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*Lweir*((Hi+Hf)^(3/2)-Hf^(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: 1.21 Meter --> 1.21 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*Lweir*((Hi+Hf)^(3/2)-Hf^(3/2)) --> 1.84*1.21*((186.1+0.17)^(3/2)-0.17^(3/2))
Evaluating ... ...
Q' = 5659.85872424329
STEP 3: Convert Result to Output's Unit
5659.85872424329 Cubic Meter per Second --> No Conversion Required
FINAL ANSWER
5659.85872424329 5659.859 Cubic Meter per Second <-- Discharge
(Calculation completed in 00.020 seconds)

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PSG College of Technology (PSGCT), Coimbatore
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17 Discharge Calculators

Discharge over Trapezoidal Notch or Weir
Go Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)
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))
Coefficient of Discharge for Time Required to Empty Reservoir
Go Coefficient of Discharge = (3*Area of Weir)/(Total Time Taken*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)))
Discharge over Rectangle Weir for Bazin's formula with Velocity of Approach
Go Discharge Weir = (0.405+0.003/(Head of Liquid+Head Due to Velocity of Approach))*Length of Weir*sqrt(2*[g])*(Head of Liquid+Head Due to Velocity of Approach)^(3/2)
Discharge with Velocity of Approach
Go 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 over Broad-Crested Weir for Head of Liquid at Middle
Go Discharge Weir = Coefficient of Discharge*Length of Weir*sqrt(2*[g]*(Head of Liquid Middle^2*Head of Liquid-Head of Liquid Middle^3))
Discharge over Broad-Crested Weir with Velocity of Approach
Go Discharge Weir = 1.705*Coefficient of Discharge*Length of Weir*((Head of Liquid+Head Due to Velocity of Approach)^(3/2)-Head Due to Velocity of Approach^(3/2))
Discharge over Rectangle Weir with Two End Contractions
Go Discharge Weir = 2/3*Coefficient of Discharge*(Length of Weir-0.2*Head of Liquid)*sqrt(2*[g])*Head 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
Discharge over Triangular Notch or Weir
Go Theoretical Discharge = 8/15*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)
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 Notch or Weir
Go Theoretical Discharge = 2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)
Discharge without Velocity of Approach
Go Discharge = 2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])*Initial Height of Liquid^(3/2)
Discharge over Rectangle Weir Considering Bazin's formula
Go Discharge Weir = (0.405+0.003/Head of Liquid)*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)
Discharge over Rectangle Weir Considering Francis's formula
Go Discharge = 1.84*Length of Weir*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2))
Discharge over Broad-Crested Weir
Go Discharge Weir = 1.705*Coefficient of Discharge*Length of Weir*Head of Liquid^(3/2)

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*Lweir*((Hi+Hf)^(3/2)-Hf^(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 (Lweir), Initial Height of Liquid (Hi) & Final Height of Liquid (Hf) 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 -> 5659.859 = 1.84*1.21*((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*Lweir*((Hi+Hf)^(3/2)-Hf^(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 (Lweir), Initial Height of Liquid (Hi) & Final Height of Liquid (Hf). 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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