Work, energy and power question

[blackcat]

The question is:
A pump raises 1800 litres of water per minute through a vertical distance of 9m. Given that 1 litre of water has a mass of 1kg, find the power developed by the pump if the water is delivered at 12m/s.

My thoughts are as follows. If the pump raises 1800kg of water per minute, then it must raise (1800/60)kg of water per second, which is 30kg per second. It's raising this against the force of gravity, so Force = ma = 30*g. Work done = force*distance = 30g*9 = 291g. Power is work done / time, but I've modelled it per second so power = 291g.

Obviously that can't be right as the thing states it's delivered at 12m/s and I haven't used that. Please help.

 

[Mentz114]

You need to work out the kinetic energy of the delivered water, and how much work is done accelerating it.

 

[blackcat]

thanks for the reply and sorry i am late.

so the kinetic energy is (0.5*30*12*12) = 2160J. And the work done is against gravity, so E = Work done = Fd = (30g*9) = (291g)J.

So is the power equal to (2160 + 291g)J/s? Because I have modelled everything in 1 second.

Is this right?

 

[blackcat]

wait. it says the water is delivered at 12m/s so work done = 30g * 12 instead of 9. but i don't understand why the vertical distance is given to me? and what does "delivered at 12m/s" mean?

 

[Trampas]

thanks for the reply and sorry i am late.

so the kinetic energy is (0.5*30*12*12) = 2160J. And the work done is against gravity, so E = Work done = Fd = (30g*9) = (291g)J.

So is the power equal to (2160 + 291g)J/s? Because I have modelled everything in 1 second.

Is this right?

Yes, it is. The pump does work, accelerating the water to 12m/s and also moving it up, doing work against the gravitational force G = mg.