Hydroxyethylcellulose (HEC) is a common thickening agent. Its 0.5%wt. solution is a non-Newtonian fluid and well described with a power-law model 5 for steady-state shear flows. rz=mdrdvzn1drdvz Above, rz is the shear stress in r-direction and vz is the velocity in z-direction. For 0.5% HEC,m=0.85Pas0.5 and n=0.5. For such a power-law fluid flowing laminarly in a circular pipe, the following steady-state velocity distribution is valid, vz=vmax[1(Rr)3/2] where the maximum velocity, vmax, depends on the pressure gradient, pipe radius R,m, and n. a. Show that the average velocity 6 is equal to (3/7)vmax. b. Show that the kinetic energy correction factor, , is equal to 2.26