Calculating Torque and Power in Radial-Flow Turbine

In this scenario, we are given the outer radius of the impeller, volume flow rate, angular velocity, and tangential component of velocity at the inlet. To calculate the torque exerted on the impeller, we use the formula:

Calculating Torque:

T = ρQ(Vt2 - Vt1)r

Given that the fluid is water with a density of 62.4 lb/ft^3, the volume flow rate Q = 1000 ft^3/s, the tangential component of velocity at the inlet Vt1 = 5 ft/s, and the impeller discharges in the axial direction, we find the torque exerted on the impeller to be 920,740 N-m.

To determine the power developed by the machine, we use the formula:

Calculating Power:

P = Tω

After substituting the torque value and the angular velocity into the formula, we calculate the power developed by the machine to be approximately 23,810 horsepower. The negative sign indicates that the power is being absorbed by the machine.

By understanding the calculations involved in determining the torque and power of a radial-flow turbine, we can appreciate the physics and mechanics behind its operation. It showcases the application of fluid mechanics principles in analyzing turbine performance.