In a pipe of diameter 350 mm and length 75 m water is flowing at a velocity of 2.8 m/s. Find the head lost due to friction using : (i) Darcy-Weisbach formula; (ii) Chezy’s formula for which C = 55 Assume kinematic viscosity of water as 0.012 stoke .

 

In a pipe of diameter 350 mm and length 75 m water is flowing at a velocity of 2.8 m/s. Find the head lost due to friction using : (i) Darcy-Weisbach formula; (ii) Chezy’s formula for which C = 55 Assume kinematic viscosity of water as 0.012 stoke .

 Solution:

Diameter of the pipe,            D = 350mm = 0.35 m

Length of the pipe,                 L = 75 m

Velocity of flow,                    V = 2.8 m/s

Chezy’s constant                    C = 55

Kinematic viscosity of water,  ν = 0.012 stoke

                                                   = 0.012*10-4 m2 /s

 Head lost due to friction, hf :

(i)Darcy-Weisbach formula:

Darcy-Weisbach formula is given by , hf=4fLV2 /2gD

where, f = co-efficeint of friction(a function of Reynolds number Re)

 Re = (v*D) / ν = (2.8*0.35) / 0.012*10-4        = 8.167*105

Therefore f = 0.0719/ (Re) 0.25      [use when Re > 4000]

                  = 0.0719/ (8.167*105 ) 0.25

                    = 0.00263

Therefore head lost due to friction,

hf=(4* 0.00263*75*(2.8)2 ) /2*9.81*0.35

hf = 0.9 m

(ii) Chezy’s formula:

mean velocity V = C√(mi)

Where C = 55, m=A /P = (π*D2 /4) /(π*D) = D/4 = 0.35/4

                                                                              = 0.0875 m

Therefore 2.8         = 55√(0.0875*i)

or 0.0875*i = (2.8/55)2 = 0.00259

                  i = 0.00296 But

                  i = hf/L = 0.0296

Therefore             

 hf/75 = 0.0296

 hf = 0.0296*75

 hf =2.22 m