Discharge given Critical Depth Calculator

✖Critical depth occurs when the flow in a channel has a minimum specific energy. Specific energy refers to the sum of the depth of flow and the velocity head.ⓘ Critical Depth [CD]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Width of throat of the parshall flume is denoted by W symbol.ⓘ Width of throat [W_t]			+10% -10%

✖Environmental Discharge is the rate of flow of a liquid.ⓘ Discharge given Critical Depth [Q_e]

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Discharge given Critical Depth

Formula

`"Q"_{"e"} = sqrt((("CD")^3)*"g"*("W"_{"t"})^2)`

Example

`"75.13188m³/s"=sqrt((("4m")^3)*"9.8m/s²"*("3m")^2)`

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Discharge given Critical Depth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Environmental Discharge = sqrt(((Critical Depth)^3)*Acceleration due to Gravity*(Width of throat)^2)
Q_e = sqrt(((CD)^3)*g*(W_t)^2)
This formula uses 1 Functions, 4 Variables

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

Environmental Discharge - (Measured in Cubic Meter per Second) - Environmental Discharge is the rate of flow of a liquid.
Critical Depth - (Measured in Meter) - Critical depth occurs when the flow in a channel has a minimum specific energy. Specific energy refers to the sum of the depth of flow and the velocity head.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Width of throat - (Measured in Meter) - Width of throat of the parshall flume is denoted by W symbol.

STEP 1: Convert Input(s) to Base Unit

Critical Depth: 4 Meter --> 4 Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Width of throat: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_e = sqrt(((CD)^3)*g*(W_t)^2) --> sqrt(((4)^3)*9.8*(3)^2)

Evaluating ... ...

Q_e = 75.1318840439929

STEP 3: Convert Result to Output's Unit

75.1318840439929 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

75.1318840439929 ≈ 75.13188 Cubic Meter per Second <-- Environmental Discharge

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Environmental Engineering » Treatment of Sewage » Constant Velocity Horizontal Flow Grit Channels » Design of Parabolic Grit Chamber » Parabolic Grit Chamber » Discharge in Channel » Discharge given Critical Depth

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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National Institute of Technology (NIT), Warangal

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< 7 Discharge in Channel Calculators

Discharge for Rectangular Channel Section using manning's equation

Go Environmental Discharge = Area Of Cross Section*(Hydraulic radius^(2/3))*(Slope of bed^(1/2))/Manning’s Roughness Coefficient

Discharge given Critical Depth

Go Environmental Discharge = sqrt(((Critical Depth)^3)*Acceleration due to Gravity*(Width of throat)^2)

Discharge Coefficient with known discharge

Go Discharge coefficient = log(Theoretical Discharge/Integration Constant,Depth)

Discharge Passing through Parshall Flume given Discharge Coefficient

Go Environmental Discharge = Integration Constant*(Depth)^(Discharge coefficient)

Discharge through Control Section

Go Environmental Discharge = Width of throat*Critical Velocity*Critical Depth

Maximum Discharge given Width of Throat

Go Peak Discharge = Width of throat*Critical Velocity*Critical Depth

Discharge given Flow Area of Throat

Go Environmental Discharge = Flow area of throat*Critical Velocity

Discharge given Critical Depth Formula

Environmental Discharge = sqrt(((Critical Depth)^3)*Acceleration due to Gravity*(Width of throat)^2)
Q_e = sqrt(((CD)^3)*g*(W_t)^2)

What is discharge ?

The amount of fluid passing a section of a stream in unit time is called the discharge. If v is the mean velocity and A is the cross sectional area, the discharge Q is defined by Q = Av which is known as volume flow rate. Discharge is also expressed as mass flow rate and weight flow rate.

How to Calculate Discharge given Critical Depth?

Discharge given Critical Depth calculator uses Environmental Discharge = sqrt(((Critical Depth)^3)*Acceleration due to Gravity*(Width of throat)^2) to calculate the Environmental Discharge, Discharge given Critical Depth is defined as amount of fluid passing section of stream in unit time. Environmental Discharge is denoted by Q_e symbol.

How to calculate Discharge given Critical Depth using this online calculator? To use this online calculator for Discharge given Critical Depth, enter Critical Depth (CD), Acceleration due to Gravity (g) & Width of throat (W_t) and hit the calculate button. Here is how the Discharge given Critical Depth calculation can be explained with given input values -> 75.13188 = sqrt(((4)^3)*9.8*(3)^2).

FAQ

What is Discharge given Critical Depth?

Discharge given Critical Depth is defined as amount of fluid passing section of stream in unit time and is represented as Q_e = sqrt(((CD)^3)*g*(W_t)^2) or Environmental Discharge = sqrt(((Critical Depth)^3)*Acceleration due to Gravity*(Width of throat)^2). Critical depth occurs when the flow in a channel has a minimum specific energy. Specific energy refers to the sum of the depth of flow and the velocity head, Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Width of throat of the parshall flume is denoted by W symbol.

How to calculate Discharge given Critical Depth?

Discharge given Critical Depth is defined as amount of fluid passing section of stream in unit time is calculated using Environmental Discharge = sqrt(((Critical Depth)^3)*Acceleration due to Gravity*(Width of throat)^2). To calculate Discharge given Critical Depth, you need Critical Depth (CD), Acceleration due to Gravity (g) & Width of throat (W_t). With our tool, you need to enter the respective value for Critical Depth, Acceleration due to Gravity & Width of throat 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 Environmental Discharge?

In this formula, Environmental Discharge uses Critical Depth, Acceleration due to Gravity & Width of throat. We can use 4 other way(s) to calculate the same, which is/are as follows -

Environmental Discharge = Integration Constant*(Depth)^(Discharge coefficient)
Environmental Discharge = Area Of Cross Section*(Hydraulic radius^(2/3))*(Slope of bed^(1/2))/Manning’s Roughness Coefficient
Environmental Discharge = Width of throat*Critical Velocity*Critical Depth
Environmental Discharge = Flow area of throat*Critical Velocity

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