<p>ME3280 / ME6160 Turbines and Centrifugal Machinery Fall 2017 Dr. T. J. Barber</p><p>Problem 4.1: Nondimensionalization</p><p>Suppose one know that the force F on a particular body immersed in a stream of fluid depended only on  body length, L  stream velocity, U  fluid density,   fluid viscosity,  that is F f L, U , ,   Suppose further that the geometry and flow conditions are so complicated that integral or differential theories fail to yield the solution for the force F.</p><p>Reduce the number of dimensional variables using Buckingham’s pi theorem, where each pi =  is the product of a number of dimensional variables.</p><p>Problem 4.2: Scaling</p><p>The design point of a compressor is defined as follows:  Inlet total pressure=1.5 bars  Inlet total temperature=345K  Mass flow rate=3.8 kg/s  Physical speed=45,000 rpm  Total temperature rise=320 K</p><p>These operating conditions are tested using air under standard sea-level conditions on 1 bars and 288K, respectively, using the full-scale compressor. Calculate the mass flow rate, speed and total temperature rise during the test.</p><p>Problem 4.3: Centrifugal Compressor</p><p>Given a centrifugal compressor with the following operating and geometric conditions:</p><p> Flow 5 lb/sec  Pt1 14.7 psia  Tt1 519 °R</p><p>N  a1 30°  N 20,000 RPM  h 82%</p><p> rtip = 5.35"</p><p> rod = 3.192"</p><p> rid = 1.596"</p><p>Assume radial exit flow in rotating frame of reference, ie, b2 = 0°</p><p>1. Sketch inlet & exit velocity diagram 2. Calculate impeller pressure ratio</p>