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Question 3 (30 points): A thin, flat plate with several holes punched through it is placed in a pipe to filter out particles that may be in the liquid flowing through the pipe. There is concern that the pressure drop across the plate may become large depending on the plate design and flow conditions. You are tasked with designing a model experiment to assess the proposed design.

(a) Assuming that the pressure drop, Ap, depends upon hole diameter, d, pipe diameter,D, viscosity, u, density, p, and velocity, V, determine a set of non-dimensional groups and their functional relationship. (b) If the prototype is proposed to have the following dimensions/operating conditions(see table), determine the diameter of holes and range of velocities you should test ina model to achieve similarity.

(c) If the pressure drop measured in the model experiment is 100 kPa for the maximum velocity, predict the pressure drop in the prototype for a velocity of 2 m/s.

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