Determine the (i) friction factor (ii) shear stress at the pipe surface

Question

A rough pipe of diameter 0.1 m carries water at 20°C at the rate of 50 lps.  If the average height of the roughness projections on the pipe surface is

         0.15 mm, determine the

         (i)   friction factor

         (ii)  shear stress at the pipe surface

         (iii) shear velocity

         (iv) maximum velocity              

         Take for water at 200C,

               Kinematic viscosity = 1$\times$10^-6 m²/s

               Mass density = 1000 kg/m³