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Chapter 8: Problem 27

For oil \(\left(S G=0.86, \mu=0.025 \mathrm{Ns} / \mathrm{m}^{2}\right)\) flow of \(0.2 \mathrm{m}^{3} / \mathrm{s}\) through a round pipe with diameter of \(500 \mathrm{mm}\), determine the Reynolds number. Is the flow laminar or turbulent?

Short Answer

Expert verified
The Reynolds number for the oil flow is 17448, and it is a turbulent flow.

Step by step solution

01

Convert units

First, all measurements need to be in the same unit for the formula to work. Convert the pipe diameter from millimeters to meters by dividing by 1000. Therefore, D = 500 mm = 0.5 m. The flow rate (\(Q = 0.2 m^3/s\)) is given in m^3/s, it has to be converted to velocity (v) using the formula \(v = Q / A\), where A is the cross sectional area of the pipe.
02

Calculate velocity

Next, we calculate the velocity. The area of the pipe \(A = \pi * (D/2)^2 = \pi * (0.5/2)^2 = 0.196 m^2\). Substitute the area into the velocity equation: \(v = Q / A = 0.2 / 0.196 = 1.02 m/s\).
03

Calculate the Reynolds number

Now we can substitute all the values into the Reynolds Number formula Re = (Rho * v * D) / mu. However, we only have the specific gravity (SG), we have to find the density (Rho) via the given specific gravity using the formula Rho = SG * Rho_water, with Rho_water = 1000 kg/m3 (standard density of water). Hence, Rho = 0.86 * 1000 = 860 kg/m3. Now we can calculate the Reynolds number: Re = (860 kg/m3 * 1.02 m/s * 0.5 m) / 0.025 Ns/m2 = 17448.
04

Determine the flow

Finally, comparing the Reynolds number with the thresholds will determine if the flow is laminar or turbulent. Since the Re = 17448 is greater than 4000, the flow is turbulent.

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Most popular questions from this chapter

A certain process requires 2.3 cfs of water to be delivered at a pressure of 30 psi. This water comes from a large-diameter supply main in which the pressure remains at 60 psi. If the galvanized iron pipe connecting the two locations is 200 ft long and contains six threaded \(90^{\circ}\) elbows, determine the pipe diameter. Elevation differences are negligible.

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