Micro hydro turbine calculations

[Baggy1]

Hi!

I'v been looking into this for way too long and have come to that point where nothing makes sense, hoping you guys could help me out!

Basically i have been given a net head of 20m and need to provide a micro hydro turbine with 5kW of power for over one minute. What i want to find out is what gross head i would need to produce this and the diameter of the pipe to supply it.

I'v selected a pipe diameter of 193.67mm schedule 80 PVC for now, and these are the calculations i made:

Flow rate = 5000/0.8x1000x9.81x20 = 0.032m3/s at 80% efficiency(turbine)

Velocity = Flow rate/0.25∏x0.19^2 = 1.12 m/s

From Bernoulli's equation i have this:

sqrt(2xgx20)= 19.81 m/s is what i get for velocity

Could someone be kind enough to explain the differences in these results?

Also...

How would i work out the pipe diameter if the one i have written is incorrect? The reason i selected this size was because it would have less friction resulting in a reduced gross head length. Id have to work out the friction losses to find the gross head, this is what i did... not sure its the right way... again

I calculated the friction factor to be 0.04

Gross head - 0.04x20x1.12^2 / 0.19x2x9.81 = 20

Gross head = 20 + 0.27

Any help would be greatly appreciated

Thanks in advance

 

[AlephZero]

Velocity = Flow rate/0.25∏x0.19^2 = 1.12 m/s

From Bernoulli's equation i have this:

sqrt(2xgx20)= 19.81 m/s is what i get for velocity

Could someone be kind enough to explain the differences in these results?

The difference is because your pipe diameter is bigger than you need to generate 5kW.

You could find the "correct" diameter (ignoring friction) by solving
Flow rate/0.25∏ x D^2 = 19.81 m/s
for D.

This is assuming that your turbine can extract all the kinetic energy (OK, 80% of it) from the water at that flow rate and velocity.