Discharge Flow through Channel Calculator

✖Coefficient of Discharge is ratio of Actual discharge to theoretical discharge.ⓘ Coefficient of Discharge [C_d]			+10% -10%
✖Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe).ⓘ Cross Section Area 1 [A_i]			+10% -10%
✖Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.ⓘ Cross Section Area 2 [A_f]			+10% -10%
✖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.ⓘ Loss of Head at Entrance [h_i]			+10% -10%
✖The Loss of Head at Exit of a pipe is due to the velocity of liquid dissipated in the form of a free jet.ⓘ Loss of Head at Exit [h_o]			+10% -10%

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

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Formula

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Discharge Flow through Channel

Formula

`"Q" = ("C"_{"d"}*"A"_{"i"}*"A"_{"f"})*(sqrt(2*"[g]"*("h"_{"i"}-"h"_{"o"})/(("A"_{"i"}^2)-("A"_{"f"}^2))))`

Example

`"12.03969m³/s"=("0.66"*"7.1m²"*"1.8m²")*(sqrt(2*"[g]"*("20m"-"15.1m")/((("7.1m²")^2)-(("1.8m²")^2))))`

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Download Metering Flumes and Momentum in Open-Channel Flow Specific Force Formulas PDF

Discharge Flow through Channel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
Q = (C_d*A_i*A_f)*(sqrt(2*[g]*(h_i-h_o)/((A_i^2)-(A_f^2))))
This formula uses 1 Constants, 1 Functions, 6 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.
Coefficient of Discharge - Coefficient of Discharge is ratio of Actual discharge to theoretical discharge.
Cross Section Area 1 - (Measured in Square Meter) - Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe).
Cross Section Area 2 - (Measured in Square Meter) - Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.
Loss of Head at Entrance - (Measured in Meter) - 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.
Loss of Head at Exit - (Measured in Meter) - The Loss of Head at Exit of a pipe is due to the velocity of liquid dissipated in the form of a free jet.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Discharge: 0.66 --> No Conversion Required
Cross Section Area 1: 7.1 Square Meter --> 7.1 Square Meter No Conversion Required
Cross Section Area 2: 1.8 Square Meter --> 1.8 Square Meter No Conversion Required
Loss of Head at Entrance: 20 Meter --> 20 Meter No Conversion Required
Loss of Head at Exit: 15.1 Meter --> 15.1 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = (C_d*A_i*A_f)*(sqrt(2*[g]*(h_i-h_o)/((A_i^2)-(A_f^2)))) --> (0.66*7.1*1.8)*(sqrt(2*[g]*(20-15.1)/((7.1^2)-(1.8^2))))

Evaluating ... ...

Q = 12.0396878404026

STEP 3: Convert Result to Output's Unit

12.0396878404026 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

12.0396878404026 ≈ 12.03969 Cubic Meter per Second <-- Discharge of Channel

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Flow in Open Channels » Metering Flumes and Momentum in Open-Channel Flow Specific Force » Metering Flumes » Discharge Flow through Channel

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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< 10+ Metering Flumes Calculators

Coefficient of Discharge through Flume given Discharge Flow through Rectangular Channel

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

Coefficient of Discharge through Flume given Discharge Flow through Channel

Discharge Flow through Rectangular Channel

Go 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 Flow through Channel

Head at Entrance of Section given Discharge Flow through Channel

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

Head at Entrance given Discharge through Channel

Go Loss of Head at Entrance = (Discharge of Channel/(Coefficient of Discharge*Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]/(Cross Section Area 1^2-Cross Section Area 2^2)))))^2+Loss of Head at Exit

Depth of Flow given Discharge through Critical Depth Flume

Go Depth of Flow = (Discharge of Channel/(Width of Throat*Coefficient of Discharge))^(2/3)

Discharge Coefficient given Discharge through Critical Depth Flume

Go Coefficient of Discharge = Discharge of Channel/(Width of Throat*(Depth of Flow^1.5))

Width of Throat given Discharge through Critical Depth Flume

Go Width of Throat = Discharge of Channel/(Coefficient of Discharge*(Depth of Flow^1.5))

Discharge through Critical Depth Flume

Go Discharge of Channel = Coefficient of Discharge*Width of Throat*(Depth of Flow^1.5)

Discharge Flow through Channel Formula

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 Flow through Channel?

Discharge Flow through Channel calculator 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 calculate 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 calculate Discharge Flow through Channel using this online calculator? To use this online calculator 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. Here is how the Discharge Flow through Channel calculation can be explained with given input values -> 12.16192 = (0.66*7.1*1.8)*(sqrt(2*[g]*(20-15.1)/((7.1^2)-(1.8^2)))).

FAQ

What is Discharge Flow through Channel?

The Discharge Flow through Channel is defined as the volume of fluid passing per unit time within a confined pathway and is represented as Q = (C_d*A_i*A_f)*(sqrt(2*[g]*(h_i-h_o)/((A_i^2)-(A_f^2)))) or 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)))). Coefficient of Discharge is ratio of Actual discharge to theoretical discharge, Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe), Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure, 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 & The Loss of Head at Exit of a pipe is due to the velocity of liquid dissipated in the form of a free jet.

How to calculate Discharge Flow through Channel?

The Discharge Flow through Channel is defined as the volume of fluid passing per unit time within a confined pathway is calculated using 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 calculate Discharge Flow through Channel, you need 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). With our tool, you need to enter the respective value for Coefficient of Discharge, Cross Section Area 1, Cross Section Area 2, Loss of Head at Entrance & Loss of Head at Exit 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 Coefficient of Discharge, Cross Section Area 1, Cross Section Area 2, Loss of Head at Entrance & Loss of Head at Exit. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)

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