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

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Notches and Weirs

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Properties of Surfaces and Solids

Viscous Flow

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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%
✖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 Head due to Velocity of Approach is considered as the elevation difference between the two circled points on the surface of the approach flow.ⓘ Head Due to Velocity of Approach [h_a]			+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 with Velocity of Approach [L_weir]

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Formula

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

Formula

`"L"_{"weir"} = "Q"/(1.705*"C"_{"d"}*(("l"_{"Arc"}+"h"_{"a"})^(3/2)-"h"_{"a"}^(3/2)))`

Example

`"0.459006m"="40m³/s"/(1.705*"0.8"*(("15m"+"1.2m")^(3/2)-("1.2m")^(3/2)))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
L_weir = Q/(1.705*C_d*((l_Arc+h_a)^(3/2)-h_a^(3/2)))
This formula uses 5 Variables

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.
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.
Head Due to Velocity of Approach - (Measured in Meter) - The Head due to Velocity of Approach is considered as the elevation difference between the two circled points on the surface of the approach flow.

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
Arc Length of Circle: 15 Meter --> 15 Meter No Conversion Required
Head Due to Velocity of Approach: 1.2 Meter --> 1.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_weir = Q/(1.705*C_d*((l_Arc+h_a)^(3/2)-h_a^(3/2))) --> 40/(1.705*0.8*((15+1.2)^(3/2)-1.2^(3/2)))

Evaluating ... ...

L_weir = 0.459005739389677

STEP 3: Convert Result to Output's Unit

0.459005739389677 Meter --> No Conversion Required

FINAL ANSWER

0.459005739389677 ≈ 0.459006 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 with Velocity of Approach

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Created by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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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 with Velocity of Approach Formula

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 is velocity of approach?

The velocity of approach or separation is defined as the rate of change of relative displacement between two bodies. The velocity of approach is defined when the displacement between the bodies is decreasing and separation when the displacement between the bodies is increasing.

How to Calculate Length of Weir for Broad-Crested Weir with Velocity of Approach?

Length of Weir for Broad-Crested Weir with Velocity of Approach calculator uses 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))) to calculate the Length of Weir, Length of Weir for Broad-Crested Weir with Velocity of Approach refers to the horizontal distance along the crest of the weir. It is an important parameter in calculating the discharge over a weir. Length of Weir is denoted by L_weir symbol.

How to calculate Length of Weir for Broad-Crested Weir with Velocity of Approach using this online calculator? To use this online calculator for Length of Weir for Broad-Crested Weir with Velocity of Approach, enter Discharge Weir (Q), Coefficient of Discharge (C_d), Arc Length of Circle (l_Arc) & Head Due to Velocity of Approach (h_a) and hit the calculate button. Here is how the Length of Weir for Broad-Crested Weir with Velocity of Approach calculation can be explained with given input values -> 0.02295 = 40/(1.705*0.8*((15+1.2)^(3/2)-1.2^(3/2))).

FAQ

What is Length of Weir for Broad-Crested Weir with Velocity of Approach?

Length of Weir for Broad-Crested Weir with Velocity of Approach refers to the horizontal distance along the crest of the weir. It is an important parameter in calculating the discharge over a weir and is represented as L_weir = Q/(1.705*C_d*((l_Arc+h_a)^(3/2)-h_a^(3/2))) or 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))). 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, Arc Length of Circle is the length of a piece of curve cut from the circumference of the Circle at particular central angle & The Head due to Velocity of Approach is considered as the elevation difference between the two circled points on the surface of the approach flow.

How to calculate Length of Weir for Broad-Crested Weir with Velocity of Approach?

Length of Weir for Broad-Crested Weir with Velocity of Approach refers to the horizontal distance along the crest of the weir. It is an important parameter in calculating the discharge over a weir is calculated using 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))). To calculate Length of Weir for Broad-Crested Weir with Velocity of Approach, you need Discharge Weir (Q), Coefficient of Discharge (C_d), Arc Length of Circle (l_Arc) & Head Due to Velocity of Approach (h_a). With our tool, you need to enter the respective value for Discharge Weir, Coefficient of Discharge, Arc Length of Circle & Head Due to Velocity of Approach 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, Arc Length of Circle & Head Due to Velocity of Approach. 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/(Coefficient of Discharge*sqrt(2*[g]*(Head of Liquid Middle^2*Arc Length of Circle-Head of Liquid Middle^3)))

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