Weir Flow Calculator Formula

Understand the math behind the weir flow calculator. Each variable explained with a worked example.

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Formulas Used

Flow Discharge (Q)

discharge = (2/3) * cd * weir_width * sqrt(2 * 9.81) * pow(head, 1.5)

Flow Rate

discharge_lps = (2/3) * cd * weir_width * sqrt(2 * 9.81) * pow(head, 1.5) * 1000

Variables

VariableDescriptionDefault
cdDischarge Coefficient (Cd)0.62
weir_widthWeir Width (b)(m)2
headHead above Weir Crest (H)(m)0.3

How It Works

Rectangular Weir Flow

A weir is a barrier across a channel over which water flows. The flow rate relates to the upstream head.

Formula

Q = (2/3) Cd b sqrt(2g) H^(3/2)

where Cd is the discharge coefficient, b is the weir width, g = 9.81 m/s^2, and H is the head (water depth above the crest measured upstream). This formula applies to rectangular, full-width (suppressed) weirs.

Worked Example

A 2 m wide suppressed weir with 0.3 m head, Cd = 0.62.

cd = 0.62weir_width = 2head = 0.3
  1. 01sqrt(2 x 9.81) = sqrt(19.62) = 4.429
  2. 02H^(3/2) = 0.3^1.5 = 0.1643
  3. 03Q = (2/3) x 0.62 x 2 x 4.429 x 0.1643
  4. 04Q = 0.4133 x 4.429 x 0.1643 = 0.601 m^3/s = 601 L/s

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