Weir Flow Calculator and Hydraulic Jump Calculator: Rectangular and V-Notch Discharge

Measure a flow with a weir, or find the depth after a hydraulic jump.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose a rectangular weir or a V-notch weir and enter the head above the crest, the crest length or notch angle and the discharge coefficient.

The calculator gives the flow Q = 2/3 Cd root 2g L H to the 3/2 for a rectangular weir, or 8/15 Cd root 2g tan(theta/2) H to the 5/2 for a V-notch.

For a hydraulic jump, enter the depth and velocity before the jump to get the Froude number, the depth after the jump, the energy lost and the length of the jump.

Formulas used

  • Q = \tfrac23C_d\sqrt{2g}\,L\,H^{3/2}
  • Q = \tfrac{8}{15}C_d\sqrt{2g}\tan\frac{\theta}{2}H^{5/2}
  • y_2 = \tfrac{y_1}{2}\left(\sqrt{1 + 8\mathrm{Fr}_1^2} - 1\right)

Worked example

With the default numbers in the calculator above:

  1. Flow over the rectangular weir: 0.60 m3/s (601.67 L/s)
  2. Flow for each metre of crest: 300.84 L/s per metre

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? Hydraulic jump.

  1. Froude number before the jump: 3.57 (a fast, supercritical flow)
  2. Depth after the jump (the conjugate depth): 0.91 m (4.57 times the depth before)
  3. Velocity after the jump: 1.09 m/s
  4. Energy lost in the jump: 0.50 m of head (33.83 percent of the energy before)
  5. Length of the jump (approximate): 5.49 m

Common questions

Where should the head be measured?

Upstream, at a distance of at least four times the head, where the water surface is still level.

Why use a V-notch?

Its flow depends on the head to the power 5/2, so it measures small flows more accurately.

What is a hydraulic jump?

The sudden change from fast shallow flow to slow deep flow, with a lot of turbulence and energy loss.

When does a jump form?

Only when the flow before it is supercritical, with a Froude number above 1.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Chow, Open-Channel Hydraulics; ISO 1438 Hydrometry: thin-plate weirs.

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