Discharge over Rectangle Weir Considering Francis's formula Calculator

✖The Length of Weir is the of the base of weir through which discharge is taking place.ⓘ Length of Weir [L_w]			+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 Final Height of Liquid is a variable from the tank emptying through an orifice at its bottom.ⓘ Final Height of Liquid [H_f]			+10% -10%

✖Discharge Weir is the rate of flow of a liquid.ⓘ Discharge over Rectangle Weir Considering Francis's formula [Q']

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Formula

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Discharge over Rectangle Weir Considering Francis's formula

Formula

Q' = 1.84 \cdot L w \cdot ({(H i + H f)}^{\frac{3}{2}} - {H f}^{\frac{3}{2}})

Example

116939.2 m³/s = 1.84 \cdot 25 m \cdot ({(186.1 m + 0.17 m)}^{\frac{3}{2}} - {0.17 m}^{\frac{3}{2}})

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Discharge over Rectangle Weir Considering Francis's formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Discharge = 1.84*Length of Weir*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2))
Q' = 1.84*L_w*((H_i+H_f)^(3/2)-H_f^(3/2))
This formula uses 4 Variables

Variables Used

Discharge - (Measured in Cubic Meter per Second) - Discharge Weir is the rate of flow of a liquid.
Length of Weir - (Measured in Meter) - The Length of Weir is the of the base of weir through which discharge is taking place.
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.
Final Height of Liquid - (Measured in Meter) - The Final Height of Liquid is a variable from the tank emptying through an orifice at its bottom.

STEP 1: Convert Input(s) to Base Unit

Length of Weir: 25 Meter --> 25 Meter No Conversion Required
Initial Height of Liquid: 186.1 Meter --> 186.1 Meter No Conversion Required
Final Height of Liquid: 0.17 Meter --> 0.17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q' = 1.84*L_w*((H_i+H_f)^(3/2)-H_f^(3/2)) --> 1.84*25*((186.1+0.17)^(3/2)-0.17^(3/2))

Evaluating ... ...

Q' = 116939.229839737

STEP 3: Convert Result to Output's Unit

116939.229839737 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

116939.229839737 ≈ 116939.2 Cubic Meter per Second <-- Discharge

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Notches and Weirs » Mechanical » Discharge » Discharge over Rectangle 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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< Discharge Calculators

Time Required to Empty Reservoir

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

Time Required to Empty Tank with Triangular Weir or Notch

Go Total Time Taken = ((5*Area of Weir)/(4*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])))*(1/(Final Height of Liquid^(3/2))-1/(Initial Height of Liquid^(3/2)))

Head of Liquid above V-notch

Go Head of Liquid = (Theoretical Discharge/(8/15*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])))^0.4

Head of Liquid at Crest

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

Discharge over Rectangle Weir Considering Francis's formula Formula

Discharge = 1.84*Length of Weir*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2))
Q' = 1.84*L_w*((H_i+H_f)^(3/2)-H_f^(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 Discharge over Rectangle Weir Considering Francis's formula?

Discharge over Rectangle Weir Considering Francis's formula calculator uses Discharge = 1.84*Length of Weir*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2)) to calculate the Discharge, Discharge over Rectangle Weir Considering Francis's formula is commonly used to calculate the discharge over a rectangular weir. It provides an estimate of the discharge based on the head of water above the weir crest and the dimensions of the weir. Discharge is denoted by Q' symbol.

How to calculate Discharge over Rectangle Weir Considering Francis's formula using this online calculator? To use this online calculator for Discharge over Rectangle Weir Considering Francis's formula, enter Length of Weir (L_w), Initial Height of Liquid (H_i) & Final Height of Liquid (H_f) and hit the calculate button. Here is how the Discharge over Rectangle Weir Considering Francis's formula calculation can be explained with given input values -> 5613.083 = 1.84*25*((186.1+0.17)^(3/2)-0.17^(3/2)).

FAQ

What is Discharge over Rectangle Weir Considering Francis's formula?

Discharge over Rectangle Weir Considering Francis's formula is commonly used to calculate the discharge over a rectangular weir. It provides an estimate of the discharge based on the head of water above the weir crest and the dimensions of the weir and is represented as Q' = 1.84*L_w*((H_i+H_f)^(3/2)-H_f^(3/2)) or Discharge = 1.84*Length of Weir*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2)). The Length of Weir is the of the base of weir through which discharge is taking place, The Initial height of liquid is a variable from the tank emptying through an orifice at its bottom & The Final Height of Liquid is a variable from the tank emptying through an orifice at its bottom.

How to calculate Discharge over Rectangle Weir Considering Francis's formula?

Discharge over Rectangle Weir Considering Francis's formula is commonly used to calculate the discharge over a rectangular weir. It provides an estimate of the discharge based on the head of water above the weir crest and the dimensions of the weir is calculated using Discharge = 1.84*Length of Weir*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2)). To calculate Discharge over Rectangle Weir Considering Francis's formula, you need Length of Weir (L_w), Initial Height of Liquid (H_i) & Final Height of Liquid (H_f). With our tool, you need to enter the respective value for Length of Weir, Initial Height of Liquid & Final Height of Liquid 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?

In this formula, Discharge uses Length of Weir, Initial Height of Liquid & Final Height of Liquid. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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