Flow Through Pipes In Series

Pipes are said to be in series if they are connected end to end (in continuation with each other) so that the fluid flows in a continuous line without any branching. The volume rate of flow through the pipes in series is the same throughout.

Suppose a pipe line consists of a number of pipes of different sizes and lengths.

Let d1, d2, d3 be the diameters of the component pipes.

Let l1, l2, l3 be the lengths of these component pipes.

Let v1, v2, v3 be the velocities in these pipes.

Pipes connected in continuation as in this case are said to be connected in series. In this arrangement the rate of discharge Q is the same in all the pipes. Ignoring secondary losses the total loss of head is equal to the sum of the friction losses in the individual pipes.

                                                              Equivalent Pipe Corresponding to a Given

Set of Pipes in Series:

Let d1, d2, d3 be the diameters, and l1, l2, l3 be the lengths of the various pipes in a series connection. Let Q be the discharge. Let hf be the total loss of head.

Let d be the diameter of an equivalent pipe of length l to replace the compound pipe to pass the same discharge at the same loss of head.

The above relation is called Dupuit’s equation.

Equivalent Length of a Pipe with Intermediate Fittings:

Suppose a pipe of length I is provided with an intermediate fitting due to which the loss of head = k(v2/2g). Let Ie be the length of pipe, the friction loss due to which is equal to k(v2/2g).

Credit:- www.engineeringenotes.com/fluids/pipes/flow-through-pipes-in-series-and-parallel-difference-diameters-equations-and-solved-problems/47568