Size Reduction Problems

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1. The average minimum or representative dimension of the material retained on a sieve in the set used for a fineness modulus determination is approximately 1.4 times the sieve opening. Why?

2. Derive equation 6.1.

3. Prove that the fineness modulus is a geometric mean of a minimum dimension weighted on the basis of quantities, that is,

where w is the weight or per cent of material of minimum dimension D.

4. Determine the fineness modulus, uniformity index, and average particle size for the following sieve analysis:

5. Assume the particles in problem 4 to be spherical and the result of a reduction from a uniform product 3/8 in. in diameter. Prepare and complete a table with the following column headings: (1) sieve mesh, (2) sieve-opening width, (3) relative number of particles retained by each sieve, using 2 on the 3/8-in. sieve as the base, (4) total relative area represented on each sieve. Discuss the data from the standpoint of ( 1) power requirements, (2) rate of oxidation of air sensitive materials, (3) importance of a minimum amount of fine material.

6. Determine the constants of equation 6.7 for shelled corn and barley ground by hammer mill from the curves of Fig. 6.10. Express an opinion as to the deviation from Kick's and Rittinger's laws.

7. If all the grinding power, Fig. 6.12, at 3400 rpm is accumulated as heat in the ground material, what is the temperature rise of the material? Assume the specific heat to be 0.30.

8. Plot the sieve analysis data of paragraph 6.2 in the two ways discussed in paragraph 6.4. Discuss the possibility of representing each curve by an equation.

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Fans Problems

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1. A pressure of 1.5 in. of water is required to move air up through a bin of grain at 20 cu ft per (min sq ft) of floor. If the floor has an area of 175 sq ft, what fan horsepower is required assuming 75 percent efficiency?

2. The air system C of Fig. 5.10, which is carrying 10,000 cu ft per min, is altered so that the resistance is less and the fan delivers 11,000 cu ft of air per min. Determine the speed at which the fan must operate to deliver exactly 10,000 cu ft per min, and the static pressure and horsepower. What is the percentage reduction in power requirement?

3. A fan geometrically similar to that of Fig. 5.10 must operate at 2.0 in. pressure, 6000 cu ft per min, and an efficiency of 75 percent. Specify the wheel diameter, speed, and power required.

4. Determine the discharge velocity of the fan of Fig. 5.10 from the outlet area and from the velocity pressure, both at 10,000 cu ft per min.

5. A forward curved blade fan delivers 380 cfm at free discharge at 1725 rpm. The rotor is 6 in. diameter, 3.25 in. wide; and the discharge edge of the vanes is 45° relative to the radius. Show the velocity vectors for the air leaving the rotor. Show the velocities by dotted vectors if the flow is throttled to 190 cfm.

6. Plot pressure gradients (static, velocity, total) for the system shown below.

7. Assume that the fan of Fig. 5.10 is connected to a long flexible tube with resistance features that permit a capacity of 7000 cfm. Now connect the discharge end of the tube to the fan inlet. The areas are the same. Discuss the effect on operating conditions-pressures, air rate, power.

8. Compute the basic shut-off or zero flow static pressure for the Fig. 5.10 fan. Explain the difference between the observed and the computed values.

9. A room is to be ventilated by an axial flow fan as shown below. Compute the conditions required for selecting a fan and the required horsepower. Assume 70% efficiency.

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Pumps Problems

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1. A whole milk homogenizer operating at a pressure of 2500 sq in. delivers 6 gal per min. If the pump efficiency is 82 percent, what size motor is required? What size motor is required if the pressure is 1500 lb per sq in.? Pipe friction may be neglected. Estimate the velocity through the homogenizing valve.

2. A 1750-rpm centrifugal pump with a 4.75-in. impeller delivers 140 gal per min against a 20-ft water head and uses 1 horsepower. What is the pump efficiency? What is the head at complete shut-off?

3. The pump of problem 2 is to operate against a 25-ft head without changing efficiency. Specify the speed, discharge rate, and power required.

4. The pump of Fig. 4.9 is connected to 40 ft of 2-in. galvanized-iron pipe. The lift is 25 ft. The system contains 2 elbows, pumps from a tank, and discharges from the pipe. What is the water pumping rate?

5. Specify a pump geometrically similar to that of Fig. 4.9 to operate at maximum efficiency at a head of 40 ft and capacity of 180 gal per min. Impeller diameter, speed, and horsepower are required.

6. Determine the efficiency of the pump of Fig. 4.14 when operating at 1150 rpm.

7. A pump delivering q1 on the system shown below must be speeded up from N1 toN2 to deliver q2. Why must N2/N1 = q2/q3?

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Fluid Mechanics - Fluid-Flow Measurements Problems

Fluid-Flow Measurements Problems

Fluid Mechanics

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1. A water pressure gauge located 4 ft above a pressure source reads 21 lb per sq in. The connecting tube is full of liquid. What is the actual pressure at the source?

2. The system of problem 1 is initially full of air at atmospheric pressure. The main line was then filled with water, no air being bled from the gage connecting pipe. What is the pressure in the main line if the gage again indicates 21 lb per sq in.?

3. Air at 70° is being measured by a venturi meter with basic diameters of 14 and 10 in., respectively. Gages attached at points 1 and 2, Fig. 3.11a, read 5.75 and 2.10 in. of water. What quantity of air is flowing?

4. The gage on an orifice meter reads 4 ½ lb per sq in. What is the velocity of water if the inside pipe diameter is 1.25 in. and the sharp-edged orifice is 0.89 in. in diameter? (C = 0.76.)

5. A nozzle meter is to be designed to fit into an 18-in. galvanized pipe. Air at room temperature flows through the pipe at velocities varying from 700 to 1400 ft per min. If a 2-in. inclined manometer containing alcohol with an S.G. of 0.89 is to be used with the nozzle, what should be the diameter of the nozzle?

6. A Thomas meter is located in an air duct of 2 sq ft cross-sectional area. The air weighs 0.083 lb per cu ft, and its specific heat is 0.24. Assume a controlled temperature differential of 5° and heater potential of 110 volts. Plot the velocity as abscissa and amperage as ordinate for velocity 0 to 300 ft per min. Assume constant amperage of 3, and plot temperature difference against velocity. Discuss the curves from the standpoint of accuracy of the system.

7. A differential pitot tube located at the center of a cylindrical air tube produces 2.6 in. of water pressure. What is the velocity at the impact end of the pitot tube? The impact gauge reads 2.6, 2.6, 2.5, 2.1, 1.8 when placed at points 1-5 in Fig. 3.10. What is the average velocity in the tube? What factor would be applied to the center reading to indicate a true average velocity? Note: In actual practice it would be necessary to check this factor through the entire range of velocities to be encountered, because variation may be expected.

8. A pump is moving soybean oil through a 1-in. (nominal) pipe. The 110-volt motor is using 285 watts. Assuming an overall pump and motor efficiency of 65 percent, what is the pumping rate in gallons per minute if the suction and discharge pressures are, respectively, -5 and 23 lb per sq in.?

9. Carbon dioxide is metered into an air conduit which is 12 sq ft in cross-sectional area at a constant rate of 7.0 lb per hour. A sample of the mixture downstream was analyzed by an Orsat apparatus and contained 11½ percent CO2 by volume. What is the air velocity?

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