# Pipes - in Series or Parallel

## Pressure loss in pipes connected in series or parallel

### Pipes in Series

For pipes connected in series the pressure loss is the sum of the individual losses:

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

*where *

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

*dp _{1..n} = individual pressure loss in each pipe (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

For pipes connected 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 loss in the equations above can be substituted with a generic expression for pressure loss like the D'Arcy-Weisbach equation.

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