2103-390 Mechanical Engineering Experimentation and laboratory I
Homework #5: Uncertainty of A Derived Quantity
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2103-390 Mechanical Engineering Experimentation and laboratory I
Homework #5: Uncertainty of A Derived Quantity
Problem 1. Uncertainty Analysis for A Derived Quantity: Report Stage
[Unless otherwise stated, the uncertainty is evaluated at 95% confidence.]
To measure the efficiency of a pump, the parameters in the following formula are usually measured and applied:

Qp
, where  is the efficiency, Q is the volumetric flowrate, p is the pressure differential between the inlet and
W
outlet of the pump, and W is the power input into the pump. The following instruments are used:
Differential pressure gage:
Flowmeter:
Power meter:
Range
0-170 psi
Accuracy
+ 0.3 % of reading (includes linearity, hysteresis, and repeatability)
Stability
+ 0.3 % of reading
Range
40 ft3/min
Accuracy
+ 1.5 % of reading
Accuracy
+ 0.10 hp. (The power is measured through the input of an electrical
motor.)
In repeating the measurement 15 times for all parameters, the following results are found:
X
Average value
Standard Deviation
Bias uncertainty
Random Uncertainty
Total uncertainty
X
SX
BX  BX
PX
UX
Q (ft3/min)
12.0
0.2
p (psi)
100.0
1.5
W (hp)
6.50
0.20

Report the result of the test as   U @ C % , and summarize various components in the table above.
Note:
Show your calculations clearly. 1 hp = 550 lbf-ft/s