Length of Weir Considering Francis's formula Calculator

✖Discharge Weir is the rate of flow of a liquid.ⓘ Discharge Weir [Q]			+10% -10%
✖The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.ⓘ Initial Height of Liquid [H_i]			+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 Considering Francis's formula [L_w]

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Length of Weir Considering Francis's formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
L_w = Q/(1.84*((H_i+h_a)^(3/2)-h_a^(3/2)))
This formula uses 4 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.
Initial Height of Liquid - (Measured in Meter) - The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom.
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
Initial Height of Liquid: 186.1 Meter --> 186.1 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_w = Q/(1.84*((H_i+h_a)^(3/2)-h_a^(3/2))) --> 40/(1.84*((186.1+1.2)^(3/2)-1.2^(3/2)))

Evaluating ... ...

L_w = 0.0084851255827039

STEP 3: Convert Result to Output's Unit

0.0084851255827039 Meter --> No Conversion Required

FINAL ANSWER

0.0084851255827039 ≈ 0.008485 Meter <-- Length of Weir

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Notches and Weirs » Mechanical » Geometric DImension » Length of Weir Considering Francis's formula

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PSG College of Technology (PSGCT), Coimbatore

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Indian Institute of Technology (IIT), Bombay

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< Geometric DImension Calculators

Length of Crest of Weir or Notch

LaTeX 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 or Notch for Velocity of Approach

LaTeX 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 Section for Discharge over Rectangle Notch or Weir

LaTeX 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

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

Length of Weir Considering Francis's formula Formula

LaTeX 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)))
L_w = Q/(1.84*((H_i+h_a)^(3/2)-h_a^(3/2)))

How Francis's formula is considered here?

Francis's on the basis of his experiments established that end contraction decreases the effective length of the crest of the weir and hence decreases the discharge.

What is a weir?

A weir or low head dam is a barrier across the width of a river that alters the flow characteristics of water and usually results in a change in the height of the river level. They are also used to control the flow of water for outlets of lakes, ponds, and reservoirs.

How to Calculate Length of Weir Considering Francis's formula?

Length of Weir Considering Francis's formula calculator uses 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))) to calculate the Length of Weir, Length of Weir Considering Francis's formula 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_w symbol.

How to calculate Length of Weir Considering Francis's formula using this online calculator? To use this online calculator for Length of Weir Considering Francis's formula, enter Discharge Weir (Q), Initial Height of Liquid (H_i) & Head Due to Velocity of Approach (h_a) and hit the calculate button. Here is how the Length of Weir Considering Francis's formula calculation can be explained with given input values -> 0.008485 = 40/(1.84*((186.1+1.2)^(3/2)-1.2^(3/2))).

FAQ

What is Length of Weir Considering Francis's formula?

Length of Weir Considering Francis's formula 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_w = Q/(1.84*((H_i+h_a)^(3/2)-h_a^(3/2))) or 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))). Discharge Weir is the rate of flow of a liquid, The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom & 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 Considering Francis's formula?

Length of Weir Considering Francis's formula 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/(1.84*((Initial Height of Liquid+Head Due to Velocity of Approach)^(3/2)-Head Due to Velocity of Approach^(3/2))). To calculate Length of Weir Considering Francis's formula, you need Discharge Weir (Q), Initial Height of Liquid (H_i) & Head Due to Velocity of Approach (h_a). With our tool, you need to enter the respective value for Discharge Weir, Initial Height of Liquid & 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, Initial Height of Liquid & Head Due to Velocity of Approach. We can use 3 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)))

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