Question

The penstock redirects water 180 degrees to distribute flow to a hydroelectric turbine generator. The flowrate is 26cu.m/s. The inside diameter is 1.3 m at the inlet and 0.9 m at the outlet. Determine (a) the sum of the inlet and discharge reaction forces in kN, (b) the minimum height of water above the penstock in meters and (d) the power in MW associated with the height in (b) and the given flow rate. The density of water, rho, is 1000 kg/cu.m. Derive (a) only and express the algebraic solution in terms of Q, din, dout, rho and g as necessary. NOTE: In (b) and (c), apply conservation of energy and ignore any and all hydrodynamic losses and the effects of turbulence. You will learn how to account for these very significant effects in more advanced studies.

Answer 1

To determine the sum of the inlet and discharge reaction forces, you can use Bernoulli's equation.

Step-by-step explanation:

To determine the sum of the inlet and discharge reaction forces, we can use Bernoulli's equation.

Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy along a streamline remains constant.

In this case, we assume the flow is steady, so the kinetic energy remains constant and the potential energy can be considered constant since any changes in height have been neglected.

Therefore, according to Bernoulli's equation, the sum of the inlet and discharge reaction forces is equal to the difference in pressure between the inlet and outlet multiplied by the cross-sectional area at the outlet:

(a) sum of inlet and discharge reaction forces = (pressure at inlet - pressure at outlet) * area at outlet

Using the given information, we can substitute the values into the equation and calculate the sum of the inlet and discharge reaction forces.