A fluid of density and coefficient of viscosity is flowing steadily through a circular pipe of radius r . If the volume flow rate of the fluid is Q , the correct expression for the Reynolds number R_e of the flow is:

Step-by-step solution

The Reynolds number is defined as: R_e = v d where v is the average velocity of the fluid and d is the diameter of the pipe. For a pipe of radius r , the diameter is d = 2r . The volume flow rate Q is the product of the cross-sectional area A and the average velocity v : Q = A v = ( r^2) v Rearranging this to solve for v gives: v = Q r^2 Now, substitute the expressions for v and d into the Reynolds number formula: R_e = ( Q r^2 ) (2r) Simplifying the expression: R_e = 2 Q r r^2 = 2 Q r Answer: 2 Q r