Answer Happy

You have been asked to consult for the company manufacturing the rocket engines for the new space shuttle engine. They are having a vibration problem with the liquid hydrogen pump which they believe is caused by some sort of flow-induced vibration, probably cavitation. They are willing to spend major dollars for you to build a dynamically similar model to investigate the flow. The prototype pump rotates at some nominal rate. In the laboratory, you propose to build a 3-times scaled model so that you can probe the flow if necessary. Also, given that liquid hydrogen is too expensive and too dangerous to keep in the lab, the only liquid with which you can reasonably work is water. A. (8 points) Explain how you will pick the scale velocity (say V=Q/L² where Q is the volumetric flow rate through the pump and I is a characteristic length scale) and pump's rotation rate (say w ) of the model relative to the real thing to get the flow dynamics right. B. (4 points) Ok, so you don't think you know anything about cavitation, right? But modelling cavitation depends mostly on getting the cavitation number correct. The cavitation number is defined as C = PP pV² where p, is the vapor pressure of the liquid that being used. This is different for liquid hydrogen and water. How do you propose to get this number right in your model (if V is already determined from part A)? Hint: The important physical variables that influence the flow-induced vibration are velocity, density, pump size, viscosity, rotation rate, and pressure difference.