Estimate the flow rate and speed of the water going into the turbine

[unknown1991]

Homework Statement

Run-of-the-river projects harness power from the natural flow and elevation drop of a river. In the
Brandywine project, water is diverted from the river into a pipe (r=0.75 m) in which it flows down the hill, through the turbine, and returns to the river. The project at Brandywine Creek produces 40,000 MWh of electricity per year (i.e., a mean power of 4.6 MW). The diverted water drops 280 m in elevation between where it leaves the river and where it reaches the turbines. Estimate the flow rate and speed of the water going into the turbine.

Homework Equations

The Attempt at a Solution

Power: ΔP Q
Power: 40000 MW/year x 1 year/365 days x 1 day /24 hr x 1 hr/3600 s= 169 MW/s
Q= Velocity x Area = (pi (0.75m)^2/4) x 169 MW/s= 74.7 MW m/s x 1/ 4.6MW= 16.2 m/s

I don't know what I just did. :S Please help.

 

[haruspex]

Power: 40000 MW/year x 1 year/365 days x 1 day /24 hr x 1 hr/3600 s= 169 MW/s

The power is 40000MWh/y, not 40000MW/y (which would make no sense dimensionally). And you are given that this turns into 4.6MW, so you don't need to do that calculation. Just use the 4.6MW figure. (Besides, the number you got was way too big. Maybe you meant kW, not MW.)

Q= Velocity x Area = (pi (0.75m)^2/4)

0.75 is the radius, not the diameter.

x 169 MW/s=

That's not a velocity. The velocity is unknown.
Consider some mass m of water passing through the pipe. How much potential energy does it lose in the process? If mass m comes out of the pipe each second, what power does that provide?

 

[Chestermiller]

Hi unknown1991. Welcome to Physics Forums.

Have you learned about the Bernoulli equation yet? If so, use the Bernoulli equation to calculate the pressure at the inlet to the turbine. The turbine is horizontal, so that the elevation of its exit is the same as the elevation of its inlet. What flow rate would be needed in conjunction with the pressure change through the turbine to generate the specified power?

On a side note, is this power plant in Delaware or Pennsylvania?