How Much Work Does a Water Pump Do to Raise Water from a Well?

[student34]

Homework Statement

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 traveling at 18.0m/s. How much work is done on the water by the pump?

Homework Equations

ƩFy = F - m*g = m*a
W = F*y
a = vf/t

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.

 

[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.

 

[haruspex]

As voko says, the question makes no sense as it stands. Some missing information?

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

That calculation doesn't make sense either. The info does not say that it takes 1 minute to accelerate the water to 18m/s.

 

[Chestermiller]

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?

 

[CWatters]

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

 

[Chestermiller]

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

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

 

[CWatters]

In that case the textbook answer is also wrong.

 

[Chestermiller]

In that case the textbook answer is also wrong.

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

 

[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".