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Chapter 2: Problem 44

A flowrate measuring device is installed in a horizontal pipethrough which water is flowing. A U-tube manometer is connected to the pipe through pressure taps located 3 in. on either side of the device. The gage fluid in the manometer has a specific weight of 112 Ib/ft \(^{3}\). Determine the differential reading of the manometer corresponding to a pressure drop between the taps of \(0.5 \mathrm{lb} / \mathrm{in.}^{2}\)

Short Answer

Expert verified
The differential reading of the manometer is 7.7 inches

Step by step solution

01

Pressure unit conversion

Convert the pressure drop from lb/in² to lb/ft². The conversion factor is 1 lb/in² = 144 lb/ft², so \(0.5 \, \mathrm{lb/in^{2}} \times 144 \, \mathrm{ft^{2}/in^{2}} = 72 \, \mathrm{lb/ft^{2}}\)
02

Pressure drop to manometer reading

Next, correlate the pressure loss to the manometer reading. To do this, we know that \( \Delta P=\gamma h \), where \( \Delta P \) is the pressure drop, \( \gamma \) is the specific weight of fluid in the manometer, and \( h \) is the height difference in the manometer. Solving for \( h \), we get \( h = \frac{\Delta P}{\gamma} \). Use the values obtained from the problem and from step 1, we get \( h = \frac{72 \, \mathrm{lb/ft^{2}}}{112 \, \mathrm{lb/ft^{3}}} = 0.643 \, \mathrm{ft}\)
03

Convert manometer reading to inches

Lastly, it's necessary to convert the manometer reading from feet to inches, because manometer readings are often described in inches. The conversion factor is 1 ft = 12 inches. Therefore, \(0.643 \, \mathrm{ft} \times 12 \, \mathrm{in/ft} = 7.7 \, \mathrm{in}\)

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