Rehbocks Formula for Discharge over Rectangular Weir Calculator

✖Height of Water above Crest of Weir is defined as the water surface height above crest.ⓘ Height of Water above Crest of Weir [S_w]			+10% -10%
✖Height of Crest is the distance between the lowest and highest points of Crest.ⓘ Height of Crest [h_Crest]			+10% -10%
✖The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Length of Weir Crest is the measurement or extent of Weir Crest from end to end.ⓘ Length of Weir Crest [L_w]			+10% -10%

✖Francis Discharge with Suppressed End is discharge of flow without the end contraction.ⓘ Rehbocks Formula for Discharge over Rectangular Weir [Q_Fr']

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Formula

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Rehbocks Formula for Discharge over Rectangular Weir

Formula

`"Q"_{"Fr'"} = 2/3*(0.605+0.08*("S"_{"w"}/"h"_{"Crest"})+(0.001/"S"_{"w"}))*sqrt(2*"g")*"L"_{"w"}*"S"_{"w"}^(3/2)`

Example

`"15.49804m³/s"=2/3*(0.605+0.08*("2m"/"12m")+(0.001/"2m"))*sqrt(2*"9.8m/s²")*"3m"*("2m")^(3/2)`

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Rehbocks Formula for Discharge over Rectangular Weir Solution

STEP 0: Pre-Calculation Summary

Formula Used

Francis Discharge with Suppressed End = 2/3*(0.605+0.08*(Height of Water above Crest of Weir/Height of Crest)+(0.001/Height of Water above Crest of Weir))*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Height of Water above Crest of Weir^(3/2)
Q_Fr' = 2/3*(0.605+0.08*(S_w/h_Crest)+(0.001/S_w))*sqrt(2*g)*L_w*S_w^(3/2)
This formula uses 1 Functions, 5 Variables

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

Francis Discharge with Suppressed End - (Measured in Cubic Meter per Second) - Francis Discharge with Suppressed End is discharge of flow without the end contraction.
Height of Water above Crest of Weir - (Measured in Meter) - Height of Water above Crest of Weir is defined as the water surface height above crest.
Height of Crest - (Measured in Meter) - Height of Crest is the distance between the lowest and highest points of Crest.
Acceleration due to Gravity - (Measured in Meter per Square Second) - The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Length of Weir Crest - (Measured in Meter) - Length of Weir Crest is the measurement or extent of Weir Crest from end to end.

STEP 1: Convert Input(s) to Base Unit

Height of Water above Crest of Weir: 2 Meter --> 2 Meter No Conversion Required
Height of Crest: 12 Meter --> 12 Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Length of Weir Crest: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_Fr' = 2/3*(0.605+0.08*(S_w/h_Crest)+(0.001/S_w))*sqrt(2*g)*L_w*S_w^(3/2) --> 2/3*(0.605+0.08*(2/12)+(0.001/2))*sqrt(2*9.8)*3*2^(3/2)

Evaluating ... ...

Q_Fr' = 15.4980380808525

STEP 3: Convert Result to Output's Unit

15.4980380808525 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

15.4980380808525 ≈ 15.49804 Cubic Meter per Second <-- Francis Discharge with Suppressed End

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Flow Over Notches and Weirs » Flow Over Rectangular Sharp-Crested Weir or Notch » Rehbocks Formula for Discharge over Rectangular Weir

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National Institute of Technology (NIT), Warangal

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< 17 Flow Over Rectangular Sharp-Crested Weir or Notch Calculators

Rehbocks Formula for Discharge over Rectangular Weir

Go Francis Discharge with Suppressed End = 2/3*(0.605+0.08*(Height of Water above Crest of Weir/Height of Crest)+(0.001/Height of Water above Crest of Weir))*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Height of Water above Crest of Weir^(3/2)

Coefficient of Discharge given Discharge if Velocity considered

Go Coefficient of Discharge = (Francis Discharge*3)/(2*(sqrt(2*Acceleration due to Gravity))*(Length of Weir Crest-0.1*Number of End Contraction*Still Water Head)*(Still Water Head^(3/2)-Velocity Head^(3/2)))

Coefficient of Discharge given Discharge if Velocity not considered

Go Coefficient of Discharge = (Francis Discharge*3)/(2*(sqrt(2*Acceleration due to Gravity))*(Length of Weir Crest-0.1*Number of End Contraction*Height of Water above Crest of Weir)*Height of Water above Crest of Weir^(3/2))

Coefficient of Discharge given Discharge Passing over Weir considering Velocity

Go Coefficient of Discharge = (Francis Discharge with Suppressed End*3)/(2*(sqrt(2*Acceleration due to Gravity))*Length of Weir Crest*((Height of Water above Crest of Weir+Velocity Head)^(3/2)-Velocity Head^(3/2)))

Coefficient of Discharge given Discharge over Weir without considering Velocity

Go Coefficient of Discharge = (Francis Discharge with Suppressed End*3)/(2*(sqrt(2*Acceleration due to Gravity))*Length of Weir Crest*Height of Water above Crest of Weir^(3/2))

Coefficient when Bazin Formula for Discharge Velocity is not considered

Go Bazins Coefficient = Bazins Discharge without Velocity/(sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Height of Water above Crest of Weir^(3/2))

