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Discharge Flow through Channel Formula

GoDischarge Flow through Rectangular Channel Formula

GoDischarge through Critical Depth Flume Formula

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Discharge of Channel is the rate of flow of a liquid. Check FAQs

Q = (C d \cdot A i \cdot A f) \cdot (\sqrt{2 \cdot [g] \cdot \frac{h i - h o}{({A i}^{2}) - ({A f}^{2})}})

Q - Discharge of Channel?C_d - Coefficient of Discharge?A_i - Cross Section Area 1?A_f - Cross Section Area 2?h_i - Loss of Head at Entrance?h_o - Loss of Head at Exit?[g] - Gravitational acceleration on Earth?

Discharge Flow through Channel Example

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Here is how the Discharge Flow through Channel equation looks like with Values.

Here is how the Discharge Flow through Channel equation looks like with Units.

Here is how the Discharge Flow through Channel equation looks like.

12.0397 = (0.66 \cdot 7.1 \cdot 1.8) \cdot (\sqrt{2 \cdot 9.8066 \cdot \frac{20 - 15.1}{({7.1}^{2}) - ({1.8}^{2})}})

12.0397m³/s = (0.66 \cdot 7.1m² \cdot 1.8m²) \cdot (\sqrt{2 \cdot 9.8066m/s² \cdot \frac{20m - 15.1m}{({7.1m²}^{2}) - ({1.8m²}^{2})}})

12.0397 = (0.66 \cdot 7.1 \cdot 1.8) \cdot (\sqrt{2 \cdot 9.8066 \cdot \frac{20 - 15.1}{({7.1}^{2}) - ({1.8}^{2})}})

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Discharge Flow through Channel Solution

Follow our step by step solution on how to calculate Discharge Flow through Channel?

FIRST Step Consider the formula

Q = (C d \cdot A i \cdot A f) \cdot (\sqrt{2 \cdot [g] \cdot \frac{h i - h o}{({A i}^{2}) - ({A f}^{2})}})

Next Step Substitute values of Variables

∴

Q = (0.66 \cdot 7.1m² \cdot 1.8m²) \cdot (\sqrt{2 \cdot [g] \cdot \frac{20m - 15.1m}{({7.1m²}^{2}) - ({1.8m²}^{2})}})

Next Step Substitute values of Constants

∴

Q = (0.66 \cdot 7.1m² \cdot 1.8m²) \cdot (\sqrt{2 \cdot 9.8066m/s² \cdot \frac{20m - 15.1m}{({7.1m²}^{2}) - ({1.8m²}^{2})}})

Next Step Prepare to Evaluate

∴

Q = (0.66 \cdot 7.1 \cdot 1.8) \cdot (\sqrt{2 \cdot 9.8066 \cdot \frac{20 - 15.1}{({7.1}^{2}) - ({1.8}^{2})}})

Next Step Evaluate

∴

Q = 12.0396878404026m³/s

LAST Step Rounding Answer

∴

Q = 12.0397m³/s

Discharge Flow through Channel Formula Elements

Variables

Constants

Functions

Discharge of Channel

Discharge of Channel is the rate of flow of a liquid.

Symbol: Q

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge of Channel

Coefficient of Discharge

The Coefficient of Discharge is ratio of actual discharge to theoretical discharge.

Symbol: C_d

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.2.

Formulas to find Coefficient of Discharge

Cross Section Area 1

Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe).

Symbol: A_i

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Section Area 1

Cross Section Area 2

Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.

Symbol: A_f

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Section Area 2

Loss of Head at Entrance

The Loss of Head at Entrance of a pipe is the loss that occurs when a liquid flows from a large tank into a pipe.

Symbol: h_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Loss of Head at Entrance

Loss of Head at Exit

The Loss of Head at Exit of a pipe is due to the velocity of liquid dissipated in the form of a free jet.

