# Pipes in Series and Parallel

## Pressure loss in pipes in series and parallel

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### Pipes in Series

The pressure loss is the sum of the individual losses:

*dp = dp _{1} + dp_{2} + .. + dp_{n} (1)*

*where *

*p = total pressure loss (Pa, psi)*

*p _{1..n} = individual pressure loss (Pa, psi)*

The mass flow rate is the same in all pipes:

*m = m _{1} = m_{2} = .... = m_{n} (1b)*

*where *

*m = mass flow (kg/s, lb/s)*

### Pipes in Parallel

The pressure loss is the same in all pipes:

*dp = dp _{1} = dp_{2} = .... = dp_{n} (2)*

The total mass flow is the sum of the flow in each pipe:

*m = m _{1} + m_{2} + .. + m_{n} (2b)*

The pressure drops in the equations above can be substituted with a generic expression for pressure drop like the D'Arcy-Weisbach equation

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