# Converting wattage to KWH?

1. Aug 20, 2008

### arranged

I'm attempting to calculate the amount of power (in KWH) produced by a water turbine based on x litres of water falling x metres vertically through a tube of x cm diameter

So far i've managed the following:
H = height (distance fallen) (m)
Time = Secs
R = Radius of the pipe (m)

Velocity (m/s) = (2 x H x G) ^ 0.5
Volume / Sec = Velocity x Time x Pi x R^2
mass (kg) / Sec = (Volume / sec) x 1000
Energy = (Mass x Velocity^2)/2 = wattage generated

My questions is.... how do i convert this wattage generated in KWH generated?

Once I have this am i correct in thinking I can do:
(KWH generated / 3600) * (time taken for x litres of water to fall through the pipe).
To calculate the KWH generated by the x litres of water falling?

Any help / guidance anyone could give me would be greatly appreciated. - As you can (maybe) tell i'm by no means a physics graduate but i do have a basic understanding.

Any help anyone could give me would be greatly appreciated.

Many Thanks

P.s For the purposes of this i'm happy to work with a turbine having 100% efficiency.

2. Aug 20, 2008

### brewnog

Power isn't measured in kWh; that's a unit of energy.

Energy (in Watt-hours) = power (in Watts) * time (in hours).

So, if your turbine produces 100kW (power) constantly for 3 hours (time), you will have produced 300kWh of energy.

The short way of finding out the amount of energy available in your example would just be to use:

Gravitational potential energy = (mass of water)*(vertical distance travelled)*g

Ok?

3. Aug 20, 2008

### arranged

thats a good point, i never thought of working it out with PE, that would have made it much simpler.

Did u happen to look at my wattage calculation? I'm fairly confident it's correct but would be useful if someone could confirm it.

4. Aug 20, 2008

### brewnog

Well your 'wattage calculation' is wrong, because (mass*velocity^2)/2 equals kinetic energy, not power.

Power is the rate of consumption/production of energy:

Power = energy / time

Also, your volumetric flow rate calculation is incorrect. Volumetric flow rate equals flow velocity multiplied by the cross-sectional area of the pipe. I don't know why you've multiplied this by time. Then, mass flow rate is just volume flow rate multiplied by density; in this instance it's water so 1 litre per second is one kilogram per second.

5. Aug 25, 2008

### Toymkr

arranged-

Do a search for "hydro power calculator". You'll find many online and several will go into the details.....frictional losses, head pressure, etc...some theoretical and some real-world.

There's loooooots of info out there online and sometimes the hardest part of finding it is the phrasing of the search term.

Toymkr