Parallel and Series

PIPING SYSTEM IN SERIES OR PARALLEL

Pipes In series

i. The Pressure loss in the sum of the individual losses.

hL = hL₁ + hL₂ + .. + hL_n    (1)

where,

hL = Total pressure loss (Pa, psi)

hL₁ .._n = Individual pressure loss (Pa, psi)

ii. The Flow rate is the same in all pipes.

Q = Q₁ = Q₂ = .. = Q_n

where,

Q = Flow rate

Q₁ .._n = Individual flow rate

Pipes in Parallel

i. The pressure loss is the same in all pipes.

hL = hL₁ = hL₂ = .. = hL_n   

where,

hL = Total pressure loss (Pa, psi)

hL₁ .._n = Individual pressure loss (Pa, psi)

ii. The total flow rate is the sum of the flow rate in each pipe.

Q = Q₁ + Q₂ + .. + Q_n

where,

Q = Flow rate

Q₁ .._n = Individual flow rate

Simplify

Comparison
Series	Parallel
hL = hL1 + hL2 + .. + hLn	hL = hL1 = hL2 = .. = hLn
Q = Q1 = Q2 = .. = Qn	Q = Q1 + Q2 + .. + Qn

*NOTE: The pressure drops in the equation above can be substituted with generic expression for pressure drop like the D’arcy-Weisbach egquation.

Example Questions of Pipe in Series

Determine the head loss and discharge for pipe system network if entrance and exit section is sharp

Take f = 0.01 (by using 
                   .

Example Questions of Pipe in Parallel

Two pipes connect two reservoirs (A and B) which have a height difference of 10m. Pipe 1 has diameter 50mm and length 100m. Pipe 2 has diameter 100mm and length 100m. Both have entry loss kL = 0.5 and exit loss kL=1.0 and Darcy f of 0.008. Calculate the rate of flow for each pipe.

Figure 1

Apply Bernoulli to each pipeseparately. For pipe 1

2)