# Horsepower in a pump

## Homework Statement

A pump has to raise water from a depth of 50m and eject it at 10m/s. If the flow rate is 2 kg/s, what horsepower is needed.

## The Attempt at a Solution

t = s/v = 5 seconds

m = t/flow rate = 2.5kg

E = mgh = 1250J

P = E/t = 250W

Horsepower = 0.34Hp

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Borek
Mentor
t = s/v = 5 seconds
Ejection speed is not necessarily the speed at which water travels up. Besides, time you have calculated doesn't matter - each second you have to move 2 kg of water 50 meters up.

m = t/flow rate = 2.5kg
Check your units - you will see it is wrong. Time divided by flow rate is not [STRIKE]seconds[/STRIKE] kg.

You need to do two things - transfer water up, and accelerate it to 10 m/s. Calculate energies involved.

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Ejection speed is not necessarily the speed at which water travels up. Besides, time you have calculated doesn't matter - each second you have to move 2 kg of water 50 meters up.
Is it not 10m? erm is the calculation Mass = flow rate/ time?

I'm still confused

Borek
Mentor
Is it not 10m? erm is the calculation Mass = flow rate/ time?
No, check units.

Don't think about formula, just how do you feel - if you transfer 2 kg per second, how much will you transfer in 5 seconds? How have you calculated it?

Flow rate means just that: each second you have to move 2 kg of water up and accelerate it to 10 m/s.

hmm it seems so simple but i'm struggling to grasp the concept. It takes 10Kg in 5 seconds then? Was any of my working correct?

D H
Staff Emeritus
Was any of my working correct?
To be brutally honest, no. You have not followed Borek's advice. I'll repeat it, highlighting the key concept:
You need to do two things - transfer water up, and accelerate it to 10 m/s. Calculate energies involved.
How much energy is needed to lift one kilogram of water 50 meters?
How much energy is needed to make that one kilogram of water move at 10 meters/second?

How much energy is needed to lift one kilogram of water 50 meters?

How much energy is needed to make that one kilogram of water move at 10 meters/second?
Ep = mgh for one kg lifted 50 meters?

Ek = 1/2 mv^2 for one kg at 10m/s?

Borek
Mentor
OK, how many kg per sec?

2 kg/s ?

Borek
Mentor
OK. How much energy is needed per sec then?

And if you think after seeing the answer I will ask any further questions, you are wrong. You are so close to the solution it is a shame you still need to be pushed.

Hi,
I calculated the Potential energy(work done)= 2*9.81*50=981 Js-1
Kinetic energy=mv^2/2= 2*100/2=100 Js^-1.
But how do you calculate using thees, the horsepower...or at least in Joules cause then converting into horsepower is easy.
Thanks.

Borek
Mentor
2*9.81*50=981 Js-1
Show the units. How did you get J/s?