To measure the efficiency of a pump, the parameters in the

Chapter , Problem 7.51

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To measure the efficiency of a pump, the parameters in the following formula are usually measured and applied: TJ = QI1PIW. In this formula, TJ is the pump's efficiency, Q is the volumetric flow rate of the pump, I1P is the pressure differential between the inlet and outlet of the pump, and W is the power input into the pump. The following equipment is used: Differential pressure gage Flowmeter Range 0-170 psi Accuracy 0.2% of span (includes linearity, hysteresis, and repeatability) Stability Range 0.2 % of span 40 ft3/min Accuracy 1.5% of reading The power is measured through the input of an electrical motor (with specified efficiency), with an expected accuracy of 0.10 horsepower. In repeating the measurements, the average values of the pressure differential, flow rate, and power are found to be 100.0 psi, 12.0 ft3/min, and 6.50 horsepower, respectively. The standard deviations of 1.5 psi, 0.2 ft3/rnin, and 0.20 hp are calculated for the respective parameters. If the number of measurements made to calculate the mean values and standard deviations is 15, (a) calculate the efficiency of the pump. (b) calculate the standard deviation of the efficiency of the pump. (c) calculate the random and systematic uncertainty of the efficiency of the pump. (d) calculate the total uncertainty of the efficiency of the pump at a 95% confidence level.