Submerged Flow over Weir using Villemonte Formula Calculator

✖Free Flow Discharge under Head H1 is the volumetric flow rate of water that is transported in a weir when there is insufficient backwater to reduce the discharge through the flume.ⓘ Free Flow Discharge under Head H1 [Q₁]			+10% -10%
✖Downstream Water Surface Elevation measured above the Weir Crest.ⓘ Downstream Water Surface Elevation [H₂]			+10% -10%
✖Upstream Water Surface Elevation measured above the Weir Crest.ⓘ Upstream Water Surface Elevation [H₁]			+10% -10%
✖Exponent of Head in free flow head discharge relation is denoted by the symbol n.ⓘ Exponent of Head [n_head]			+10% -10%

✖Submerged Discharge for the flow over a weir is denoted by the symbol Q_s.ⓘ Submerged Flow over Weir using Villemonte Formula [Q_s]

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Submerged Flow over Weir using Villemonte Formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Submerged Discharge = Free Flow Discharge under Head H1*(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385
Q_s = Q₁*(1-(H₂/H₁)^n_head)^0.385
This formula uses 5 Variables

Variables Used

Submerged Discharge - (Measured in Cubic Meter per Second) - Submerged Discharge for the flow over a weir is denoted by the symbol Q_s.
Free Flow Discharge under Head H1 - (Measured in Cubic Meter per Second) - Free Flow Discharge under Head H1 is the volumetric flow rate of water that is transported in a weir when there is insufficient backwater to reduce the discharge through the flume.
Downstream Water Surface Elevation - (Measured in Meter) - Downstream Water Surface Elevation measured above the Weir Crest.
Upstream Water Surface Elevation - (Measured in Meter) - Upstream Water Surface Elevation measured above the Weir Crest.
Exponent of Head - (Measured in Meter) - Exponent of Head in free flow head discharge relation is denoted by the symbol n.

STEP 1: Convert Input(s) to Base Unit

Free Flow Discharge under Head H1: 20 Cubic Meter per Second --> 20 Cubic Meter per Second No Conversion Required
Downstream Water Surface Elevation: 5 Meter --> 5 Meter No Conversion Required
Upstream Water Surface Elevation: 10.01 Meter --> 10.01 Meter No Conversion Required
Exponent of Head: 2.99 Meter --> 2.99 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_s = Q₁*(1-(H₂/H₁)^n_head)^0.385 --> 20*(1-(5/10.01)^2.99)^0.385

Evaluating ... ...

Q_s = 18.9936618149729

STEP 3: Convert Result to Output's Unit

18.9936618149729 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

18.9936618149729 ≈ 18.99366 Cubic Meter per Second <-- Submerged Discharge

(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< Flow Measuring Structures Calculators

Free Flow Discharge under Head using Submerged Flow over Weir

LaTeX Go Free Flow Discharge under Head H1 = Submerged Discharge/(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385

Submerged Flow over Weir using Villemonte Formula

LaTeX Go Submerged Discharge = Free Flow Discharge under Head H1*(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385

Head over Weir given Discharge

LaTeX Go Head over Weir = (Flow Discharge/System Constant k)^(1/System Constant n)

Discharge at Structure

LaTeX Go Flow Discharge = System Constant k*(Head over Weir^(System Constant n))

Submerged Flow over Weir using Villemonte Formula Formula

LaTeX Go

Submerged Discharge = Free Flow Discharge under Head H1*(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385
Q_s = Q₁*(1-(H₂/H₁)^n_head)^0.385

What is Submerged Discharge?

Submerged Flow occurs when the water surface downstream from the flume is high enough to reduce flow through a flume. Unlike free-flow, submerged flow requires the measurement of the head at the primary and secondary points of measurement occurring in the throat of the weir.

What is a Weir & Basic Principle governing the Use of Weir?

A weir or low-head dam is a barrier across the width of a river that alters the flow characteristics of water and usually results in a change in the height of the river level. They are also used to control the flow of water for outlets of lakes, ponds, and reservoirs.
The basic principle governing the use of a weir, flume or similar flow-measuring structures is that structures produce a unique control section in the flow.

How to Calculate Submerged Flow over Weir using Villemonte Formula?

Submerged Flow over Weir using Villemonte Formula calculator uses Submerged Discharge = Free Flow Discharge under Head H1*(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385 to calculate the Submerged Discharge, The Submerged Flow over Weir using Villemonte Formula formula is defined as the equation of the free weir to which the flooding coefficient proposed by Villemonte applies. This flooding coefficient is also used for the triangular and truncated triangular weir formulas. Submerged Discharge is denoted by Q_s symbol.

How to calculate Submerged Flow over Weir using Villemonte Formula using this online calculator? To use this online calculator for Submerged Flow over Weir using Villemonte Formula, enter Free Flow Discharge under Head H1 (Q₁), Downstream Water Surface Elevation (H₂), Upstream Water Surface Elevation (H₁) & Exponent of Head (n_head) and hit the calculate button. Here is how the Submerged Flow over Weir using Villemonte Formula calculation can be explained with given input values -> 19.00092 = 20*(1-(5/10.01)^2.99)^0.385.

FAQ

What is Submerged Flow over Weir using Villemonte Formula?

The Submerged Flow over Weir using Villemonte Formula formula is defined as the equation of the free weir to which the flooding coefficient proposed by Villemonte applies. This flooding coefficient is also used for the triangular and truncated triangular weir formulas and is represented as Q_s = Q₁*(1-(H₂/H₁)^n_head)^0.385 or Submerged Discharge = Free Flow Discharge under Head H1*(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385. Free Flow Discharge under Head H1 is the volumetric flow rate of water that is transported in a weir when there is insufficient backwater to reduce the discharge through the flume, Downstream Water Surface Elevation measured above the Weir Crest, Upstream Water Surface Elevation measured above the Weir Crest & Exponent of Head in free flow head discharge relation is denoted by the symbol n.

How to calculate Submerged Flow over Weir using Villemonte Formula?

The Submerged Flow over Weir using Villemonte Formula formula is defined as the equation of the free weir to which the flooding coefficient proposed by Villemonte applies. This flooding coefficient is also used for the triangular and truncated triangular weir formulas is calculated using Submerged Discharge = Free Flow Discharge under Head H1*(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385. To calculate Submerged Flow over Weir using Villemonte Formula, you need Free Flow Discharge under Head H1 (Q₁), Downstream Water Surface Elevation (H₂), Upstream Water Surface Elevation (H₁) & Exponent of Head (n_head). With our tool, you need to enter the respective value for Free Flow Discharge under Head H1, Downstream Water Surface Elevation, Upstream Water Surface Elevation & Exponent of Head and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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