An incompressible fluid oscillates harmonically (V = V0 sin(wt),where V is the velocity) with a certain frequency in a 19 cmdiameter pipe. A 1/4 scale model is to be used to determine thepressure difference per unit length, ∆?? at any instant along thepipe. Assume that ∆?? = ?(?, ?0,?,?,?,?)
Where D is the pipe diameter, ω the frequency, t the time, μ thefluid viscosity, and Ï the fluid density.
a) Determine the similarity requirements for the model and theprediction equation for ∆??.
b) If the same fluid is used in the model and the prototype, andthe model frequency is 250 rad/s, what is the prototypefrequency?
