Calculate Horsepower for Pumping Water from 50m Depth at 10m/s Flow Rate

In summary: The potential energy is calculated using the equation:E = mgh. So, in this case, 981 Js-1. The kinetic energy is calculated using the equation:Ek = 1/2 mv^2. So, in this case, 100 Js^-1. In summary, a pump needs to raise water from a depth of 50m and eject it at 10m/s. To do this, it needs 250 watts.
  • #1
jamesjd
13
0

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.

Homework Equations





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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  • #2
jamesjd said:
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.
 
Last edited:
  • #3
Borek said:
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
 
  • #4
jamesjd said:
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.
 
  • #5
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?
 
  • #6
jamesjd said:
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:
Borek said:
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?
 
  • #7
D H said:
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?
 
  • #8
OK, how many kg per sec?
 
  • #9
2 kg/s ?
 
  • #10
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.
 
  • #11
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.
 
  • #12
micuklein said:
2*9.81*50=981 Js-1

Show the units. How did you get J/s?
 

1. How do you calculate horsepower for pumping water from 50m depth?

To calculate the horsepower for pumping water from 50m depth, you will need to know the flow rate of the water in meters per second and the efficiency of the pump. The formula for calculating horsepower is: Horsepower = (Head x Flow rate x Specific gravity) / (3960 x Efficiency). In this case, the head would be 50m, the flow rate would be 10m/s, and the specific gravity would be 1 (for water). The efficiency of the pump can vary, but a typical value is around 70-80%.

2. What is the specific gravity of water?

The specific gravity of water is a measure of its density compared to the density of pure water at 4 degrees Celsius. It is typically given a value of 1, but this can vary slightly depending on temperature and impurities in the water.

3. How do you convert meters per second to feet per minute?

To convert meters per second to feet per minute, you can use the conversion factor of 196.85. This means that for every meter per second, there are approximately 196.85 feet per minute. So for a flow rate of 10m/s, the equivalent in feet per minute would be approximately 1968.5 fpm.

4. What is the efficiency of a typical pump?

The efficiency of a pump can vary depending on the type and size of the pump, as well as the conditions it is operating under. However, a typical efficiency for a pump can range from 70-80%. This means that 70-80% of the energy put into the pump is converted into useful work, while the rest is lost as heat or other forms of energy.

5. Is horsepower the only factor to consider when selecting a pump?

No, horsepower is not the only factor to consider when selecting a pump. Other important factors include the type and size of the pump, the flow rate and head required for your specific application, and the efficiency and reliability of the pump. It is important to carefully consider all of these factors when selecting a pump to ensure it meets your needs and operates effectively.

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