Bazins Formula for Discharge if Velocity is not considered

Go Bazins Discharge without Velocity = Bazins Coefficient*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Height of Water above Crest of Weir^(3/2)

Francis Formula for Discharge for Rectangular Notch if Velocity is considered

Go Francis Discharge = 1.84*(Length of Weir Crest-0.1*Number of End Contraction*Still Water Head)*(Still Water Head^(3/2)-Velocity Head^(3/2))

Coefficient when Bazin Formula for Discharge if Velocity is considered

Go Bazins Coefficient = Bazins Discharge with Velocity/(sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Still Water Head^(3/2))

Bazins Formula for Discharge if Velocity is considered

Go Bazins Discharge with Velocity = Bazins Coefficient*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Still Water Head^(3/2)

Francis Formula for Discharge for Rectangular Notch if Velocity not considered

Go Francis Discharge = 1.84*(Length of Weir Crest-0.1*Number of End Contraction*Height of Water above Crest of Weir)*Height of Water above Crest of Weir^(3/2)

Rehbocks Formula for Coefficient of Discharge

Go Coefficient of Discharge = 0.605+0.08*(Height of Water above Crest of Weir/Height of Crest)+(0.001/Height of Water above Crest of Weir)

Depth of Water Flow in Channel given Velocity Approach

Go Depth of Flow = Discharge by Approach Velocity/(Width of Channel1*Velocity of Flow 1)

Width of Channel given Velocity Approach

Go Width of Channel1 = Discharge by Approach Velocity/(Velocity of Flow 1*Depth of Flow)

Approach Velocity

Go Velocity of Flow 1 = Discharge by Approach Velocity/(Width of Channel1*Depth of Flow)

Coefficient for Bazin Formula

Go Bazins Coefficient = 0.405+(0.003/Height of Water above Crest of Weir)

Coefficient for Bazin Formula if Velocity is considered

Go Bazins Coefficient = 0.405+(0.003/Still Water Head)

Rehbocks Formula for Discharge over Rectangular Weir Formula

What is meant by Head?

In hydraulics, Head is defined as a measure of the potential of fluid at the measurement point. it is the measure of height of water.

How to Calculate Rehbocks Formula for Discharge over Rectangular Weir?

Rehbocks Formula for Discharge over Rectangular Weir calculator uses Francis Discharge with Suppressed End = 2/3*(0.605+0.08*(Height of Water above Crest of Weir/Height of Crest)+(0.001/Height of Water above Crest of Weir))*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Height of Water above Crest of Weir^(3/2) to calculate the Francis Discharge with Suppressed End, The Rehbocks Formula for Discharge over Rectangular Weir is a measure of the quantity of any fluid flow passing over unit time. The quantity may be either volume or mass. Francis Discharge with Suppressed End is denoted by Q_Fr' symbol.

How to calculate Rehbocks Formula for Discharge over Rectangular Weir using this online calculator? To use this online calculator for Rehbocks Formula for Discharge over Rectangular Weir, enter Height of Water above Crest of Weir (S_w), Height of Crest (h_Crest), Acceleration due to Gravity (g) & Length of Weir Crest (L_w) and hit the calculate button. Here is how the Rehbocks Formula for Discharge over Rectangular Weir calculation can be explained with given input values -> 15.49804 = 2/3*(0.605+0.08*(2/12)+(0.001/2))*sqrt(2*9.8)*3*2^(3/2).

FAQ

What is Rehbocks Formula for Discharge over Rectangular Weir?

The Rehbocks Formula for Discharge over Rectangular Weir is a measure of the quantity of any fluid flow passing over unit time. The quantity may be either volume or mass and is represented as Q_Fr' = 2/3*(0.605+0.08*(S_w/h_Crest)+(0.001/S_w))*sqrt(2*g)*L_w*S_w^(3/2) or Francis Discharge with Suppressed End = 2/3*(0.605+0.08*(Height of Water above Crest of Weir/Height of Crest)+(0.001/Height of Water above Crest of Weir))*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Height of Water above Crest of Weir^(3/2). Height of Water above Crest of Weir is defined as the water surface height above crest, Height of Crest is the distance between the lowest and highest points of Crest, The Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Length of Weir Crest is the measurement or extent of Weir Crest from end to end.

How to calculate Rehbocks Formula for Discharge over Rectangular Weir?

The Rehbocks Formula for Discharge over Rectangular Weir is a measure of the quantity of any fluid flow passing over unit time. The quantity may be either volume or mass is calculated using Francis Discharge with Suppressed End = 2/3*(0.605+0.08*(Height of Water above Crest of Weir/Height of Crest)+(0.001/Height of Water above Crest of Weir))*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest*Height of Water above Crest of Weir^(3/2). To calculate Rehbocks Formula for Discharge over Rectangular Weir, you need Height of Water above Crest of Weir (S_w), Height of Crest (h_Crest), Acceleration due to Gravity (g) & Length of Weir Crest (L_w). With our tool, you need to enter the respective value for Height of Water above Crest of Weir, Height of Crest, Acceleration due to Gravity & Length of Weir Crest and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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