4. A prototype gate valve which will control the flow in a pipe system conveying paraffin is to be studied in a model. The pressure drop across the valve is thought to depend on the gate opening h, the pipe diameter d, the velocity V, density p and viscosity u. The density and viscosity of paraffin are 800 kg m-3 and 0.002 kg m--s-1 respectively. Take the kinematic viscosity of water as 1.0 10-6 m?s-1. a) The ratio h/d and the Reynolds number are two non-dimensional groups which describe the problem. Use the Buckingham Pi Theorem to find the third non-dimensional group. S b) A 1:5 scale model of the prototype is built and tested in the lab using water. If the required volume flow rate of paraffin is 0.1 m*s-1 in the prototype, find the volume flow rate of water which will give dynamically similar conditions in the model. c) When run in dynamically similar conditions, the pressure drop in the model is 60 kPa. Find the pressure drop expected in the prototype