Discharge through Area Calculator

✖Cross-Sectional Area of Channel is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.ⓘ Cross-Sectional Area of Channel [A_cs]			+10% -10%
✖Total Energy is the sum of the kinetic energy and the potential energy of the system under consideration.ⓘ Total Energy [E_total]			+10% -10%
✖Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights.ⓘ Depth of Flow [d_f]			+10% -10%

✖Discharge of Channel is the rate of flow of a liquid.ⓘ Discharge through Area [Q]

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Formula

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Discharge through Area

Formula

`"Q" = sqrt(2*"[g]"*"A"_{"cs"}^2*("E"_{"total"}-"d"_{"f"}))`

Example

`"34.66508m³/s"=sqrt(2*"[g]"*("3.4m²")^2*("8.6J"-"3.3m"))`

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Download Specific Energy and Critical Depth Formulas PDF

Discharge through Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Discharge of Channel = sqrt(2*[g]*Cross-Sectional Area of Channel^2*(Total Energy-Depth of Flow))
Q = sqrt(2*[g]*A_cs^2*(E_total-d_f))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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., sqrt(Number)

Variables Used

Discharge of Channel - (Measured in Cubic Meter per Second) - Discharge of Channel is the rate of flow of a liquid.
Cross-Sectional Area of Channel - (Measured in Square Meter) - Cross-Sectional Area of Channel is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.
Total Energy - (Measured in Joule) - Total Energy is the sum of the kinetic energy and the potential energy of the system under consideration.
Depth of Flow - (Measured in Meter) - Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights.

STEP 1: Convert Input(s) to Base Unit

Cross-Sectional Area of Channel: 3.4 Square Meter --> 3.4 Square Meter No Conversion Required
Total Energy: 8.6 Joule --> 8.6 Joule No Conversion Required
Depth of Flow: 3.3 Meter --> 3.3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = sqrt(2*[g]*A_cs^2*(E_total-d_f)) --> sqrt(2*[g]*3.4^2*(8.6-3.3))

Evaluating ... ...

Q = 34.6650784565678

STEP 3: Convert Result to Output's Unit

34.6650784565678 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

34.6650784565678 ≈ 34.66508 Cubic Meter per Second <-- Discharge of Channel

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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NSS College of Engineering (NSSCE), Palakkad

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< 23 Specific Energy and Critical Depth Calculators

Discharge through Area

Go Discharge of Channel = sqrt(2*[g]*Cross-Sectional Area of Channel^2*(Total Energy-Depth of Flow))

Area of Section given Discharge

Go Cross-Sectional Area of Channel = Discharge of Channel/sqrt(2*[g]*(Total Energy-Depth of Flow))

Volume of Liquid Considering Condition of Maximum Discharge

Go Volume of Water = sqrt((Cross-Sectional Area of Channel^3)*[g]/Top Width)*Time Interval

Mean Velocity of Flow for Total Energy per Unit Weight of Water in Flow Section

Go Mean Velocity = sqrt((Total Energy-(Depth of Flow+Height above Datum))*2*[g])

Total Energy per unit Weight of Water in Flow Section given Discharge

Go Total Energy = Depth of Flow+(((Discharge of Channel/Cross-Sectional Area of Channel)^2)/(2*[g]))

Area of Section Considering Condition of Maximum Discharge

Go Cross-Sectional Area of Channel = (Discharge of Channel*Discharge of Channel*Top Width/[g])^(1/3)

Depth of Flow given Discharge

Go Depth of Flow = Total Energy-(((Discharge of Channel/Cross-Sectional Area of Channel)^2)/(2*[g]))

Discharge through Section Considering Condition of Minimum Specific Energy

Go Discharge of Channel = sqrt((Cross-Sectional Area of Channel^3)*[g]/Top Width)

Discharge through Section Considering Condition of Maximum Discharge

Go Discharge of Channel = sqrt((Cross-Sectional Area of Channel^3)*[g]/Top Width)

Top Width of Section Considering Condition of Maximum Discharge

Go Top Width = sqrt((Cross-Sectional Area of Channel^3)*[g]/Discharge of Channel)

Depth of Flow given Total Energy per Unit Weight of Water in Flow Section

Go Depth of Flow = Total Energy-(((Mean Velocity^2)/(2*[g]))+Height above Datum)

Datum Height for Total Energy per unit Weight of Water in Flow Section

Go Height above Datum = Total Energy-(((Mean Velocity^2)/(2*[g]))+Depth of Flow)

