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In several practical situations, flow takes place under a given head through different pipes jointed together either in series or in parallel or in a combination of both of them.

- If a pipeline is joined to one or more pipelines in continuation, these are said to constitute pipes in series. A typical example of pipes in series is shown in Fig. 36.1. Here three pipes
*A, B*and*C*are joined in series.

n this case, rate of flow *Q *remains same in each pipe. Hence,

If the total head available at Sec. 1 (at the inlet to pipe A) is H_{1 }which is greater than H2 ,^{ }the total head at Sec. 2 (at the exit of pipe C), then the flow takes place from 1 to 2 through the system of pipelines in series.

Application of Bernoulli's equation between Secs.1 and 2 gives

H_{1 - }H_{2 } = h_{f}

where, h_{f }is the loss of head due to the flow from 1 to 2. Recognizing the minor and major losses associated with the flow, h_{f } can be written as

(36.1)

Friction loss Loss due to

enlargement at

entry to pipe B

in pipe AFriction loss

in pipe B

The subscripts *A, B *and *C *refer to the quantities in pipe A, B and C respectively. C_{c} is the coefficient of contraction.

- The flow rate Q satisfies the equation

Velocities V_{A}, V_{B} and V_{C} in Eq. (36.1) are substituted from Eq. (36.2), and we get

(36.3)

(36.4)

Equation (36.4) states that the total flow resistance is equal to the sum of the different resistance components. Therefore, the above problem can be described by an equivalent electrical network system as shown in Fig. 36.2.

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