi, the pressure at r = 6 in is 6.773 psi
II. Across a centrifugal pump, the increase in energy per unit mass of liquid is gh, where g is
the gravitational acceleration and h is the increase in head. This quantity gh may be a function
of the impeller diameter D, the rotational speed N, liquid density , and the flow rate Q. A
centrifugal pump operating at 2,000 rpm is to be designed to handle a liquid hydrocarbon of
specific gravity 0.95. To predict its performance, a half-scale model is to be tested, operating at
750 rpm, pumping a light oil of specific gravity 0.80. The scale model is found to deliver 400
gpm with a head increase of 20 ft. Assuming dynamical similarity, for the full-size pump
4) Q = 8,533 gpm
5) h = 569 ft
III. A rodlike wire of radius r1= .05 cm is pulled steadily with velocity V = 2.0 cm/s through a
horizontal die of length L = 20 cm and internal radius r2 = .1 cm. The wire and the die are
coaxial,
and the space between them is filled with a liquid of viscosity  = 1.2 g/(cm-s). The pressure at
both ends of the die is atmospheric. The wire is coated with the liquid as it leaves the die, and the
thickness of the coating eventually settles down to a uniform value, . The velocity profile within
the annular space is
vz = C1ln r + C2 , where (numerical value with r in cm)
6) C1 = - 2.885 cm/s
7) C2 = 6.64 cm/s
8) If the total volumetric flow rate through the annulus is 0.02 cm3/s,  = 0.0254 cm
9) If C1 = - 3 cm/s, the force F needed to pull the wire is 452 dyne
IV. The force components Rx and Ry of the air acting on
the deflecting blade are desired. The vane is fixed and
the air velocity is 30 ft/s. Air density is 0.078 lb/ft3.
10) Rx = 0.08875 lbf
11) Ry = 0.02378 lbf
If the vane moves to the left at 10 ft/s,
12) Rx = 0.1578 lbf
13) Ry = 0.04228 lbf
14) If the air velocity is not given, determine the air velocity from the stagnation tube connected to a
U-tube manometer located in the free air jet. Water density is 62.4 lb/ft3.
Air velocity = 173.4 ft/s
V. The pump shown on the right adds 25 kW of power to
the flowing water (0.05 m3/s) that is then discharged to
the atmosphere. The only loss is that which occurs across
the filter at the inlet of the pump.
15) The head loss for this filter is
17.95 m
16) If the pump head is 30 m and there is no filter at the
pump inlet, the inlet pressure
is (instead of –20 kPa) 9.66103 Pa
VI. Water flows through a horizontal bend and discharges
into the atmosphere as shown. The pressure gage reads 10
psi, and the flow rate Q is 5.0 ft3/s.
17) The retaining force FAx =
872.8 lbf
18) The retaining force FAy =
342.6 llb
19) If the retaining force FAx is 1440 lbf, Q = 7.03 ft3/s
VII. The tank and pipe shown in Fig. 6 are initially fill
with a liquid of viscosity 1.2 g/(cm-s) and density 1
g/cm3. Assuming laminar flow (fF = 16/Re), taking pipe
friction to be the only resistance, and ignoring exit
kinetic-energy effects, determine the volume flow rate Q
in cm3/s when h = 30 cm.
Fig. 6
Data: R = 20 cm, r = 0.5 cm, L = 100 cm, H = 50 cm, g =
981 cm/s2. Frictional dissipation F = 2fF(um)2(L/D).
20) Q = 26.03 cm3/s
VIII. A packed bed is composed of cylinders having a diameter D = 2 cm and a length h = 3 cm. The
bulk density of the overall packed bed is 902 kg/m3 and the density of the solid cylinder is 1600 kg/m3.
21) The void fraction of the bed is
0.436
22) If the effective diameter Dp = 6/av, where av = surface area of particle/volume of particle,
Dp = 2.25 cm
IX. Solid particles having a size of 0.12 mm and a density of 1200 kg/m3 are to be fluidized using air at
2 atm and 25oC. The void fraction at minimum fluidizing conditions is 0.40. If the cross section of the
empty bed is 0.40 m2 and the bed contains 500 kg of solid, the minimum height ho of the fluidized bed is
23) ho = 1.736 m
24) If ho = 1.5 m and air density is 2.4 kg/m3, P across the bed is 1.061104 Pa
X. Natural gas flows steadily in a 12-in ID pipeline that is 10 miles long, with fF = 0.004. If the
inlet pressure is 80 psia, determine the exit pressure that would correspond to the maximum flow
rate through the pipeline. (1 mile = 5280 ft)
2
2
 p1 
p 
4 fF L
 *  - ln  1*  = 1 +
D
 p2 
 p2 
2.745 psia