# Calculate Power from Water flow

1. Jan 3, 2012

### waterturbine

Hi,
I am interested in building a water turbine.
I am not sure how to calculate the theoretical maximum power that can be derived from a flow.

If I assume I have a flow of 5m/s and a channel (or pipe) 1m^2
then I have a volume of 5,000 l/s
How do I calculate the energy that this flow could transfer to a turbine (excluding losses)?

Ek = 1/2 * m * v^2
water has density 1 so mass of 5,000 l is 5,000 kg
Ek = 0.5 * 5,000 * 5^2
= 2,500 * 25
= 62,500 J
Power = 62.5kW ?

(This doesn't seem correct and it is over 40 years since I did any physics)
So maybe I am missing that the change in flow from input of 5m/s will not be to 0?

Am I missing anything else and is there some other method to resolve this?

Or do I have to determine the Differential pressure across the turbine (I do not have any specs for a turbine yet).

thanks

2. Jan 3, 2012

### bbbeard

It's almost that simple -- except (1) the water needs to exit the turbine at some speed, and (2) typically there are pressure and gravity terms that have to be accounted for. You haven't indicated a geometry (is this an axial-flow turbine with equal inlet and exit areas? a centrifugal turbine that extracts gravitational potential energy?) but in general you have to compute the total mechanical power flowing into the turbine and subtract the total mechanical power flowing out, and the difference is the shaft power. The specific mechanical energy (energy per unit mass) is

$P / \rho +gz+V^2/2$

You have to multiply this by the mass flow rate $\dot{m}$ to get the mechanical power.

BBB

3. Jan 4, 2012

Hi BBB,