A rectangular tank that is 3 feet long, 9 feet wide and 3 feet deep is filled wi
ID: 2878784 • Letter: A
Question
A rectangular tank that is 3 feet long, 9 feet wide and 3 feet deep is filled with a heavy liquid that weighs 90 pounds per cubic foot. In each part below, assume that the tank is initially full. Your answers must include the correct units. (You may enter lbf or lb*ft for ft-lb.) How much work is done pumping all of the liquid out over the top of the tank? How much work is done pumping all of the liquid out of a spout 2 feet above the top of the tank? How much work is done pumping two-thirds of the liquid out over the top of the tank? How much work is done pumping two-thirds of the liquid out of a spout 2 feet above the top of the tank?Explanation / Answer
Solution:
Volume of tank = 3×9×3 = 81,
Weight = 81 x 90 = 7,290 lbm total mass.
Linearity permits assignment of a Center of Gravity at height 1.5ft.
(A) work done for pumping all of the liquid out over the top of the tank is
= 1.5×7290 = 10935 ft lbs
(B) work done for pumping all of the liquid out of a spout 4 feet above the top of the tank
The liquid at the top of the tank needs to be pumped 2 feet to get to the spout.
The liquid at the bottom of the tank needs to be pumped 3 + 2 = 5 feet to get to the spout
Averaging out those two numbers (2 and 5) gives: the AVERAGE molecule of liquid needs to be pumped 3.5 feet to get to the top of the tank.
= 3.5×7290 = 25515 ft lbs
(C) New CG is 2ft (½ of upper )
Weight of the liquid to be pumped is (2/3)*7290 = 4860
If you're only pumping out 2/3 (2 feet in height) of the liquid, then the bottom 1/3 (1 feet in height) can remain in the tank, therefore:
The liquid at the top of the tank needs to be pumped 0 feet to get to the top of the tank
The liquid at the bottom of the top 2/3 of the tank (2/3)*3 = 2 feet to get to the top of the tank
Averaging out those two numbers (0 and 2) gives: the AVERAGE molecule of liquid needs to be pumped 1 feet to get to the top of the tank.
= 1 * 4860 = 4860 ft- lbs
(D)
Weight of the liquid to be pumped is (2/3)*7290 = 4860
If you're only pumping out 2/3 (2 feet in height) of the liquid, then the bottom 1/3 (1 feet in height) can remain in the tank, therefore:
The liquid at the top of the tank needs to be pumped 2 feet to get to the spout.
The liquid at the bottom of the top 2/3 of the tank (2/3)*3 = 2 feet to get to the top of the tank, then another 2 feet to get to the spout, so that's 4 feet in total
Averaging out those two numbers (2 and 4) gives: the AVERAGE molecule of liquid needs to be pumped 3 feet to get to the top of the tank.
= 3 * 4860 = 14580 ft lb
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