Fluid V Air SI, kg/m 1.24 British, slugs/ft SI, m/s 0.00242 1.4110-5 British, ft/s 1.5210-4 Water 1000 1.3110-6 1.4110-5 1.94 Patm = 101.3 kPa, 14.7 psi The pressure gradient dp/dx, in a pipe is found to be a function of the discharge Q, the density of the fluid p, dynamic viscosity of the fluid , diameter of the pipe D, and the average roughness height of the pipe surface, ks. (a) Derive the dimensionless groups that can be formed from these variables. Write the non-dimensional form of the pressure gradient as a function of the other dimensionless groups. (25 points) (b) In order to conduct a model test using 1:5 scale model of the pipe using the same fluid of the prototype what should be the average velocity in the model pipe if the protype average velocity is 2 m/s? (8 points)