CHE 30101 (Spring 2000)



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

2. If the level hB falls by 0.6 cm, the level hC will rise by a distance ((cm) = 0.15 cm

3. If hC = 3 cm and hA = 2 cm, then 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 2-in. 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

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

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. - 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 Fall 2000

QUIZ #4

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.

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

CHE31101 MOMENTUM TRANSFER Fall ‘2000

QUIZ #5

I. 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 = 2fF[pic]. Water density is 1000 kg/m3, and water viscosity is 0.008 g/cm-sec.

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

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): 100 200

p2 - p1 (psi): 20 50

The pressure in the bed is related to the flow rate by the Ergun equation

[pic]= a[pic]+ b[pic]

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,

[pic]

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.

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)

[pic]- ln[pic]= 1 + [pic] 2.745 psia

-----------------------

C

B

A

disk

Pipe

Siphon

Fig. 1. U-tube with immiscible liquids

hC

hA

hB

Siphon

r1

r2

Fig. 6

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