•    When the pipes of different lengths and diameters are connected to each other to form a pipeline the such a pipeline is called as a compound pipe or pipes in series.

•    As the pipes are in series, the discharge through each pipe will be same (continuous)

Q  = A₁ V₁ = A₂ V₂ = A₃ V₃

•    If a pipeline connecting two reservoirs by compound pipes, then the difference in liquid surface level is equal to the sum of the head losses in all the sections.


Let  Q = discharge through pipeline
       H = total loss of head
       d₁ = diameter of pipe 1
       L₁ = length of pipe 1
       f₁ = friction factor

d₂, ι₂, f₂  = corresponding value of pipe 2,
d₃, ι₃, f₃  = corresponding value of pipe 3.

1.    Considering all losses,

Total loss of head  = Major losses + Minor losses

H = hL₁+ hL₂

Major losses = head loss due to friction in each pipe

hL₁  = hf₁ + hf₂ + hf₃

hL₁ = f₁ L₁ V₁² / 2g d₁ + f₂ L₂ V₂² / 2g d₂ + f₃ L₃ V² / 2g d₃

Minor losses  = Entrance + Contraction + Expansion + Exit
                              loss              loss                loss            loss

hL₂ = 0.5 V₁²/ 2g + 0.5 V₂² / 2g + (V₂ - V₃)² / 2g + V₃² / 2g

2.    If minor losses are neglected, then

Total loss of head  = Major losses

H  = 1/2g [f₁L₁V₁2 / d₁ + f₂L₂V₂²/d₂ + f₃L₃V₃²/d₃

3.    If discharge through the pipe is given, then

H = f₁L₁Q^₂/12.1d₁⁵ + f₂L₂Q²/12.1d₂⁵ + f₃L₃Q²/12.1d₃⁵

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