Mean Velocity of Flow given Froude Number

Go Mean Velocity for Froude Number = Froude Number*sqrt(Diameter of Section*[g])

Froude Number given Velocity

Go Froude Number = Mean Velocity for Froude Number/sqrt([g]*Diameter of Section)

Total Energy per unit Weight of Water in Flow Section

Go Total Energy = ((Mean Velocity^2)/(2*[g]))+Depth of Flow+Height above Datum

Mean Velocity of flow given Total Energy in flow section taking Bed Slope as Datum

Go Mean Velocity = sqrt((Total Energy-(Depth of Flow))*2*[g])

Diameter of Section given Froude Number

Go Diameter of Section = ((Mean Velocity for Froude Number/Froude Number)^2)/[g]

Area of Section of Open Channel Considering Condition of Minimum Specific Energy

Go Cross-Sectional Area of Channel = (Discharge of Channel*Top Width/[g])^(1/3)

Top Width of Section through Section Considering Condition of Minimum Specific Energy

Go Top Width = ((Cross-Sectional Area of Channel^3)*[g]/Discharge of Channel)

Total Energy per unit Weight of Water in Flow Section considering Bed Slope as Datum

Go Total Energy = ((Mean Velocity for Froude Number^2)/(2*[g]))+Depth of Flow

Depth of Flow given Total Energy in Flow Section taking Bed Slope as Datum

Go Depth of Flow = Total Energy-(((Mean Velocity^2)/(2*[g])))

Mean Velocity of Flow through Section Considering Condition of Minimum Specific Energy

Go Mean Velocity = sqrt([g]*Diameter of Section)

Diameter of Section through Section Considering Condition of Minimum Specific Energy

Go Diameter of Section = (Mean Velocity^2)/[g]

Discharge through Area Formula

Discharge of Channel = sqrt(2*[g]*Cross-Sectional Area of Channel^2*(Total Energy-Depth of Flow))
Q = sqrt(2*[g]*A_cs^2*(E_total-d_f))

What is Rate of flow?

In physics and engineering, in particular fluid dynamics, the volumetric flow rate is the volume of fluid which passes per unit time; usually it is represented by the symbol Q. The SI unit is cubic metres per second. Another unit used is standard cubic centimetres per minute. In hydrometry, it is known as discharge.

How to Calculate Discharge through Area?

Discharge through Area calculator uses Discharge of Channel = sqrt(2*[g]*Cross-Sectional Area of Channel^2*(Total Energy-Depth of Flow)) to calculate the Discharge of Channel, The Discharge through Area formula is defined as the amount of liquid flowing through the section per unit time in the channel. Discharge of Channel is denoted by Q symbol.

How to calculate Discharge through Area using this online calculator? To use this online calculator for Discharge through Area, enter Cross-Sectional Area of Channel (A_cs), Total Energy (E_total) & Depth of Flow (d_f) and hit the calculate button. Here is how the Discharge through Area calculation can be explained with given input values -> 152.9342 = sqrt(2*[g]*3.4^2*(8.6-3.3)).

FAQ

What is Discharge through Area?

The Discharge through Area formula is defined as the amount of liquid flowing through the section per unit time in the channel and is represented as Q = sqrt(2*[g]*A_cs^2*(E_total-d_f)) or Discharge of Channel = sqrt(2*[g]*Cross-Sectional Area of Channel^2*(Total Energy-Depth of Flow)). Cross-Sectional Area of Channel is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point, Total Energy is the sum of the kinetic energy and the potential energy of the system under consideration & Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights.

How to calculate Discharge through Area?

The Discharge through Area formula is defined as the amount of liquid flowing through the section per unit time in the channel is calculated using Discharge of Channel = sqrt(2*[g]*Cross-Sectional Area of Channel^2*(Total Energy-Depth of Flow)). To calculate Discharge through Area, you need Cross-Sectional Area of Channel (A_cs), Total Energy (E_total) & Depth of Flow (d_f). With our tool, you need to enter the respective value for Cross-Sectional Area of Channel, Total Energy & Depth of Flow and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Discharge of Channel?

In this formula, Discharge of Channel uses Cross-Sectional Area of Channel, Total Energy & Depth of Flow. We can use 2 other way(s) to calculate the same, which is/are as follows -

Discharge of Channel = sqrt((Cross-Sectional Area of Channel^3)*[g]/Top Width)
Discharge of Channel = sqrt((Cross-Sectional Area of Channel^3)*[g]/Top Width)

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