FLOW THROUGH PIPES IN SERIES AND PARALLEL

We were discussing the concept of laminar and turbulent flow, Reynolds experiment, frictional loss in pipes, derivation of expression for loss of head due to friction in pipes, co-efficient of friction in terms of shear stress, basics of shear stress in turbulent flow, minor head losses in pipe flow, basic concept and working of syphon and also the concept of hydraulic gradient and total energy line, in the subject of fluid mechanics, in our recent posts.

Now we will go ahead to see the, flow through pipes in series and parallel, in the subject of fluid mechanics, with the help of this post.

Flow through pipes in series

When pipes of different lengths and different diameters are connected end to end to form a pipe line, such arrangement or connection of pipes will be considered as pipes in series or compound pipes.

Important Point: Discharge passing through each pipe will be same.

Following figure, displayed here, indicates the arrangement of connection of three pipes in series.

Let us consider the following terms from above figure

L₁, L₂ and L₃: Length of pipes 1, 2 and 3 respectively
d₁, d₂ and d₃: Diameter of pipes 1, 2 and 3 respectively
V₁, V₂ and V₃: Velocity of flow through pipes 1, 2 and 3 respectively
f₁, f₂ and f₃: Co-efficient of friction for pipes 1, 2 and 3 respectively
H = Difference of water level in two tanks

We must note it here that difference in liquid surface level will be equal to the sum of total head loss in the pipes.

If we neglect the minor head losses, we will have following equation for total head loss as mentioned here.

Let us consider that co-efficient of friction i.e. f is same for all three pipes and therefore we can write the equation for head loss as mentioned here.

Further we will go ahead to find out the basic concept, Flow through pipes in parallel, in the subject of fluid mechanics, with the help of our next post.

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