Conjugate Depth y1 given Discharge per Unit Width of Channel 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%
✖The Discharge per Unit Width is the ratio of total discharge in the channel to the width considered.ⓘ Discharge per Unit Width [q]			+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 Discharge per Unit Width of Channel [d_1R]

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Conjugate Depth y1 given Discharge per Unit Width of Channel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
d_1R = 0.5*d_2R*(-1+sqrt(1+(8*(q^2))/([g]*d_2R*d_2R*d_2R)))
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 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.
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 2 for Rectangular Channel: 1.2 Meter --> 1.2 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

d_1R = 0.5*d_2R*(-1+sqrt(1+(8*(q^2))/([g]*d_2R*d_2R*d_2R))) --> 0.5*1.2*(-1+sqrt(1+(8*(10.02^2))/([g]*1.2*1.2*1.2)))

Evaluating ... ...

d_1R = 3.57412497156528

STEP 3: Convert Result to Output's Unit

3.57412497156528 Meter --> No Conversion Required

FINAL ANSWER

3.57412497156528 ≈ 3.574125 Meter <-- Depth of Point 1 for Rectangular Channel

(Calculation completed in 00.020 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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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 Discharge per Unit Width of Channel Formula

LaTeX Go

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 Discharge per Unit Width of Channel?

Conjugate Depth y1 given Discharge per Unit Width of Channel calculator uses 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))) to calculate the Depth of Point 1 for Rectangular Channel, The Conjugate Depth y1 given Discharge per Unit Width of Channel is defined as the water depth ensuring critical flow. Depth of Point 1 for Rectangular Channel is denoted by d_1R symbol.

How to calculate Conjugate Depth y1 given Discharge per Unit Width of Channel using this online calculator? To use this online calculator for Conjugate Depth y1 given Discharge per Unit Width of Channel, enter Depth of Point 2 for Rectangular Channel (d_2R) & Discharge per Unit Width (q) and hit the calculate button. Here is how the Conjugate Depth y1 given Discharge per Unit Width of Channel calculation can be explained with given input values -> 3.574125 = 0.5*1.2*(-1+sqrt(1+(8*(10.02^2))/([g]*1.2*1.2*1.2))).

FAQ

What is Conjugate Depth y1 given Discharge per Unit Width of Channel?

The Conjugate Depth y1 given Discharge per Unit Width of Channel is defined as the water depth ensuring critical flow and is represented as d_1R = 0.5*d_2R*(-1+sqrt(1+(8*(q^2))/([g]*d_2R*d_2R*d_2R))) or 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 2 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 y1 given Discharge per Unit Width of Channel?

The Conjugate Depth y1 given Discharge per Unit Width of Channel is defined as the water depth ensuring critical flow is calculated using 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))). To calculate Conjugate Depth y1 given Discharge per Unit Width of Channel, you need Depth of Point 2 for Rectangular Channel (d_2R) & Discharge per Unit Width (q). With our tool, you need to enter the respective value for Depth of Point 2 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 1 for Rectangular Channel?

In this formula, Depth of Point 1 for Rectangular Channel uses Depth of Point 2 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 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)))))
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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