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 = dp₁ + dp₂ + .. + 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 = m₁ = m₂ = .... = 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 = dp₁ = dp₂ = .... = dp_n                                    (2)

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

m = m₁ + m₂ + .. + 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.