# Power Consumption of a Pump: Solve at 500kPa, 60m3/h, 80% Efficiency

• jderulo
In summary, the power consumed by the pump can be determined by using the formula P = q_v * p * h_p, where q_v is the volumetric flow rate, p is the pressure, and h_p is the energy head. This formula can be modified to include the 80% efficiency of the pump.

## Homework Statement

Determine the power consumed by a pump when it is pumping a fluid of density 1,200kg/m^-3 60m3/h at 500kPa with an 80% overall efficiency.

## Homework Equations

I believe it to be: $$P = q_m ρ g h_p$$

## The Attempt at a Solution

Stuck at the above part, I don't have enough info?

jderulo said:
I believe it to be: $$P = q_m ρ g h_p$$
The formula looks useful. What is qm?

Instead of g and a height, you are given the pressure. How are those concepts related?

mfb said:
The formula looks useful. What is qm?

Instead of g and a height, you are given the pressure. How are those concepts related?

qm is mass flow-rate. g is gravity, h isn't height but energy head..

jderulo said:
g is gravity, h isn't height but energy head..
Similar enough.

The main idea is that you can write down a similar formula where you replace ρ, g and hp to include pressure instead of those two parameters.

I am surprised that it is the mass flow rate and not the volume flow rate.

Anyway, you need the delivered power output of the pump (that's what your formula can do).
Once you have that, you can see how you can include the 80% efficiency.

mfb said:
Similar enough.

The main idea is that you can write down a similar formula where you replace ρ, g and hp to include pressure instead of those two parameters.

I am surprised that it is the mass flow rate and not the volume flow rate.

Anyway, you need the delivered power output of the pump (that's what your formula can do).
Once you have that, you can see how you can include the 80% efficiency.

My mistake it's volumetric flow. - but unsure how to do the first point.

Last edited:
$$h_p = p / ρ g$$

?

Am I right in thinking the final formula would be

$$P = q_v ρ g (p / ρ g)$$

Last edited:
jderulo said:
$$h_p = p / ρ g$$

?

Am I right in thinking the final formula would be

$$P = q_v ρ g (p / ρ g)$$
Right. You can simplify that formula, ρ and g will drop out and you are left with a simple product.