Conjugate Depth y1 given Froude Number Fr2 Calculator

✖Depth of Point 2 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid.ⓘ Depth of Point 2 for Rectangular Channel [d_2R]			+10% -10%
✖Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.ⓘ Froude Number [Fr]			+10% -10%

✖Depth of Point 1 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid.ⓘ Conjugate Depth y1 given Froude Number Fr2 [d_1R]

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Conjugate Depth y1 given Froude Number Fr2 Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))
d_1R = d_2R*(0.5*(-1+sqrt(1+(8*(Fr^2)))))
This formula uses 1 Functions, 3 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

Depth of Point 1 for Rectangular Channel - (Measured in Meter) - Depth of Point 1 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid.
Depth of Point 2 for Rectangular Channel - (Measured in Meter) - Depth of Point 2 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid.
Froude Number - Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.

STEP 1: Convert Input(s) to Base Unit

Depth of Point 2 for Rectangular Channel: 1.2 Meter --> 1.2 Meter No Conversion Required
Froude Number: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_1R = d_2R*(0.5*(-1+sqrt(1+(8*(Fr^2))))) --> 1.2*(0.5*(-1+sqrt(1+(8*(10^2)))))

Evaluating ... ...

d_1R = 16.3811660377019

STEP 3: Convert Result to Output's Unit

16.3811660377019 Meter --> No Conversion Required

FINAL ANSWER

16.3811660377019 ≈ 16.38117 Meter <-- Depth of Point 1 for Rectangular Channel

(Calculation completed in 00.004 seconds)

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< Hydraulic Jump in Rectangular Channel Calculators

Conjugate Depth y1 given Discharge per Unit Width of Channel

LaTeX Go Depth of Point 1 for Rectangular Channel = 0.5*Depth of Point 2 for Rectangular Channel*(-1+sqrt(1+(8*(Discharge per Unit Width^2))/([g]*Depth of Point 2 for Rectangular Channel*Depth of Point 2 for Rectangular Channel*Depth of Point 2 for Rectangular Channel)))

Conjugate Depth y2 given Discharge per Unit Width of Channel

LaTeX Go Depth of Point 2 for Rectangular Channel = 0.5*Depth of Point 1 for Rectangular Channel*(-1+sqrt(1+(8*(Discharge per Unit Width^2))/([g]*Depth of Point 1 for Rectangular Channel*Depth of Point 1 for Rectangular Channel*Depth of Point 1 for Rectangular Channel)))

Discharge Per Unit Width of Channel given Conjugate Depths

LaTeX Go Discharge per Unit Width = sqrt((Depth of Point 1 for Rectangular Channel*Depth of Point 2 for Rectangular Channel*(Depth of Point 1 for Rectangular Channel+Depth of Point 2 for Rectangular Channel))*[g]*0.5)

Conjugate Depth y2 given Critical Depth

LaTeX Go Depth of Point 2 for Rectangular Channel = 0.5*Depth of Point 1 for Rectangular Channel*(-1+sqrt(1+(8*(Critical Depth of Weir^3))/(Depth of Point 1 for Rectangular Channel^3)))

Conjugate Depth y1 given Froude Number Fr2 Formula

LaTeX Go

Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))
d_1R = d_2R*(0.5*(-1+sqrt(1+(8*(Fr^2)))))

What is Conjugate Depth?

In fluid dynamics, the conjugate depths refer to the depth upstream and the depth downstream of the hydraulic jump whose momentum fluxes are equal for a given discharge q. The depth upstream of a hydraulic jump is always supercritical.

How to Calculate Conjugate Depth y1 given Froude Number Fr2?

Conjugate Depth y1 given Froude Number Fr2 calculator uses Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2))))) to calculate the Depth of Point 1 for Rectangular Channel, The Conjugate Depth y1 given Froude Number Fr2 is defined as the depth where the flow velocity matches the wave speed. Depth of Point 1 for Rectangular Channel is denoted by d_1R symbol.

How to calculate Conjugate Depth y1 given Froude Number Fr2 using this online calculator? To use this online calculator for Conjugate Depth y1 given Froude Number Fr2, enter Depth of Point 2 for Rectangular Channel (d_2R) & Froude Number (Fr) and hit the calculate button. Here is how the Conjugate Depth y1 given Froude Number Fr2 calculation can be explained with given input values -> 16.38117 = 1.2*(0.5*(-1+sqrt(1+(8*(10^2))))).

FAQ

What is Conjugate Depth y1 given Froude Number Fr2?

The Conjugate Depth y1 given Froude Number Fr2 is defined as the depth where the flow velocity matches the wave speed and is represented as d_1R = d_2R*(0.5*(-1+sqrt(1+(8*(Fr^2))))) or Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2))))). Depth of Point 2 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid & Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.

How to calculate Conjugate Depth y1 given Froude Number Fr2?

The Conjugate Depth y1 given Froude Number Fr2 is defined as the depth where the flow velocity matches the wave speed is calculated using Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2))))). To calculate Conjugate Depth y1 given Froude Number Fr2, you need Depth of Point 2 for Rectangular Channel (d_2R) & Froude Number (Fr). With our tool, you need to enter the respective value for Depth of Point 2 for Rectangular Channel & Froude Number 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 Depth of Point 1 for Rectangular Channel?

In this formula, Depth of Point 1 for Rectangular Channel uses Depth of Point 2 for Rectangular Channel & Froude Number. We can use 3 other way(s) to calculate the same, which is/are as follows -

Depth of Point 1 for Rectangular Channel = 0.5*Depth of Point 2 for Rectangular Channel*(-1+sqrt(1+(8*(Discharge per Unit Width^2))/([g]*Depth of Point 2 for Rectangular Channel*Depth of Point 2 for Rectangular Channel*Depth of Point 2 for Rectangular Channel)))
Depth of Point 1 for Rectangular Channel = 0.5*Depth of Point 2 for Rectangular Channel*(-1+sqrt(1+(8*(Critical Depth of Weir^3))/(Depth of Point 2 for Rectangular Channel^3)))
Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel/(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))

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