Pipes in Parallel

Pipes In Parallel When two or more pipes are connected, as shown in Fig. 36.3, so that the flow divides and subsequently comes together again, the pipes are said to be in parallel. In this case (Fig. 36.3), equation of continuity gives Q =  QA + QB (36.5) where, Q is the total flow rate and QA and QB are the flow rates through pipes A and B respectively. Loss of head between the locations 1 and 2 can be expressed by applying Bernoulli's equation either through the path 1-A-2 or 1-B-2.  Therefore, we can write Fig 36.3 Pipes in Parallel The flow system can be described by an equivalent electrical circuit as shown in Fig. 36.4. Fig 36.4 Equivalent electrical network system for flow through pipes in parallel From the above discussion on flow through branched pipes (pipes in series or in parallel, or in combination of both), the following principles can be summarized: The friction equation must be satisfied for each pipe. There can be only one value of head at any point. Algebraic sum of the flow rates at any junction must be zero. i.e., the total mass flow rate towards the junction must be equal to the total mass flow rate away from it. Algebraic sum of the products of the flux (Q2) and the flow resistance (the sense being determined by the direction of flow) must be zero in any closed hydraulic circuit. The principles 3 and 4 can be written analytically as at a node (Junction) (36.9)                       in a loop (36.10)

While Eq. (36.9) implies the principle of continuity in a hydraulic circuit, Eq. (36.10) is referred to as pressure equation of the circuit.

 

Example of question

Numerical Example

A supply line is divided at a junction (A) into two 100m long pipes one of 1″ dia. and the other of ½” dia. which run parallel and connect at junction (B) further down the gradient. If the flow rate through the supply pipe is 1LPS, what are the flow rates through each parallel pipe and the frictional head loss between points A and B ?

Answer

We know the total flow through the system (Q) is 1LPS so we can substitute this into the flow equation above:

           1  = Q1 + Q2

And we can rewrite this as:

         Q2  = 1 - Q1

We will assume that the flow through the 1″ dia. pipe is designated Q₁ and through the ½” dia. pipe, Q₂. We will now choose values of Q₂ and calculate the frictional head loss (f_h2) for pipe 2 from the friction charts. Using the rearranged flow equation we will calculate the corresponding flow rate in pipe 1 (Q₁) and from the friction charts the frictional head loss in pipe 1 (f_h1). This data is shown below:

Q2 (LPS)	Frictional head loss fh2 (m/100m)	Q1 (LPS)	Frictional head loss fh1 (m/100m)
0.06	1.05	0.94	12.30
0.13	3.77	0.87	10.67
0.19	7.99	0.81	9.32
0.25	13.61	0.75	8.01

As both pipes are 100m long we can plot the two frictional head losses on a graph against the flow rate for Pipe 2 (Q₂).

Figure 20

The point where the two lines intersect is the flow rate in Pipe 2 when the two frictional head losses are similar. In this case it is approximately:

Which means that the flow in Pipe 1 is:

And from the graph, the frictional head loss at the point of intersection is approximately: