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Chapter 5: Problem 135

Water enters an axial-flow turbine rotor with an absolute velocity tangential component, \(V_{\theta},\) of 15 fus. The corresponding blade velocity, \(U,\) is \(50 \mathrm{ft} / \mathrm{s}\). The water leaves the rotor blade row with no angular momentum. If the stagnation pressure drop across the turbine is 12 psi, determine the hydraulic efficiency of the turbine.

Short Answer

Expert verified
The hydraulic efficiency of the turbine is 3.05%.

Step by step solution

01

Identify Given Values

The given values in the problem are the tangential component of the absolute velocity (\(V_{\theta}\)), which is 15 ft/s, the corresponding blade velocity (\(U\)), which is 50 ft/s, and the stagnation pressure drop, which is 12 psi.
02

Calculate the Power Delivered

The power developed by the turbine, also known as the shaft power, can be found using the formula \(P = U * V_{\theta}\). Substituting the given values, we calculate \(P = 50 \, \text{ft/s} * 15 \, \text{ft/s} = 750 \, \text{ft}^2/\text{s}^2\).
03

Convert Pressure Drop to Same Units as Power

To calculate the hydraulic efficiency, the units of the pressure drop need to be the same as the units of the power. Therefore, the pressure drop needs to be converted from psi to \(\text{ft}^2/\text{s}^2\). One psi is equivalent to 2048 \(\text{ft}^2/\text{s}^2\), so the pressure drop in the same units as power would be \(12 \, \text{psi} * 2048 \, \text{ft}^2\text{/s}^2\text{/psi} = 24576 \, \text{ft}^2/\text{s}^2\).
04

Calculate Hydraulic Efficiency

The hydraulic efficiency, \(η\), of the turbine can now be found using the formula \(η = P / \text{Pressure Drop}\). Substituting the calculated values, we get \(η = 750 \text{ft}^2\text{/s}^2 / 24576 \text{ft}^2/\text{s}^2 = 0.0305\) or 3.05% when converted to percentage.

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Most popular questions from this chapter

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