Length of Section for Discharge over Rectangle Notch or Weir Calculator

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Geometric DImension

Discharge

✖The Theoretical Discharge is given by the theoretical area and velocity.ⓘ Theoretical Discharge [Q_th]			+10% -10%
✖The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.ⓘ Coefficient of Discharge [C_d]			+10% -10%
✖Arc Length of Circle is the length of a piece of curve cut from the circumference of the Circle at particular central angle.ⓘ Arc Length of Circle [l_Arc]			+10% -10%

✖The Length of Weir is the of the base of weir through which discharge is taking place.ⓘ Length of Section for Discharge over Rectangle Notch or Weir [L_weir]

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Formula

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Length of Section for Discharge over Rectangle Notch or Weir

Formula

`"L"_{"weir"} = "Q"_{"th"}/(2/3*"C"_{"d"}*sqrt(2*"[g]")*"l"_{"Arc"}^(3/2))`

Example

`"0.655891m"="90m³/s"/(2/3*"0.8"*sqrt(2*"[g]")*("15m")^(3/2))`

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Length of Section for Discharge over Rectangle Notch or Weir Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Weir = Theoretical Discharge/(2/3*Coefficient of Discharge*sqrt(2*[g])*Arc Length of Circle^(3/2))
L_weir = Q_th/(2/3*C_d*sqrt(2*[g])*l_Arc^(3/2))
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

Length of Weir - (Measured in Meter) - The Length of Weir is the of the base of weir through which discharge is taking place.
Theoretical Discharge - (Measured in Cubic Meter per Second) - The Theoretical Discharge is given by the theoretical area and velocity.
Coefficient of Discharge - The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.
Arc Length of Circle - (Measured in Meter) - Arc Length of Circle is the length of a piece of curve cut from the circumference of the Circle at particular central angle.

STEP 1: Convert Input(s) to Base Unit

Theoretical Discharge: 90 Cubic Meter per Second --> 90 Cubic Meter per Second No Conversion Required
Coefficient of Discharge: 0.8 --> No Conversion Required
Arc Length of Circle: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_weir = Q_th/(2/3*C_d*sqrt(2*[g])*l_Arc^(3/2)) --> 90/(2/3*0.8*sqrt(2*[g])*15^(3/2))

Evaluating ... ...

L_weir = 0.655890827310509

STEP 3: Convert Result to Output's Unit

0.655890827310509 Meter --> No Conversion Required

FINAL ANSWER

0.655890827310509 ≈ 0.655891 Meter <-- Length of Weir

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Notches and Weirs » Geometric DImension » Length of Section for Discharge over Rectangle Notch or Weir

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Created by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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< 10+ Geometric DImension Calculators

Length of Crest of Weir or Notch

Go Length of Weir = (3*Area of Weir)/(Coefficient of Discharge*Total Time Taken*sqrt(2*[g]))*(1/sqrt(Final Height of Liquid)-1/sqrt(Initial Height of Liquid))

Length of Weir Considering Bazin's formula with Velocity of Approach

Go Length of Notches = Discharge Weir/(0.405+0.003/(Arc Length of Circle+Head Due to Velocity of Approach))*sqrt(2*[g])*(Arc Length of Circle+Head Due to Velocity of Approach)^(3/2)

Length of Weir or Notch for Velocity of Approach

Go Length of Weir = Discharge Weir/(2/3*Coefficient of Discharge*sqrt(2*[g])*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2)))

Length of Weir for Broad-Crested Weir and Head of Liquid at Middle

Go Length of Weir = Discharge Weir/(Coefficient of Discharge*sqrt(2*[g]*(Head of Liquid Middle^2*Arc Length of Circle-Head of Liquid Middle^3)))

Length of Weir for Broad-Crested Weir with Velocity of Approach

Go Length of Weir = Discharge Weir/(1.705*Coefficient of Discharge*((Arc Length of Circle+Head Due to Velocity of Approach)^(3/2)-Head Due to Velocity of Approach^(3/2)))

Length of Weir Considering Francis's formula

Go Length of Weir = Discharge Weir/(1.84*((Initial Height of Liquid+Head Due to Velocity of Approach)^(3/2)-Head Due to Velocity of Approach^(3/2)))

Length of Weir Considering Bazin's formula without Velocity of Approach

Go Length of Notches = Discharge Weir/(0.405+0.003/Arc Length of Circle)*sqrt(2*[g])*Arc Length of Circle^(3/2)

Length of Section for Discharge over Rectangle Notch or Weir

Go Length of Weir = Theoretical Discharge/(2/3*Coefficient of Discharge*sqrt(2*[g])*Arc Length of Circle^(3/2))

Length of Weir or Notch without Velocity of Approach

Go Length of Weir = Discharge Weir/(2/3*Coefficient of Discharge*sqrt(2*[g])*Initial Height of Liquid^(3/2))

Length of Weir for Discharge over Broad-Crested Weir

Go Length of Weir = Discharge Weir/(1.705*Coefficient of Discharge*Arc Length of Circle^(3/2))

Length of Section for Discharge over Rectangle Notch or Weir Formula

Length of Weir = Theoretical Discharge/(2/3*Coefficient of Discharge*sqrt(2*[g])*Arc Length of Circle^(3/2))
L_weir = Q_th/(2/3*C_d*sqrt(2*[g])*l_Arc^(3/2))

What is a notch?

