check this please: A turbine in a dam converts potential energy to mechanical po

Question

check this please:

A turbine in a dam converts potential energy to mechanical power, which is ultimately used to power a generator. This is accomplished by allowing water from the reservoir (left side of the dam) to flow through the turbine and discharge downstream (right side of the dam). Why can the velocity of the free surface of the reservoir be neglected? If it were considered, could a steady-state analysis be conducted? If the water discharges at a rate of 30 m3/s, d = 2.7 m, z1 = 20 m and Z2 = 6 m, what power can be generated from the turbine? Is the sign of work what you would expect?

Explanation / Answer

From the equation of continuity,

A1*V1 = A2*V2

therefore,V1 = A2*V2/A1

if A1 is very large,then the V1 is small which is true in this case.If the A1 is not considered large with respect to the A2,then A1 must be given to find different parameters.

Q = 30 = 0.785*(2.7^2)*V   

therefore,V = 5.24 m/sec and the power P =rho_w*9.8*(z1-z2)*V*0.785*(2.7^2) =4113.70 KW

The sign depends upon your convention but the important point is that we get the work out of this system.

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