Flow through pipes is a type of flow in which a fluid flows through a closed conduit. In these cases, fluid experiences certain resistance, losing some energy. Also, pipes of different cross-sections and lengths could be connected in series and parallel in a water supply network, which requires the calculation of equivalent diameters. All the aspects of flow through pipes mentioned above are discussed in this blog.

## Flow Through Pipes

As said, flow through pipes is the flow of a fluid through a closed conduit without or with a free surface of the flow. Flow through pipes having a free surface is treated as open channel flow and is dealt with separately. Here we will see about full flowing fluids in pipes i.e., under pressure flows.

Also, there are two types of flows i.e., laminar flow and turbulent flow. If Reynold's number is less than 2000 then the flow is called laminar flow. And if Reynol's number is greater than 4000 then it is called turbulent flow.

## Losses in Pipes

The fluid flowing through a pipe experience some resistance to its flow due to which some of the energy of the flow is lost. Based on the magnitude of energy lost it is classified into two types.

### Major Energy Losses

It is the energy lost due to frictional resistance offered by the pipe material. It depends on the length of the pipe, the velocity of flow, the diameter of the pipe, and the frictional coefficient. Methods for calculating major energy losses are listed and explained below.

Darcy-Weisbach Formula

Chezy's Formula

### Darcy-Weisbach Formula

Loss of head due to friction is calculated as,

*hf = (4*f*L*V^2) / (2*d*g)*

where

hf - head loss due to friction

f - coefficient of friction which is calculated as,

*f = 16/Re,*

for Re<2000 (Laminar flow)

*f = 0.079 / (Re^(1/4)),*

for Re varying from 4000 to 10^6 (Turbulent flow)

L - length of the pipe

V - mean velocity of flow

d - diameter of the pipe

### Chezy's Formula

Chezy's formula for headloss s given as,

*V = C * (mi)^(1/2)*

where,

C - Chezy's constant

m - hydraulic mean depth or hydraulic radius = d/4 for pipes

i - headloss per unit length

### Minor Energy Losses

Losses that happen because of the below-mentioned reasons are grouped as minor losses.

Sudden expansion of the pipe

Sudden contraction of the pipe

Bend in pipe

Pipe fittings

Obstruction in pipe

Formulas for calculating the losses that happen because of the above-mentioned reasons are explained further.

#### Loss of Head due to Sudden Expansion of the Pipe

*he = ((V1 - V2)^2) / (2*g)*

where

V1 - velocity of flow before the expansion of the pipe

V2 - velocity of flow after the expansion of the pipe

#### Loss of Head due to Sudden Contraction of the Pipe

*he = (0.5*V2^2) / 2*g*

where

V2 - velocity of low after contraction of the pipe

#### Loss of Head at the Entrance of a Pipe

This loss occurs when a liquid enters the pipe from a reservoir or a tank.

*hi = (0.5*V^2) / 2*g*

where

V - velocity of flow

#### Loss of Head at the Exit of Pipe

This loss happens at the exit where the velocity of flow is dissipated as a free jet or is lost in the reservoir.

*ho = (V^2) / 2*g*

where

V - velocity at the outlet of the pipe

#### Loss of Head due to an Obstruction in a Pipe

Obstruction in a pipe causes a reduction in the cross-sectional area of the pipe, which then leads to losses.

*Hob = ((V^2) / 2*g) * ( (A / (Cc (A -a)) - 1)*

where

V - velocity of floe

A - area of the pipe

a - maximum area of obstruction

#### Loss of Head due to Bend or Fitting in Pipe

*hb = (k*V^2) / 2*g*

where

k - coefficient of bend/pipe fitting

V - velocity of flow

## Equivalent Diameter of Pipes in Series

When pipes of different lengths and different diameters are connected from end to end it is called a series connection. Here, the rate of flow remains the same in a series connection. But the total head loss is obtained as the sum of head losses. In general, minor losses are neglected to obtain the equivalent diameter of pipes connected in series. Applying this, we get the formula for equivalent diameter as,

## Equivalent Diameter of Pipes in Parallel

When single pipe branches out into two or more pipes, the branched pipes are called parallel pipes. Here, the head loss remains the same in all the pipes. But the total discharge is given as the sum of discharges through each pipe. In general, minor losses are neglected to obtain the equivalent diameter of pipes connected in parallel. Applying this, we get the formula for equivalent diameter as,

## Practice Problem

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