Consider predicting the pressure drop p between two points along a smooth horizontal pipe under the condition of steady laminar flow. Assume: where s is

Consider predicting the pressure drop Δp between two points along a smooth horizontal
pipe under the condition of steady laminar flow. Assume:

where s is the control distance between two points in the pipe, d is the diameter of the
pipe, ρ is the fluid density, μ is the fluid viscosity, and v is the velocity of the fluid.
a. Determine the design conditions for a scaled model of the prototype.
b. Must the model be geometrically similar to the prototype?
c. May the same fluid be used for model and prototype?
d. Show that if the same fluid is used for both model and prototype, then the equation is:

Ap = f(s. d. p. u. v)