A researcher wants to measure the pulsatile flow though a prosthetic heart valve using a laser-based technique. The instantaneous velocity at each point of the flow can be expressed as: u = f(row,mu,U,omega,D) where U is a reference inlet velocity and is the frequency of the flow pulsatility. Using dimensional analysis, the researcher derives an expression for the dimensionless velocity u/U: u/U = g((row*U*D)/mu,D*sqrt((row*omega)/mu) (a) Briefly discuss the dimensionless Pi groups found. What do you notice? In order to improve the measurement spatial resolution, the researcher decides to design a scaled-up experiment. For simplicity, he uses water as a test fluid (the viscosity of water relative to that of blood is 2/1 = 1/3.5 and it is a reasonable assumption that the density of water is equal to that of blood) and the model geometric scaling factor is D2/D1 = 5.8. (b) Calculate the frequency scaling factor needed to preserve dynamic similarity. (c) If the peak velocity in the physiological flow is of the order of 1 m/s, what peak velocity should the researcher expect to measure in his scaled-up experiment