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Chapter 4: Problem 205

A centrifugal water pump with a 0.1-m-diameter inlet and a 0.1 -m-diameter discharge pipe has a flow rate of \(0.02 \mathrm{m}^{3} / \mathrm{s}\). The inlet pressure is \(0.2 \mathrm{m}\) Hg vacuum and the exit pressure is \(240 \mathrm{kPa}\). The inlet and outlet sections are located at the same elevation. The measured power input is \(6.75 \mathrm{kW}\). Determine the pump efficiency.

Short Answer

Expert verified
The centrifugal pump efficiency is approximately 1.39%.

Step by step solution

01

Find absolute pressures

First, convert the given pressures to absolute pressures to use in calculations. The inlet pressure is given as a vacuum, so subtract it from the standard atmospheric pressure. Standard atmospheric pressure is 101.3kPa, thus inlet pressure = 101.3kPa - \(0.2 \,m \times 13.6 \times 9.81 \,kPa/m = 97.13 \,kPa\). The outlet pressure is given as 240kPa.
02

Calculate the work done by pump

Next, calculate the actual work done by the pump which is equal to the power input to the pump. The power input is given as 6.75kW. Therefore, the work done \(W_a = 6750 \,W\)
03

Calculate the theoretical work done

Calculate the theoretical work done, or the ideal work required to move the fluid through the pump. Given the Bernoulli鈥檚 equation, work done by the pump theoretically \(W_t = \rho Q (P2 - P1) / g\). Here \rho is the density of water \(1000 \,kg/m^3\), Q is the flow rate \(0.02 \,m^3/s\), P2 and P1 are outlet and inlet pressures respectively, and g is acceleration due to gravity \(9.81 \,m/s^2\). Substituting the values, we get \(W_t = 484626.7 \,W\).
04

Calculate the pump efficiency

Finally, the pump efficiency can be calculated by dividing the actual work done by the pump by the theoretical work and then multiplying by 100 to get a percentage. Thus, pump efficiency = \(W_a / W_t 脳 100 = 1.39%\).

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