5.2 ) \ \

Water density ρ = 1000 kg/m^3 \ \

Diameter d = 25 mm \ \

d = 25/1000 = 0.0025 m \ \

Length l = 50 m \ \

Velocity v = 2.5 m/s \ \

Coefficient of friction f = 0.005 \ \

Darcy’s formula : \ \

Loss of head due to friction  h = 4flv²/2gd \ \

h = (4(0.005)(50)(2.5)²) / (2(9.8)(0.0025)) \ \

Testing the answer using the Chezy formula \ \

v = C√(mi) \ \

head loss due to fiction i = h/l \ \

i = h/50 \ \

Hydraulic radius m = A/p \ \

Area A = (¼)πd²

Peremeter p = πd \ \

m = (¼)πd²/(πd)

m = d/4

m = 0.0025/4 \ \

m = 0.000625 \ \

Constant of Chezy C = √(2g/f) \ \

C = √(2*9.8/0.005) \ \

C = 62.61 \ \

Chezy formula : v = C√(mi) \ \

Substitute C = 62.61 , m = 0.000625 v = 2.5 and i = h/50 \ \

2.5 = 62.61√(0.000625*(h/50)) \ \

(0.000625/50)h = (2.5/62.61)² \ \

(0.000625/50)h = 0.001594 \ \

h = ( 0.00159 * 50 ) / 0.000625 \ \

h = 127.52 m \ \

Solution: \ \

The loss of head due to friction = 127.52 m \ \