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Chapter 8: Problem 23

A 3 -in. schedule 40 commercial steel pipe (with an actual inside diameter of 3.068 in.) carries 210 'F SAE 40 crankcase oil at the rate of 6.0 gal/min. The oil specific gravity is \(0.89,\) and the absolute viscosity is \(6,6 \times 10^{-7} 1 \mathrm{b} \cdot\) sec/ft \(^{2}\). For the same pressure drop, what must the acw pipe size be to carry the oil at 10.7 gal/min?

Short Answer

Expert verified
The new pipe size needed to carry the oil at the rate of 10.7 gal/min for the same pressure drop must be approximately 4.38 inches in diameter.

Step by step solution

01

Identifying Given Quantities

The problem provides the following information: \(\dfrac{Q_1}{d_1^5} = \dfrac{Q_2}{d_2^5}\), with given diameters and flows \((d_1 = 3.068 \, in, Q_1 = 6 \, gal/min)\) and \((Q_2=10.7 \, gal/min)\) and an unknown second diameter \(d_2\).
02

Converting Units

To solve, the units must match. Therefore, convert \(3.068 \, in\) into feet: \(d_1 = 3.068 \, in \times 1 \, ft/12 \, in = 0.25567 \, ft\). The flow rates are converted to \(ft^3/s\). 1 gallon equals 0.13368 cubic feet and 1 minute equals 60 seconds. Therefore, \(Q_1 = 6 \, gal/min \times 0.13368 \, ft^3/gal \times 1 \, min/60 \, s = 0.002239 \, ft^3/s\) and \(Q_2 = 10.7 \, gal/min \times 0.13368 \, ft^3/gal \times 1 \, min/60 \, s = 0.003991 \, ft^3/s\).
03

Substituting into the Formula

Substitute these values into the equation: \(\dfrac{0.002239 \, ft^3/s}{(0.25567 \, ft)^5} = \dfrac{0.003991 \, ft^3/s}{(d_2)^5}\). This simplifies to \(d_2 = 0.3648 \, ft\)
04

Convert to Appropriate Units

The solution needs to be in inches, so convert this back: \(d_2 = 0.3648 \, ft \times 12 \, in/ft = 4.38 \, in\)

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Most popular questions from this chapter

The vented storage tank shown in Fig. \(\mathrm{P} 8.90\) is used to refuel race cars at a race track. A total of \(40 \mathrm{ft}\) of steel pipe \((\mathrm{I.D},=0.957 \text { in. })\) two \(90^{\circ}\) regular elbows, and a globe valve make up the system. Calculate the time needed to put 20 gal of fuel in a car tank. The pressures, \(p_{2}\) and \(p_{1},\) are aqual, the connections are threaded, and the fuel has the properties of \(68^{\circ} \mathrm{F}\) normal octane \(\left(\nu=8.31 \times 10^{-6} \mathrm{ft}^{2} / \mathrm{s}\right)\)

A 0.064 -m-diameter nozzle meter is installed in a 0.097 -m-diameter pipe that carries water at \(60^{\circ} \mathrm{C}\). If the inverted air-water U-tube manometer used to measure the pressure difference across the meter indicates a reading of \(1 \mathrm{m}\), determine the flowrate.

Water is to be moved from a large, closed tank in which the air pressure is 20 psi into a large, open tank through 2000 ft of smooth pipe at the rate of \(3 \mathrm{ft}^{3} / \mathrm{s}\). The fluid level in the open tank is \(150 \mathrm{ft}\) below that in the closed tank. Determine the required diameter of the pipe. Neglect minor losses.

Asphalt at \(120^{\circ} \mathrm{F}\), considered to be a Newtonian fluid with a viscosity 80,000 times that of water and a specific gravity of 1.09 flows through a pipe of diameter 2.0 in. If the pressure gradient is 1.6 psi/ft determine the flowrate assuming the pipe is (a) horizontal; (b) vertical with flow up.

Carbon dioxide at a temperature of \(0^{\circ} \mathrm{C}\) and a pressure of \(600 \mathrm{kPa}(\text { abs })\) flows through a horizontal \(40-\mathrm{mm}\) -diameter pipe with an average velocity of \(2 \mathrm{m} / \mathrm{s}\). Determine the friction factor if the pressure drop is \(235 \mathrm{N} / \mathrm{m}^{2}\) per 10 -m length of p pe.
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