A Notch is a device used for measuring the rate of flow of a liquid through a small channel or a tank. It may be defined as an opening in the side of a tank or vessel such as liquid surface in the tank is below the level of opening.

What is the difference between notch and weir?

A notch is generally meant to measure the flow of water from a tank. A weir is also a notch but it is made on a large scale. The weir is a notch cut in a dam to discharge the surplus quantity of water. A notch is usually made of metal plate whereas a weir is made of masonry or concrete.

How to Calculate Length of Section for Discharge over Rectangle Notch or Weir?

Length of Section for Discharge over Rectangle Notch or Weir calculator uses Length of Weir = Theoretical Discharge/(2/3*Coefficient of Discharge*sqrt(2*[g])*Arc Length of Circle^(3/2)) to calculate the Length of Weir, Length of Section for Discharge over Rectangle Notch or Weir refers to the horizontal distance of the rectangular opening through which the liquid flows. It represents the width of the notch or weir. Length of Weir is denoted by L_weir symbol.

How to calculate Length of Section for Discharge over Rectangle Notch or Weir using this online calculator? To use this online calculator for Length of Section for Discharge over Rectangle Notch or Weir, enter Theoretical Discharge (Q_th), Coefficient of Discharge (C_d) & Arc Length of Circle (l_Arc) and hit the calculate button. Here is how the Length of Section for Discharge over Rectangle Notch or Weir calculation can be explained with given input values -> 0.000292 = 90/(2/3*0.8*sqrt(2*[g])*15^(3/2)).

FAQ

What is Length of Section for Discharge over Rectangle Notch or Weir?

Length of Section for Discharge over Rectangle Notch or Weir refers to the horizontal distance of the rectangular opening through which the liquid flows. It represents the width of the notch or weir and is represented as L_weir = Q_th/(2/3*C_d*sqrt(2*[g])*l_Arc^(3/2)) or Length of Weir = Theoretical Discharge/(2/3*Coefficient of Discharge*sqrt(2*[g])*Arc Length of Circle^(3/2)). The Theoretical Discharge is given by the theoretical area and velocity, The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge & Arc Length of Circle is the length of a piece of curve cut from the circumference of the Circle at particular central angle.

How to calculate Length of Section for Discharge over Rectangle Notch or Weir?

Length of Section for Discharge over Rectangle Notch or Weir refers to the horizontal distance of the rectangular opening through which the liquid flows. It represents the width of the notch or weir is calculated using Length of Weir = Theoretical Discharge/(2/3*Coefficient of Discharge*sqrt(2*[g])*Arc Length of Circle^(3/2)). To calculate Length of Section for Discharge over Rectangle Notch or Weir, you need Theoretical Discharge (Q_th), Coefficient of Discharge (C_d) & Arc Length of Circle (l_Arc). With our tool, you need to enter the respective value for Theoretical Discharge, Coefficient of Discharge & Arc Length of Circle 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 Length of Weir?

In this formula, Length of Weir uses Theoretical Discharge, Coefficient of Discharge & Arc Length of Circle. We can use 7 other way(s) to calculate the same, which is/are as follows -

Length of Weir = (3*Area of Weir)/(Coefficient of Discharge*Total Time Taken*sqrt(2*[g]))*(1/sqrt(Final Height of Liquid)-1/sqrt(Initial Height of Liquid))
Length of Weir = Discharge Weir/(2/3*Coefficient of Discharge*sqrt(2*[g])*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2)))
Length of Weir = Discharge Weir/(2/3*Coefficient of Discharge*sqrt(2*[g])*Initial Height of Liquid^(3/2))
Length of Weir = Discharge Weir/(1.84*((Initial Height of Liquid+Head Due to Velocity of Approach)^(3/2)-Head Due to Velocity of Approach^(3/2)))
Length of Weir = Discharge Weir/(1.705*Coefficient of Discharge*Arc Length of Circle^(3/2))
Length of Weir = Discharge Weir/(Coefficient of Discharge*sqrt(2*[g]*(Head of Liquid Middle^2*Arc Length of Circle-Head of Liquid Middle^3)))
Length of Weir = Discharge Weir/(1.705*Coefficient of Discharge*((Arc Length of Circle+Head Due to Velocity of Approach)^(3/2)-Head Due to Velocity of Approach^(3/2)))

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