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

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Notches and Weirs

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Geometric DImension

Discharge

✖Discharge Weir is the rate of flow of a liquid.ⓘ Discharge Weir [Q]			+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%
✖The Head of Liquid Middle of weir which is a constant is considered in the broad-crested weir.ⓘ Head of Liquid Middle [h]			+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 Weir for Broad-Crested Weir and Head of Liquid at Middle [L_weir]

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

Formula

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

Example

`"0.512126m"="40m³/s"/("0.8"*sqrt(2*"[g]"*(("9m")^2*"15m"-("9m")^3)))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
L_weir = Q/(C_d*sqrt(2*[g]*(h^2*l_Arc-h^3)))
This formula uses 1 Constants, 1 Functions, 5 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.
Discharge Weir - (Measured in Cubic Meter per Second) - Discharge Weir is the rate of flow of a liquid.
Coefficient of Discharge - The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge.
Head of Liquid Middle - (Measured in Meter) - The Head of Liquid Middle of weir which is a constant is considered in the broad-crested weir.
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

Discharge Weir: 40 Cubic Meter per Second --> 40 Cubic Meter per Second No Conversion Required
Coefficient of Discharge: 0.8 --> No Conversion Required
Head of Liquid Middle: 9 Meter --> 9 Meter 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/(C_d*sqrt(2*[g]*(h^2*l_Arc-h^3))) --> 40/(0.8*sqrt(2*[g]*(9^2*15-9^3)))

Evaluating ... ...

L_weir = 0.512125656966266

STEP 3: Convert Result to Output's Unit

0.512125656966266 Meter --> No Conversion Required

FINAL ANSWER

0.512125656966266 ≈ 0.512126 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 Weir for Broad-Crested Weir and Head of Liquid at Middle

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

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)))
L_weir = Q/(C_d*sqrt(2*[g]*(h^2*l_Arc-h^3)))

What is broad-crested weir?

Broad crested weirs are robust structures that are generally constructed from reinforced concrete and which usually span the full width of the channel. They are used to measure the discharge of rivers and are much more suited for this purpose than the relatively flimsy sharp-crested weirs.

What are the types of weirs based on shape of the crest?

It is of four types they are, sharp-crested weir, broad- crested weir, narrow-crested weir, and ogee-shaped weir.

How to Calculate Length of Weir for Broad-Crested Weir and Head of Liquid at Middle?

Length of Weir for Broad-Crested Weir and Head of Liquid at Middle calculator uses 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))) to calculate the Length of Weir, The Length of weir for broad-crested weir and head of liquid at middle formula is known by considering the coefficient of discharge, discharge over the broad-crested weir, and the head of liquid without the velocity approach. Length of Weir is denoted by L_weir symbol.

How to calculate Length of Weir for Broad-Crested Weir and Head of Liquid at Middle using this online calculator? To use this online calculator for Length of Weir for Broad-Crested Weir and Head of Liquid at Middle, enter Discharge Weir (Q), Coefficient of Discharge (C_d), Head of Liquid Middle (h) & Arc Length of Circle (l_Arc) and hit the calculate button. Here is how the Length of Weir for Broad-Crested Weir and Head of Liquid at Middle calculation can be explained with given input values -> 0.025606 = 40/(0.8*sqrt(2*[g]*(9^2*15-9^3))).

FAQ

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

The Length of weir for broad-crested weir and head of liquid at middle formula is known by considering the coefficient of discharge, discharge over the broad-crested weir, and the head of liquid without the velocity approach and is represented as L_weir = Q/(C_d*sqrt(2*[g]*(h^2*l_Arc-h^3))) or 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))). Discharge Weir is the rate of flow of a liquid, The Coefficient of Discharge or efflux coefficient is the ratio of the actual discharge to the theoretical discharge, The Head of Liquid Middle of weir which is a constant is considered in the broad-crested weir & 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 Weir for Broad-Crested Weir and Head of Liquid at Middle?

The Length of weir for broad-crested weir and head of liquid at middle formula is known by considering the coefficient of discharge, discharge over the broad-crested weir, and the head of liquid without the velocity approach is calculated using 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))). To calculate Length of Weir for Broad-Crested Weir and Head of Liquid at Middle, you need Discharge Weir (Q), Coefficient of Discharge (C_d), Head of Liquid Middle (h) & Arc Length of Circle (l_Arc). With our tool, you need to enter the respective value for Discharge Weir, Coefficient of Discharge, Head of Liquid Middle & 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 Discharge Weir, Coefficient of Discharge, Head of Liquid Middle & Arc Length of Circle. We can use 7 other way(s) to calculate the same, which is/are as follows -

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