The Reynolds number Re is a dimensionless group that characterizes the intensity of a flow. For large Re, a flow is turbulent; for small Re, it is laminar. For pipe flow, Re ?u?D/?, where D is pipe diameter and ? is dynamic viscosity.

Question

(a) If D and ? are fixed, what is the effect of increasing mass flow rate ? on Re?
(b) If ? and ? are fixed, what is the effect of increasing D on Re?

Answer 1

The mass flowrate, ?, is related to the density, diameter, and average velocity by



Thus,



And



Thus, the Reynolds number is directly proportional to the mass flow rate.

a. The expression in part (a) shows that in this case the Reynolds number is inversely proportional to the diameter, D.