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?

Answer 1

A .
`\mathbf{W = 7133.2 (ft. lb_f)/(min) }`

B.
`\mathbf{W = 4245.24 (ft. lb_f)/(min) }`

C. The system is at steady state but not at equilibrium

Step-by-step explanation:

Given that:

The volumetric flow rate of the water = 15 gallons per minute

The diameter of the pipe that leaves the pump is 1 inch.

A. The objective here is to determine how much work flow is done by the water as it leaves the pump and enters the pipe

The work flow that is said to be done can be expressed by the relation :

W = P × V

where;

P = pressure

V = volume

Also the given outlet pressure is the gauge pressure

The pressure in the pump P is can now be expressed by the relation:

`P_(absolute) = P_(guage) + P_(atmospheric)`

`P_(absolute)` = 10 psig + 14.7 psig

`P_(absolute)` = 24.7 psig

W = P × V

W = 24.7 psig × 15 gal/min

`W = (24.7 \ psig * ((lb_f)/(in^2))/(psig)) * ( 15 (gal)/(min)* (0.1337 \ ft^3)/(1 \ gal )* (144 \ in^2)/(1 \ ft^2))`

`\mathbf{W = 7133.2 (ft. lb_f)/(min) }`

Thus ; the rate of flow of work is said to be done by the water at
`\mathbf{W = 7133.2 (ft. lb_f)/(min) }`

B.

Given that :

The water returns to the pool through an opening that is 1.5 inches in diameter.

where the pressure is 1 atm.

Then ; the rate of work done by the water as it leaves the pipe and enter the pool is as follows:

W = P × V

W = 1 atm × 15 gal/min

`W = 1 \ atm * ( 15 (gal)/(min)* (0.1337 \ ft^3)/(1 \ gal )* (144 \ in^2)/(1 \ ft^2))`

`\mathbf{W = 4245.24 (ft. lb_f)/(min) }`

Thus ; the rate of flow of work done by the water leaving the pipe and enters into the pool is at
`\mathbf{W = 4245.24 (ft. lb_f)/(min) }`

C.

We can consider the system to be at steady state due to the fact that; the data given for the flow rate and pressure doesn't reflect upon the change in time in the space between the pump and the pool.

On the other-hand the integral factor why the system is not at equilibrium is that :

the pressure leaving the pipe is different from that of the water at the surface of the pool as stated in the question.