Conjugate Depth y2 given Critical Depth Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
d2R = 0.5*d1R*(-1+sqrt(1+(8*(hc^3))/(d1R^3)))
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 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.
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.
Critical Depth of Weir - (Measured in Meter) - The Critical Depth of Weir is defined as the depth of flow where energy is at a minimum for a particular discharge.
STEP 1: Convert Input(s) to Base Unit
Depth of Point 1 for Rectangular Channel: 1.1 Meter --> 1.1 Meter No Conversion Required
Critical Depth of Weir: 1.001 Meter --> 1.001 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d2R = 0.5*d1R*(-1+sqrt(1+(8*(hc^3))/(d1R^3))) --> 0.5*1.1*(-1+sqrt(1+(8*(1.001^3))/(1.1^3)))
Evaluating ... ...
d2R = 0.908129562144599
STEP 3: Convert Result to Output's Unit
0.908129562144599 Meter --> No Conversion Required
FINAL ANSWER
0.908129562144599 0.90813 Meter <-- Depth of Point 2 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 y2 given Critical Depth Formula

​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)))
d2R = 0.5*d1R*(-1+sqrt(1+(8*(hc^3))/(d1R^3)))

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 y2 given Critical Depth?

Conjugate Depth y2 given Critical Depth calculator uses 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))) to calculate the Depth of Point 2 for Rectangular Channel, The Conjugate Depth y2 given Critical Depth is defined as the depth at which parallel flow transitions to critical flow conditions. Depth of Point 2 for Rectangular Channel is denoted by d2R symbol.

How to calculate Conjugate Depth y2 given Critical Depth using this online calculator? To use this online calculator for Conjugate Depth y2 given Critical Depth, enter Depth of Point 1 for Rectangular Channel (d1R) & Critical Depth of Weir (hc) and hit the calculate button. Here is how the Conjugate Depth y2 given Critical Depth calculation can be explained with given input values -> 0.90813 = 0.5*1.1*(-1+sqrt(1+(8*(1.001^3))/(1.1^3))).

FAQ

What is Conjugate Depth y2 given Critical Depth?
The Conjugate Depth y2 given Critical Depth is defined as the depth at which parallel flow transitions to critical flow conditions and is represented as d2R = 0.5*d1R*(-1+sqrt(1+(8*(hc^3))/(d1R^3))) or 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))). Depth of Point 1 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid & The Critical Depth of Weir is defined as the depth of flow where energy is at a minimum for a particular discharge.
How to calculate Conjugate Depth y2 given Critical Depth?
The Conjugate Depth y2 given Critical Depth is defined as the depth at which parallel flow transitions to critical flow conditions is calculated using 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))). To calculate Conjugate Depth y2 given Critical Depth, you need Depth of Point 1 for Rectangular Channel (d1R) & Critical Depth of Weir (hc). With our tool, you need to enter the respective value for Depth of Point 1 for Rectangular Channel & Critical Depth of Weir 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 2 for Rectangular Channel?
In this formula, Depth of Point 2 for Rectangular Channel uses Depth of Point 1 for Rectangular Channel & Critical Depth of Weir. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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)))
  • Depth of Point 2 for Rectangular Channel = Depth of Point 1 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))
  • Depth of Point 2 for Rectangular Channel = Depth of Point 1 for Rectangular Channel/(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))
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