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Pipe In Series

•    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 = f1L1Q2/12.1d15 + f2L2Q2/12.1d25 + f3L3Q2/12.1d35

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