2.27. The Reynolds number is a dimensionless group defined for a fluid flowing i
ID: 700885 • Letter: 2
Question
2.27. The Reynolds number is a dimensionless group defined for a fluid flowing in a pipe as Re = Dupju where D is pipe diameter, u is fluid velocity, is fluid density, and is fluid viscosity. When the value ofthe Reynolds number is less than about 2100, the flow is laminar- that is, the fluid flows in smooth streamlines For Reynolds numbers above 2100, the flow is turbulent, characterized by a great deal of agitation. Liquid methyl ethyl ketone (MEK) flows through a pipe with an inner diameter of 2.067 inches at an average velocity of 0.48 fuls. At the fluid temperature of 20°C the density of liquid MEK is 0.805 g/cm and the viscosity is 0.43 centipoise [ 1 cP = 1 .00 x10" kg/(m-s) . without using a calculator, determine whether the flow is laminar or turbulent. Show your calculations.Explanation / Answer
Pipe diameter D= 2.067 inches
Average velocity u= 0.48 ft/s
Density of liquid MEK = 0.805 g/cm3
viscosity = 0.43 centipoise
1 centipoise = 0.001 kg/(m.s)
==> viscosity = 0.43*0.001 = 0.00043 kg/(m.s)
The problem main intention to test the unit conversions.
So, 1 feet = 12 inches
1 inch = 0.0254 m
Therefore, Diameter D = 2.067*0.0254 =0.0525 m
Average velocity u = 0.48*12*0.0254 = 0.1463 m/s
density = 805 kg/m3
viscosity = 0.00043 kg/(m.s)
Reynolds number = (D*u*p)/viscoity = (0.0525*0.1463*805)/0.00043 = 14,379
Reynolds number is more than 2100. So the flow is TURBULENT.
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