Calculate and compare the efficiency of the two turbines of Prob. 14123. They should be the same

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Calculate and compare the efficiency of the two turbines of Prob. 14–123. They should be the same since we are assuming dynamic similarity. However, the larger turbine will actually be slightly more efficient than the smaller turbine. Use the Moody efficiency correction equation to predict the actual expected efficiency of the new turbine. Discuss.


Data from Prob. 14–123.

A group of engineers is designing a new hydroturbine by scaling up an existing one. The existing turbine (turbine A) has diameter DA = 1.50 m, and spins at ṅA = 150 rpm. At its best efficiency point, V̇A = 162 m3/s, HA = 90.0 m of water, and bhpA = 132 MW. The new turbine (turbine B) will spin at 105 rpm, and its net head will be HB = 95 m. Calculate the diameter of the new turbine such that it operates most efficiently, and calculate V̇B and bhpB.

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