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Free Flow Discharge under Head using Submerged Flow over Weir Formula

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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. Check FAQs

Q 1 = \frac{Q s}{{(1 - {(\frac{H 2}{H 1})}^{n head})}^{0.385}}

Q₁ - Free Flow Discharge under Head H1?Q_s - Submerged Discharge?H₂ - Downstream Water Surface Elevation?H₁ - Upstream Water Surface Elevation?n_head - Exponent of Head?

Free Flow Discharge under Head using Submerged Flow over Weir Example

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Here is how the Free Flow Discharge under Head using Submerged Flow over Weir equation looks like with Values.

Here is how the Free Flow Discharge under Head using Submerged Flow over Weir equation looks like with Units.

Here is how the Free Flow Discharge under Head using Submerged Flow over Weir equation looks like.

20.0067 = \frac{19}{{(1 - {(\frac{5}{10.01})}^{2.99})}^{0.385}}

20.0067m³/s = \frac{19m³/s}{{(1 - {(\frac{5m}{10.01m})}^{2.99m})}^{0.385}}

20.0067 = \frac{19}{{(1 - {(\frac{5}{10.01})}^{2.99})}^{0.385}}

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Free Flow Discharge under Head using Submerged Flow over Weir Solution

Follow our step by step solution on how to calculate Free Flow Discharge under Head using Submerged Flow over Weir?

FIRST Step Consider the formula

Q 1 = \frac{Q s}{{(1 - {(\frac{H 2}{H 1})}^{n head})}^{0.385}}

Next Step Substitute values of Variables

∴

Q 1 = \frac{19m³/s}{{(1 - {(\frac{5m}{10.01m})}^{2.99m})}^{0.385}}

Next Step Prepare to Evaluate

∴

Q 1 = \frac{19}{{(1 - {(\frac{5}{10.01})}^{2.99})}^{0.385}}

Next Step Evaluate

∴

Q 1 = 20.0066740000837m³/s

LAST Step Rounding Answer

∴

Q 1 = 20.0067m³/s

Free Flow Discharge under Head using Submerged Flow over Weir Formula Elements

Variables

Free Flow Discharge under Head H1

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.

Symbol: Q₁

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Free Flow Discharge under Head H1

Submerged Discharge

Submerged Discharge for the flow over a weir is denoted by the symbol Q_s.

Symbol: Q_s

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Submerged Discharge

Downstream Water Surface Elevation

Downstream Water Surface Elevation measured above the Weir Crest.

Symbol: H₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Downstream Water Surface Elevation

Upstream Water Surface Elevation

Upstream Water Surface Elevation measured above the Weir Crest.

Symbol: H₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Upstream Water Surface Elevation

Exponent of Head

Exponent of Head in free flow head discharge relation is denoted by the symbol n.

Symbol: n_head

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exponent of Head

Other formulas in Flow Measuring Structures category

Go Head over Weir given Discharge

H = {(\frac{Q f}{k})}^{\frac{1}{n system}}

Go Discharge at Structure

Q f = k \cdot (H^{n system})

Go Submerged Flow over Weir using Villemonte Formula

Q s = Q 1 \cdot {(1 - {(\frac{H 2}{H 1})}^{n head})}^{0.385}

How to Evaluate Free Flow Discharge under Head using Submerged Flow over Weir?

Free Flow Discharge under Head using Submerged Flow over Weir evaluator uses Free Flow Discharge under Head H1 = Submerged Discharge/(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385 to evaluate 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 evaluate Free Flow Discharge under Head using Submerged Flow over Weir using this online evaluator? To use this online evaluator 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.

FAQs on Free Flow Discharge under Head using Submerged Flow over Weir

What is the formula to find Free Flow Discharge under Head using Submerged Flow over Weir?

The formula of Free Flow Discharge under Head using Submerged Flow over Weir is expressed as Free Flow Discharge under Head H1 = Submerged Discharge/(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385. Here is an example- 19.99903 = 19/(1-(5/10.01)^2.99)^0.385.

How to calculate Free Flow Discharge under Head using Submerged Flow over Weir?

With Submerged Discharge (Q_s), Downstream Water Surface Elevation (H₂), Upstream Water Surface Elevation (H₁) & Exponent of Head (n_head) we can find Free Flow Discharge under Head using Submerged Flow over Weir using the formula - Free Flow Discharge under Head H1 = Submerged Discharge/(1-(Downstream Water Surface Elevation/Upstream Water Surface Elevation)^Exponent of Head)^0.385.

Can the Free Flow Discharge under Head using Submerged Flow over Weir be negative?

Yes, the Free Flow Discharge under Head using Submerged Flow over Weir, measured in Volumetric Flow Rate can be negative.

Which unit is used to measure Free Flow Discharge under Head using Submerged Flow over Weir?

Free Flow Discharge under Head using Submerged Flow over Weir is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Free Flow Discharge under Head using Submerged Flow over Weir can be measured.

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Free Flow Discharge under Head using Submerged Flow over Weir Formula

Free Flow Discharge under Head using Submerged Flow over Weir Example

Free Flow Discharge under Head using Submerged Flow over Weir Solution

Free Flow Discharge under Head using Submerged Flow over Weir Formula Elements

Other formulas in Flow Measuring Structures category

How to Evaluate Free Flow Discharge under Head using Submerged Flow over Weir?

FAQs on Free Flow Discharge under Head using Submerged Flow over Weir

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