Finding Turbine Angular Velocity given Net Head, GPM, and power from Alternator.

[MaxMoon]

An alternator attached to a water turbine generates 35 Watts given 50 feet of head and 10 gallons per minute. Assuming that the efficiency of the alternator is 50%, is it possible for me to find the angular velocity from this information?

If so, how would I do it?

 

[d00dz]

humm...im not sure if I am right but assuming your trying to find the angular velocity of the turbine blades? then i think you need more information such as average radius of the turbine where the blades are. But I am not even sure if your taking about that...

 

[ravenprp]

Yes, it is possible to find the angular velocity of the turbine using the given information. The formula for calculating the power output of a turbine is P = (Q x H x 9.81)/1000, where P is power in kilowatts, Q is flow rate in cubic meters per second, and H is the net head in meters. Since we have been given the power output in watts and the flow rate in gallons per minute, we need to convert them to the appropriate units.

First, we convert 35 watts to kilowatts by dividing by 1000, which gives us 0.035 kW. Then, we convert the flow rate of 10 gallons per minute to cubic meters per second by multiplying by 0.000063, which gives us 0.00063 m^3/s. Plugging these values into the formula, we get:

0.035 = (0.00063 x 50 x 9.81)/1000

Solving for Q, we get Q = 1.141 m^3/s.

Next, we can use the formula for angular velocity (ω) in terms of flow rate (Q) and turbine diameter (D), which is ω = Q/(π x D^2/4). Since we do not have the diameter of the turbine, we can rearrange the formula to solve for D:

D = √(4 x Q/ω x π)

Plugging in the values of Q and ω, we get D = √(4 x 1.141/ω x π).

Assuming a standard turbine efficiency of 50%, we can divide the calculated diameter by 0.5 to get the actual diameter of the turbine. This diameter can then be used to calculate the angular velocity of the turbine using the original formula.

In summary, to find the angular velocity of the turbine, we need to convert the given values to the appropriate units, use the formula for power output to calculate the flow rate, and then use the formula for angular velocity to solve for the unknown.