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ChE 354 Unit Ops I - Homework Set #1 Due: Fri. 9/13/13

1. Your supervisor wants you to replace the broken inclined manometer draft tubes used to measure

the low pressures in the firebox of an industrial furnace. The colored water in the manometers and the

clear tubes are hard to maintain. She suggests you consider a 0 to 1 inch of water Magnehelic gauge.

This measures the slight pressures lower than atmospheric that draw air into the burners at the base of

the furnace. First, you must calculate the maximum expected pressure (actually vacuum) to see if the

range of the instrument is reasonable. You determine that the highest

reading (lowest pressure in the firebox) is with an average temperature of

500 deg F in the furnace body and stack. Their total height is 105 ft. This

is a low firing rate scenario with the furnace damper wide open so that no

pressure loss occurs in the rising gases of the furnace. Thus, it can be

considered a static column of hot combustion gases. The static outside air

column in this scenario can be as low as 40 deg F. What is the gauge

pressure (vacuum) in inches of water in this scenario? Neglect the

difference in molecular weights between the combustion gases and the

normal atmosphere. [You should be able to calculate this given some level of excess O2.]

2. In a garage there is a hydraulic lift for raising a car on a rack. A small air compressor can keep 1

bar of pressure (gauge) on a reservoir of hydraulic fluid. The piston that raises the rack and the car has

an area of 0.2 m 2. The rack and the piston have a mass of 230 kg. When there is no motion, how

heavy a car can be supported on the rack?

3. A flat top and bottom, cylindrical heavy oil storage tank is 150 ft across and 60 ft tall. The vapor

conservation vent on the top opens at 2 inches of water positive pressure and 1 inch of water negative

pressure. This minimizes breathing losses that cause pollution and product loss. a). What is the net

lbfthe atmosphere exerts downward on the roof at the point at which the vent opens and lets air into

the tank when the pressure is negative? b). One cold night the vent freezes over with ice (This canreally happen) so that it no longer operates. Oil is then pumped out of the tank so that the level goes

from 50 ft to 40 ft. Now what is the calculated net atmospheric force on the tank roof? What has

happened to the tank by this point?

4. The current $400M effort to salvage the cruise ship Costa Concordia off the coast of Italy includes

welding caissons or sponsons to the sides of the ship so it will float again. The box-like caissons are

about 40 X 40 X 100of 1-1/8 inch steel plate (s.g. = 7.9). They will be full of air and about 90 %

submerged. a). About how many need to be attached to each side of the 114K ton ship (about

submerged, bottom open to the water, all steel) to float it to the scrap yard? b). Manziel Engineering of

College Station Texas has proposed an alternative solution. They say getting the ship upright in the

current location is too risky. The ship should be allowed to slide off into deep water where it will right

itself. A steel harness can use the existing attachment points welded to the ship and the ship pulled to

the surface by steel cable. The rate of pulling the ship upward is so slow that there is no added

resistance caused by the water. This is a classic statics problem Manziel proudly announced in their

press release. What they did not include was the size of the required steel cable. Using an allowable

25,000 psi tensile strength what is the diameter of the required cable? If the cable is 1000 ft long how

much weight is added to the lift? What does this say about buoyant forces?

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5. A float is used by a magnetic linkage to note the position of a gasoline (s.g. = 0.72) and wash water

(s.g.=1.01) interface in a vessel. To calibrate the linkage one must know how much of the float is in

the gasoline and how much is in the water layer. If the float has a s.g. = 0.92, what fraction of the float

is in the water layer?

6. For unloading of ships a new oil storage tank must be built. It will be vented to the atmosphere, be

60 feet deep and 120 ft in diameter. The oil has

a specific gravity of 0.88. How thick must the

steel plate be along the bottom ring of the tank

using the cylindrical thin-wall assumption with a

uniform tensile strength, , of 20,000 psi? See

the nearby drawing and calculate the tensile

stress or hoop stress (working on both ends of

the one-half hoop) that offsets the pressure force

of the oil across the diameter of the tank.

7. For a pressure test, a tank is completely full of 180 deg F. water from just under the fill valve on the

top of the tank to the top of the drain valve on the bottom of the tank. The tank is 6 feet in diameter

and 20 feet tall with dish-shaped top and bottom heads. It is rated for 20 psig pressure and 10 psig

vacuum. An operating technician has been asked to drain the tank. Not wanting to drain the tank too

quickly and overflow the sewer system, he leaves the top fill valve shut and opens the bottom drain

valve. What is the minimum pressure reached in the top of the tank? What might happen?

8. A common method for level measurements in watery pits and tanks is the bubble dip tube as shown

in the drawing. Why must the air flow be regulated to a smallamount? The pressure gauge shows 2.5 psig. The dip tube

stops 6 inches from the bottom. The liquid density is 61 lbm /

ft3. What is the depth of the liquid in the tank? About what

is the % error in assuming the air in the 10 ft long dip leg has

zero density versus the actual density?

9. Chinook winds occur in the winter in the US when warm, moist, eastward flowing winds come over a

mountain range. They cool and drop their moisture rising on the west side, and then descend rapidly on

the other side. With limited mixing the air mass is compressed isentropically as it descends in altitude.

The effects can be quite dramatic and occur within minutes. Calculate the temperature rise in Denver

Colorado in the following scenario. The wind tops the front range of the Colorado Rockies at 14,000 ft

and at a temperature of 10 deg F. The beginning temperature in Denver at 5300 feet elevation is 15

deg F. The heat capacity ratio, , for air is about 1.4.10. Thinking in part of Prof Dinsmoors home water system pressure problems what can you do to have

safe water pressures (say 30-60 psig) in a 100 story office building starting with a 100 psig pressure

main just under street level?