The head loss due to friction in a pipe of 1 m diameter and 1.5 km long when water is flowing with a velocity of 1 m/s is (Darcy's friction factor f_D= 0.02 and acceleration due to gravity g =10m/s²)

Concept:

Head loss due to friction is given by:

\({\rm{h\;}} = {\rm{\;}}\frac{{{\rm{f}}L{{\rm{v}}^2}}}{{2{\rm{gd}}}}\)

d = diameter of pipe, f = friction factor, L = length of pipe, and v = velocity of flow

Calculation:

Given:

d = 1 m, L = 1.5 km = 1500 m, v = 1 m/s, f = 0.02, g = 10 m/s²

Head loss due to friction is

\({\rm{h\;}} = {\rm{\;}}\frac{{{\rm{f}}L{{\rm{v}}^2}}}{{2{\rm{gd}}}}\)

\({\rm{h\;}} = {\rm{\;}}\frac{{{\rm{0.02}}\times 1500 \times{{\rm{1}}^2}}}{{2{\rm{\times10\times1}}}}\)

h = 1.5 m