Question

Electric power is to be generated by installing a hydraulic turbine-generator at a site 115m below the free surface of a large reservoir. If water falling from the surface this height is flowing at a rate of 1350 kg/s determine the power generation potetial.

Answer 1

Answer:

$W=1523kW$

Explanation:

First, define the control volume for the energy balance. The most suitable control volume is that between the free surfaces of two reservoirs, the feeding reservoir, which is 115m above the turbine, and the final reservoir which is expected to be so close to the turbine because it will mean an energy waste if not.

With this control volume, write the energy balance:

$Q+W=m*(\frac{P_{2}-P_{1}}{p}+g(z_{2}-z_{1})+\frac{v_{2}^{2}-v_{1}^{2}}{2}+H)$

(Its formulation can be studied in Cengel (Fluid mechanics, chapter five).

Consider that both surfaces are at the same pressures (atmospheric pressure is expected for both), and both fluid velocities at the surfaces are close to zero because both reservoirs are so large and there is not considerable height change in the process. Q the heat flow (there is none), and H is the mechanic energy lost, which will be neglected because we are calculating the power generation potential, it means, its better possible power generation. Then the energy balance will be:

$W=m*g(z_{2}-z_{1})$

$z_{2}$ is the height of the surface near the turbine, and $z_{1}$ the height of the surface of the reservoir above. So, the power is:

$W=1350*9.81*115=-1523002.5W$

The sign is negative because the balance equation was formulated thinking that the energy is going out of the fluid, but it will be considered positive if we are considering the produced energy (the sign depends on what you are analyzing).

So, the power generation potential is:

$W=1523kW$