Symbol: h_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Loss of Head at Exit

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Discharge of Channel

Go Discharge Flow through Rectangular Channel

Q = (C d \cdot A i \cdot A f) \cdot (\sqrt{2 \cdot [g] \cdot \frac{h i - h o}{({A i}^{2}) - ({A f}^{2})}})

Go Discharge through Critical Depth Flume

Q = C d \cdot W t \cdot ({d f}^{1.5})

Other formulas in Metering Flumes category

Go Coefficient of Discharge through Flume given Discharge Flow through Channel

C d = (\frac{Q}{A i \cdot A f} \cdot (\sqrt{\frac{({A i}^{2}) - ({A f}^{2})}{2 \cdot [g] \cdot (h i - h o)}}))

Go Head at Entrance given Discharge through Channel

h i = {(\frac{Q}{C d \cdot A i \cdot A f \cdot (\sqrt{2 \cdot \frac{[g]}{{A i}^{2} - {A f}^{2}}})})}^{2} + h o

Go Head at Entrance of Section given Discharge Flow through Channel

h o = h i - {(\frac{Q}{C d \cdot A i \cdot A f \cdot (\sqrt{2 \cdot \frac{[g]}{{A i}^{2} - {A f}^{2}}})})}^{2}

Go Coefficient of Discharge through Flume given Discharge Flow through Rectangular Channel

C d = (\frac{Q}{A i \cdot A f} \cdot (\sqrt{\frac{({A i}^{2}) - ({A f}^{2})}{2 \cdot [g] \cdot (h i - h o)}}))

How to Evaluate Discharge Flow through Channel?

Discharge Flow through Channel evaluator uses Discharge of Channel = (Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2)*(sqrt(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)/((Cross Section Area 1^2)-(Cross Section Area 2^2)))) to evaluate the Discharge of Channel, The Discharge Flow through Channel is defined as the volume of fluid passing per unit time within a confined pathway. Discharge of Channel is denoted by Q symbol.

How to evaluate Discharge Flow through Channel using this online evaluator? To use this online evaluator for Discharge Flow through Channel, enter Coefficient of Discharge (C_d), Cross Section Area 1 (A_i), Cross Section Area 2 (A_f), Loss of Head at Entrance (h_i) & Loss of Head at Exit (h_o) and hit the calculate button.

FAQs on Discharge Flow through Channel

What is the formula to find Discharge Flow through Channel?

The formula of Discharge Flow through Channel is expressed as Discharge of Channel = (Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2)*(sqrt(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)/((Cross Section Area 1^2)-(Cross Section Area 2^2)))). Here is an example- 12.16192 = (0.66*7.1*1.8)*(sqrt(2*[g]*(20-15.1)/((7.1^2)-(1.8^2)))).

How to calculate Discharge Flow through Channel?

With Coefficient of Discharge (C_d), Cross Section Area 1 (A_i), Cross Section Area 2 (A_f), Loss of Head at Entrance (h_i) & Loss of Head at Exit (h_o) we can find Discharge Flow through Channel using the formula - Discharge of Channel = (Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2)*(sqrt(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)/((Cross Section Area 1^2)-(Cross Section Area 2^2)))). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Discharge of Channel?

Here are the different ways to Calculate Discharge of Channel-

Discharge of Channel=(Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2)*(sqrt(2*[g]*(Loss of Head at Entrance-Loss of Head at Exit)/((Cross Section Area 1^2)-(Cross Section Area 2^2))))
Discharge of Channel=Coefficient of Discharge*Width of Throat*(Depth of Flow^1.5)

Can the Discharge Flow through Channel be negative?

No, the Discharge Flow through Channel, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Discharge Flow through Channel?

Discharge Flow through Channel 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 Discharge Flow through Channel can be measured.

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Discharge Flow through Channel Formula

​GoDischarge Flow through Rectangular Channel Formula

​GoDischarge through Critical Depth Flume Formula

Discharge Flow through Channel Example

Discharge Flow through Channel Solution

Discharge Flow through Channel Formula Elements

Other Formulas to find Discharge of Channel

Other formulas in Metering Flumes category

How to Evaluate Discharge Flow through Channel?

FAQs on Discharge Flow through Channel

Variable Name

GoDischarge Flow through Rectangular Channel Formula

GoDischarge through Critical Depth Flume Formula