An incompressible fluid oscillates harmonically with an angular frequency of 10 rad/s in a 4- inch-diameter pipe. The fluid motion can be described as , where V is the velocity, is the angular velocity or frequency (rad/s) and t is the time. A 1/4 geometrical scale model (the length ratio of the model to the prototype is 1/4) is to be used to determine the pressure difference per unit length, (at any instant) along the pipe. Assume that where: D is the pipe diameter, the fluid viscosity, and the fluid density (20 Pts).

(a). Apply dimensional analysis to determine the similarity requirements for the model and the prediction equation for Δp.
(b). If the same fluid is used in the model and the prototype, at what angular frequency should the model operate?