Free Flow Discharge under Head using Submerged Flow over Weir Calculator

✖Submerged Discharge for the flow over a weir is denoted by the symbol Q_s.ⓘ Submerged Discharge [Q_s]			+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%

✖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 using Submerged Flow over Weir [Q₁]

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Free Flow Discharge under Head using Submerged Flow over Weir Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
Submerged Discharge - (Measured in Cubic Meter per Second) - Submerged Discharge for the flow over a weir is denoted by the symbol Q_s.
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

Submerged Discharge: 19 Cubic Meter per Second --> 19 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

Q₁ = Q_s/(1-(H₂/H₁)^n_head)^0.385 --> 19/(1-(5/10.01)^2.99)^0.385

Evaluating ... ...

Q₁ = 20.0066740000837

STEP 3: Convert Result to Output's Unit

20.0066740000837 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

20.0066740000837 ≈ 20.00667 Cubic Meter per Second <-- Free Flow Discharge under Head H1

(Calculation completed in 00.004 seconds)

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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))

Free Flow Discharge under Head using Submerged Flow over Weir Formula

LaTeX Go

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

What is Submerged Flow?

Submerged (or drowned) flow occurs when the water surface downstream from the flume is high enough to reduce flow through a flume. When the resistance to the flow in the downstream channel is sufficient to reduce the velocity out of the flume, flow depths increase and cause a backwater effect, as water cannot exit the flume quickly enough.

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 Free Flow Discharge under Head using Submerged Flow over Weir?

Free Flow Discharge under Head using Submerged Flow over Weir calculator uses Free Flow Discharge under Head H1 = Submerged Discharge/(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385 to calculate the Free Flow Discharge under Head H1, The Free Flow Discharge under Head using Submerged Flow over Weir formula is defined as 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 is denoted by Q₁ symbol.

How to calculate Free Flow Discharge under Head using Submerged Flow over Weir using this online calculator? To use this online calculator for Free Flow Discharge under Head using Submerged Flow over Weir, enter Submerged Discharge (Q_s), Downstream Water Surface Elevation (H₂), Upstream Water Surface Elevation (H₁) & Exponent of Head (n_head) and hit the calculate button. Here is how the Free Flow Discharge under Head using Submerged Flow over Weir calculation can be explained with given input values -> 19.99903 = 19/(1-(5/10.01)^2.99)^0.385.

FAQ

What is Free Flow Discharge under Head using Submerged Flow over Weir?

The Free Flow Discharge under Head using Submerged Flow over Weir formula is defined as the volumetric flow rate of water that is transported in a weir when there is insufficient backwater to reduce the discharge through the flume and is represented as Q₁ = Q_s/(1-(H₂/H₁)^n_head)^0.385 or Free Flow Discharge under Head H1 = Submerged Discharge/(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385. Submerged Discharge for the flow over a weir is denoted by the symbol Q_s, 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 Free Flow Discharge under Head using Submerged Flow over Weir?

The Free Flow Discharge under Head using Submerged Flow over Weir formula is defined as the volumetric flow rate of water that is transported in a weir when there is insufficient backwater to reduce the discharge through the flume is calculated using Free Flow Discharge under Head H1 = Submerged Discharge/(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385. To calculate Free Flow Discharge under Head using Submerged Flow over Weir, you need Submerged Discharge (Q_s), 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 Submerged Discharge, 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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