Conjugate Depth y2 given Discharge per Unit Width of Channel 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*(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)))
d2R = 0.5*d1R*(-1+sqrt(1+(8*(q^2))/([g]*d1R*d1R*d1R)))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
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.
Discharge per Unit Width - (Measured in Square Meter per Second) - The Discharge per Unit Width is the ratio of total discharge in the channel to the width considered.
STEP 1: Convert Input(s) to Base Unit
Depth of Point 1 for Rectangular Channel: 1.1 Meter --> 1.1 Meter No Conversion Required
Discharge per Unit Width: 10.02 Square Meter per Second --> 10.02 Square Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d2R = 0.5*d1R*(-1+sqrt(1+(8*(q^2))/([g]*d1R*d1R*d1R))) --> 0.5*1.1*(-1+sqrt(1+(8*(10.02^2))/([g]*1.1*1.1*1.1)))
Evaluating ... ...
d2R = 3.79937123291651
STEP 3: Convert Result to Output's Unit
3.79937123291651 Meter --> No Conversion Required
FINAL ANSWER
3.79937123291651 3.799371 Meter <-- Depth of Point 2 for Rectangular Channel
(Calculation completed in 00.004 seconds)

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11 Hydraulic Jump in Rectangular Channel Calculators

Conjugate Depth y1 given Discharge per Unit Width of Channel
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
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
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)
Energy Loss in Hydraulic Jump given Mean Velocities
Go Energy loss for Rectangular Channel = ((Depth of Point 2 for Rectangular Channel-Depth of Point 1 for Rectangular Channel)^3)/(4*Depth of Point 1 for Rectangular Channel*Depth of Point 2 for Rectangular Channel)*Mean velocity
Energy loss in Hydraulic Jump
Go Energy loss for Rectangular Channel = ((Depth of Point 2 for Rectangular Channel-Depth of Point 1 for Rectangular Channel)^3)/(4*Depth of Point 1 for Rectangular Channel*Depth of Point 2 for Rectangular Channel)
Conjugate Depth y2 given Critical Depth
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 Critical Depth
Go 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)))
Conjugate Depth y1 given Froude Number Fr1
Go Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel/(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))
Conjugate Depth y2 given Froude Number Fr1
Go Depth of Point 2 for Rectangular Channel = Depth of Point 1 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))
Conjugate Depth y1 given Froude Number Fr2
Go Depth of Point 1 for Rectangular Channel = Depth of Point 2 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))
Conjugate Depth y2 given Froude Number Fr2
Go Depth of Point 2 for Rectangular Channel = Depth of Point 1 for Rectangular Channel/(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))

Conjugate Depth y2 given Discharge per Unit Width of Channel Formula

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)))
d2R = 0.5*d1R*(-1+sqrt(1+(8*(q^2))/([g]*d1R*d1R*d1R)))

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 Discharge per Unit Width of Channel?

Conjugate Depth y2 given Discharge per Unit Width of Channel calculator uses 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))) to calculate the Depth of Point 2 for Rectangular Channel, The Conjugate Depth y2 given Discharge per Unit Width of Channel formula is defined as the alternate water depth in a varying flow. Depth of Point 2 for Rectangular Channel is denoted by d2R symbol.

How to calculate Conjugate Depth y2 given Discharge per Unit Width of Channel using this online calculator? To use this online calculator for Conjugate Depth y2 given Discharge per Unit Width of Channel, enter Depth of Point 1 for Rectangular Channel (d1R) & Discharge per Unit Width (q) and hit the calculate button. Here is how the Conjugate Depth y2 given Discharge per Unit Width of Channel calculation can be explained with given input values -> 3.799371 = 0.5*1.1*(-1+sqrt(1+(8*(10.02^2))/([g]*1.1*1.1*1.1))).

FAQ

What is Conjugate Depth y2 given Discharge per Unit Width of Channel?
The Conjugate Depth y2 given Discharge per Unit Width of Channel formula is defined as the alternate water depth in a varying flow and is represented as d2R = 0.5*d1R*(-1+sqrt(1+(8*(q^2))/([g]*d1R*d1R*d1R))) or 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 1 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid & The Discharge per Unit Width is the ratio of total discharge in the channel to the width considered.
How to calculate Conjugate Depth y2 given Discharge per Unit Width of Channel?
The Conjugate Depth y2 given Discharge per Unit Width of Channel formula is defined as the alternate water depth in a varying flow is calculated using 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))). To calculate Conjugate Depth y2 given Discharge per Unit Width of Channel, you need Depth of Point 1 for Rectangular Channel (d1R) & Discharge per Unit Width (q). With our tool, you need to enter the respective value for Depth of Point 1 for Rectangular Channel & Discharge per Unit Width 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 & Discharge per Unit Width. 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*(Critical Depth of Weir^3))/(Depth of Point 1 for Rectangular Channel^3)))
  • 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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