Question

A reaction turbine works under a head of 180 m. the flow rate of water being 26 m3/s. The overall turbine efficiency is 88%. Determine the required specific speed if the rotative speed is 550rpm

Answer 1

The required specific speed for the turbine, given a head of 180 m, a flow rate of 26 m3/s, an overall efficiency of 88%, and a rotative speed of 550 rpm, is approximately 46.9 rpm(m3/s)0.5/(m)0.75.

Step-by-step explanation:

To determine the specific speed of a reaction turbine given a head (H) of 180 m, a flow rate (Q) of 26 m3/s, an overall efficiency (η) of 88%, and a rotative speed (N) of 550 rpm, we use the formula for the specific speed (Ns) of a turbine:

Ns = N * Q0.5 / H0.75

First, we need to convert the unit of efficiency into a decimal which is already in a decimal form (0.88). Then, we can proceed with the calculations:

Step-by-step calculation:

1. Insert the given values into the formula:
   
   Ns = 550 * 260.5 / 1800.75
2. Calculate the flow rate and the head values raised to the respective powers: Q0.5 = 260.5 ≈ 5.1, H0.75 = 1800.75 ≈ 60.3.
3. Perform the division to find Ns: Ns = 550 * 5.1 / 60.3 ≈ 46.9.

Thus, the required specific speed for the turbine is approximately 46.9 rpm(m3/s)0.5/(m)0.75.