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Pump Power Question - Power Required To Transport Water Between Elevations?
So there's this question I'm stuck on:
A pump is pumping water at 900 L/min (240 gpm) for an elevation of 45m (or 152 feet).
The answer is supposedly 9.32 hp.
After applying the energy equation, I get the Hp = 45 m or 152 ft (since the headloss is not mentioned and assumed as 0).
I then use the equation Wp = y*Q*hp, getting an answer thousands greater then what it should be.
Could someone please tell me what I'm doing wrong?
The model I have with the closest units so far is:
Wp = (0.015 m^3 / s)*(9800 N/m^3) * 45m
where the 0.015 is obtained by taking the 900 L/min, converting that to 0.9 m^3 / min, and then dividing by 60 to get the seconds.
Please help?
Thanks!
A pump is pumping water at 900 L/min (240 gpm) for an elevation of 45m (or 152 feet).
The answer is supposedly 9.32 hp.
After applying the energy equation, I get the Hp = 45 m or 152 ft (since the headloss is not mentioned and assumed as 0).
I then use the equation Wp = y*Q*hp, getting an answer thousands greater then what it should be.
Could someone please tell me what I'm doing wrong?
The model I have with the closest units so far is:
Wp = (0.015 m^3 / s)*(9800 N/m^3) * 45m
where the 0.015 is obtained by taking the 900 L/min, converting that to 0.9 m^3 / min, and then dividing by 60 to get the seconds.
Please help?
Thanks!
Choose another answer as the right one
E=mgh
m=density * volume
g=9.81m/s^2
h=45m
be careful with units, make sure to convert them to get proper result.
for example flow of 900L/min is problematic because energy (Joule) , gravity (m/s^2) etc all use time unit which is second.
So flow is 900L/min=15L/s (note that for water 15L is 15kg since density is 1kg/L)
so in one second we get
W=mgh=15kg*9.81m/s^2*45m=6621.75J
and since W=P*t=6621.75J*1s=6621.75W
now, 1HP=746W so
P=(6621.75W)/(746W/HP)=8.876 HP, that is if we assume efficiency of 100%.
edit-----
if efficiency is say 95%, you get 9.32HP
not sure if the question is complete or if there is any other factor to take into consideration (you mention headloss=0) or rounding etc. also HP is not always used as one value (most common 735-750W) etc.
but at any rate, this is correct approach and all one can offer using provided info.
Choose another answer as the right one