# Work Done by a Water Pump

1. Apr 17, 2013

### student34

1. The problem statement, all variables and given/known data

Water is pumped from a well at 800kg/minute. The well is 14.0 meters deep. By the time the water reaches the top of the well, it is travelling at 18.0m/s. How much work is done on the water by the pump?

2. Relevant equations

ƩFy = F - m*g = m*a
W = F*y
a = vf/t

3. The attempt at a solution

a = vf/t = (18.0m/s)/60.0s = 0.300m/s^2

F = m*a + m*g = 8080 N

W = F*y = 8080N*14.0m = 113,120 J

But the answer in my textbook is 1.30*10^5 J.

2. Apr 17, 2013

### voko

The question does not make sense. The pump does some definite amount of work in some definite period of time. As time goes on, the work done by the pump increases without any limit.

3. Apr 17, 2013

### haruspex

As voko says, the question makes no sense as it stands. Some missing information?
That calculation doesn't make sense either. The info does not say that it takes 1 minute to accelerate the water to 18m/s.

4. Apr 17, 2013

### Staff: Mentor

What is the kinetic energy per unit volume of the water at the top of the well? What is the kinetic energy per unit volume of the water before it is acted upon by the pump? What is the potential energy per unit volume of the water at the top of the well, compared to at the bottom of the well? What is the volume rate of flow of the water? What is the rate at which work is done by the pump on the water?

5. Apr 18, 2013

### CWatters

Something is wrong with the question or the text book answer. The question only has enough info to calculate the power (Watts) not the energy (Joules).

6. Apr 18, 2013

### Staff: Mentor

I think the implication of the question was to get the power, although the question certainly was worded poorly.

7. Apr 18, 2013

### CWatters

In that case the text book answer is also wrong.

8. Apr 18, 2013

### Staff: Mentor

Yes. I agree. I get about 4 kW. Does that agree with your result?

9. Apr 18, 2013

### CWatters

Yes that's what I got.

I couldn't see an obvious way to modify the question to get the answer 1.30*10^5 J unless they missed out..
"How much energy is consumed if it pumps the water for 30 seconds".