Problem 27. In this problem we consider pipe flow with a restriction in the pipe. Experiments show that the pressure drop, AP, for flow through an orifice plate of diameter

d mounted in a length of pipe of diameter D may be expressed as AP = f(p,µ,V,d, D), where p is the fluid density, µ is the fluid viscosity, and V is the average velocity of the fluid. Use this information to non dimensionalize the relationship AP = f(e, µ,V,d, D) in the form: \Pi_{2}=1 / R e, \Pi_{3}=L_{p} / D \text { ) } \quad \Pi_{2}=1 / R e, \Pi_{3}=D / L_{p}, \Pi_{4}=e / L_{p} \text { (c) } \quad \Pi_{2}=1 / R e, \Pi_{3}=L_{p} / e, \Pi_{4}=D / e \mathrm{II}_{2}=1 / R e, \mathrm{\Pi}_{3}=L_{p} / D, \Pi_{4}=e / D \text { (e) None of these }