申論題

3. The Reynolds number is a dimensionless group defined for a fluid flowing in a pipe as Re = Duplfi where D is pipe diameter, u is fluid velocity, p is fluid density, and fj, is fluid viscosity. When the value of the Reynolds number is less than about 2100, the flow is laminarthat 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 ft/s. 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 centipoise = 1 cP = 1.00✖ 10^-3 kg/(m-s)]. Determine whether the flow is laminar or turbulent. Show your calculations. (25%)