Two-branch quadratic flow split

Split known total flow between two parallel branches with supplied quadratic resistances.

How this calculation works

The two branches in this model share the same inlet and outlet pressure nodes, so they must have the same pressure drop. Enter their positive quadratic resistance coefficients and the total flow that reaches the split. Each coefficient relates pressure drop in kilopascals to the square of flow in liters per second. The calculator combines equal pressure drop with conservation of total flow to determine the two branch flows. The lower-resistance branch carries more flow, and the common drop is calculated using either branch. Resistance values must already be known for the relevant operating range; pipe dimensions are not converted into resistance here. Static pressure offsets, pumps within branches, control devices and linear laminar losses are excluded from this simple quadratic network balance.

Inputs and units

Total volume flow (L/s)
Branch 1 resistance (kPa/(L/s)²)
Branch 2 resistance (kPa/(L/s)²)

Method and formula

Δp = R1Q1² = R2Q2²; Q1+Q2 = Qtotal; Q1 = Qtotal sqrt(R2)/(sqrt(R1)+sqrt(R2)); Q2 = Qtotal−Q1.

Worked example

Example inputs

Total volume flow: 6 L/s
Branch 1 resistance: 4 kPa/(L/s)²
Branch 2 resistance: 1 kPa/(L/s)²

Calculation steps

Square roots of resistance coefficients are √4 = 2 and √1 = 1.
Branch 1 flow = 6 × 1 / (2 + 1) = 2 L/s. Branch 2 flow = 6 − 2 = 4 L/s.
Common pressure drop = 4 × 2² = 16 kPa; the second branch gives 1 × 4² = 16 kPa.

Example results

Branch 1 flow: 2 L/s
Branch 2 flow: 4 L/s
Common branch pressure drop: 16 kPa

Assumptions

Branches connect the same two pressure nodes; each resistance is constant and positive.

Limitations

No pipe sizing or resistance estimation; coefficients must match the stated units and operating range.
No static pressure offsets, pumps, pressure controls, check-valve thresholds or laminar linear losses.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

DOE Fundamentals: Fluid Flow: Continuity and Bernoulli energy balance; centrifugal pumps, equations 3-19 through 3-25; series and parallel piping