A filtration system continuously removes water from a swimming pool, passes the water through filters and then returns it to the pool. Both pipes are located near the surface of the water. The flow rate is 15 gallons per minute. The water entering the pump is at 0 psig, and the water leaving the

Question

A filtration system continuously removes water from a swimming pool, passes the water through filters and then returns it to the pool. Both pipes are located near the surface of the water. The flow rate is 15 gallons per minute. The water entering the pump is at 0 psig, and the water leaving the pump is at 10 psig.

A) The diameter of the pipe that leaves the pump is 1 inch. How much flow work is done by the water as it leaves the pump and enters the pipe?
B) The water returns to the pool through an opening that is 1.5 inches in diameter, located at the surface of the water, where the pressure is 1 atm. How much work is done by the water as it leaves the pipe and enters the pool?
C) “The system” consists of the water in the pump and in the pipes that transport water between the pump and the pool. Is the system at steady state, equilibrium, both, or neither?

Accepted Answer

A) [latex] m Work _{ ext {flow }}= m Pressure imes m Volume[/latex]

Convert gauge pressure into absolute.

[latex]\begin{aligned} ext { Work }_{ ext {flow }}=\left(14.7+10 \frac{\mathrm{lb}_{\mathrm{f}}}{\mathrm{in}^2} ight)\left(15 \frac{ ext { gal }}{\min } ight)\left(0.1337 \frac{\mathrm{ft}^3}{ ext { gal }} ight)\left(144 \frac{\mathrm{in}^2}{\mathrm{ft}^2} ight)=7133 \frac{\mathbf{f t}~ \mathbf{l b}_{\mathbf{f}}}{\mathbf{m i n}}\end{aligned}[/latex]

B) [latex] m Work_{ ext {flow }}= m Pressure imes m Volume[/latex]

[latex]\begin{aligned} ext { Work }_{ ext {flow }}=(1 \mathrm{~atm})\left(15 \frac{ ext { gal }}{\min } ight)\left(0.1337 \frac{\mathrm{ft}^3}{ ext { gal }} ight)\left(\frac{14.7 \frac{\mathrm{lb}_{\mathrm{f}}}{\mathrm{in}^2}}{1 \mathrm{~atm}} ight)\left(144 \frac{\mathrm{in}^2}{\mathrm{ft}^2} ight)=\mathbf{4 2 4 5 . 2 4} \frac{\mathbf{ft}~ \mathbf{lb}_{\mathbf{f}}}{\mathbf{m i n}}\end{aligned}[/latex]

C) Based upon the problem description, it might appear that this system is operating at steady state; the parameters of the system (flow rates, pressures) as described do not change with time. However, if the filter system is working as described, then the water coming in is dirty and the water leaving the filtration system is cleaner, and anything that is removed from the water is accumulating in the filter. If mass is accumulating in the system then it is not at steady state.

The system is not at equilibrium with the surroundings because the conditions of the liquid leaving the pipe (~10 psig) are significantly different from the water at the surface of the pool (~0 psig); there is a significant pressure difference between the system and the surroundings at this point.

Question 1.24: A filtration system continuously removes water from a swimmi...

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