Estimating the pipe wall friction is one of the most common tasks in fluids engineering. For long circular pipes in turbulent flow, the wall shear stress Tw is a function of the density p, viscosity , the average velocity V, pipe diameter d and wall roughness height . Thus functionally, one can write = Tufcn(p, , V, d, e). (1) (a) Using dimensional analysis, rewrite this function in dimensionless form. Show all steps. (b) A certain pipe d 50cm, = 0.25mm. For flow of water, measurements show the fol- lowing values of wall shear stress. Plot these data using the dimensionless form obtained above. Plot it on a log-log scale. Suggest a curve-fit formula. Does your plot reveal the entire functional relation obtained above for all possible values of the variables? Q, gal/min Tw Pa 1.5 3.0 6.0 0.05 0.18 0.37 9.0 12.0 14.0 0.64 0.86 1.25 Use p 998 kg/m and = 0.001 kg/m.s for water.