Calculating the efficiency of a water turbine

[bmwm3]

Hi,


I am having trouble calculating the efficiency of a water turbine. The turbine in question closely represents a cross flow water turbine.

I have tested the power rating experimentally using a small DC motor and have found the output to be 400 mW.

I now need to find the power rating theoretically, I know there is a force of 155 N acting upon the blade of the turbine. The distance between the centre of the shaft and the edge of the blade is 25mm.

I know the velocity of water before hitting the turbine to be 20 m/s.

Many thanks in advance for any help you can give me!

 

[Valkarie]

The first step is to calculate the theoretical power rating of the turbine. You can do this by calculating the torque produced by the force of 155 N acting on the blade. The torque (T) is equal to the force (F) multiplied by the distance (d): T = F x d T = 155 N x 0.025 m T = 3.875 Nm The power rating of the turbine is then equal to the torque (T) multiplied by the angular velocity (ω): P = T x ω P = 3.875 Nm x 2π/60 s P = 0.32 W This is the theoretical power rating of the turbine. To calculate the efficiency of the turbine, you need to divide the measured power rating (400 mW) by the theoretical power rating (0.32 W) and multiply by 100. This will give you the efficiency of the turbine as a percentage: Efficiency = (400 mW / 0.32 W) x 100 Efficiency = 125%