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Conjugate Depth y1 given Discharge per Unit Width of Channel Formula

GoConjugate Depth y1 given Critical Depth Formula

GoConjugate Depth y1 given Froude Number Fr1 Formula

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Depth of Point 1 for Rectangular Channel is the depth of point below the free surface in a static mass of liquid. Check FAQs

d 1R = 0.5 \cdot d 2R \cdot (- 1 + \sqrt{1 + \frac{8 \cdot (q^{2})}{[g] \cdot d 2R \cdot d 2R \cdot d 2R}})

d_1R - Depth of Point 1 for Rectangular Channel?d_2R - Depth of Point 2 for Rectangular Channel?q - Discharge per Unit Width?[g] - Gravitational acceleration on Earth?

Conjugate Depth y1 given Discharge per Unit Width of Channel Example

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Here is how the Conjugate Depth y1 given Discharge per Unit Width of Channel equation looks like with Values.

Here is how the Conjugate Depth y1 given Discharge per Unit Width of Channel equation looks like with Units.

Here is how the Conjugate Depth y1 given Discharge per Unit Width of Channel equation looks like.

3.5741 = 0.5 \cdot 1.2 \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({10.02}^{2})}{9.8066 \cdot 1.2 \cdot 1.2 \cdot 1.2}})

3.5741m = 0.5 \cdot 1.2m \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({10.02m²/s}^{2})}{9.8066m/s² \cdot 1.2m \cdot 1.2m \cdot 1.2m}})

3.5741 = 0.5 \cdot 1.2 \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({10.02}^{2})}{9.8066 \cdot 1.2 \cdot 1.2 \cdot 1.2}})

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Conjugate Depth y1 given Discharge per Unit Width of Channel Solution

Follow our step by step solution on how to calculate Conjugate Depth y1 given Discharge per Unit Width of Channel?

FIRST Step Consider the formula

d 1R = 0.5 \cdot d 2R \cdot (- 1 + \sqrt{1 + \frac{8 \cdot (q^{2})}{[g] \cdot d 2R \cdot d 2R \cdot d 2R}})

Next Step Substitute values of Variables

∴

d 1R = 0.5 \cdot 1.2m \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({10.02m²/s}^{2})}{[g] \cdot 1.2m \cdot 1.2m \cdot 1.2m}})

Next Step Substitute values of Constants

∴

d 1R = 0.5 \cdot 1.2m \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({10.02m²/s}^{2})}{9.8066m/s² \cdot 1.2m \cdot 1.2m \cdot 1.2m}})

Next Step Prepare to Evaluate

∴

d 1R = 0.5 \cdot 1.2 \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({10.02}^{2})}{9.8066 \cdot 1.2 \cdot 1.2 \cdot 1.2}})

Next Step Evaluate

∴

d 1R = 3.57412497156528m

LAST Step Rounding Answer

∴

d 1R = 3.5741m

Conjugate Depth y1 given Discharge per Unit Width of Channel Formula Elements

Variables

Constants

Functions

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.

Symbol: d_1R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Point 1 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.

Symbol: d_2R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Point 2 for Rectangular Channel

Discharge per Unit Width

The Discharge per Unit Width is the ratio of total discharge in the channel to the width considered.

Symbol: q

Measurement: Kinematic ViscosityUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Discharge per Unit Width

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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.

Syntax: sqrt(Number)

Other Formulas to find Depth of Point 1 for Rectangular Channel

Go Conjugate Depth y1 given Critical Depth

d 1R = 0.5 \cdot d 2R \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({h c}^{3})}{{d 2R}^{3}}})

Go Conjugate Depth y1 given Froude Number Fr1

d 1R = \frac{d 2R}{0.5 \cdot (- 1 + \sqrt{1 + (8 \cdot ({Fr}^{2}))})}

Go Conjugate Depth y1 given Froude Number Fr2

d 1R = d 2R \cdot (0.5 \cdot (- 1 + \sqrt{1 + (8 \cdot ({Fr}^{2}))}))

Other formulas in Hydraulic Jump in Rectangular Channel category

Go Discharge Per Unit Width of Channel given Conjugate Depths

q = \sqrt{(d 1R \cdot d 2R \cdot (d 1R + d 2R)) \cdot [g] \cdot 0.5}

Go Conjugate Depth y2 given Discharge per Unit Width of Channel

d 2R = 0.5 \cdot d 1R \cdot (- 1 + \sqrt{1 + \frac{8 \cdot (q^{2})}{[g] \cdot d 1R \cdot d 1R \cdot d 1R}})

Go Conjugate Depth y2 given Critical Depth

d 2R = 0.5 \cdot d 1R \cdot (- 1 + \sqrt{1 + \frac{8 \cdot ({h c}^{3})}{{d 1R}^{3}}})

Go Conjugate Depth y2 given Froude Number Fr1

d 2R = d 1R \cdot (0.5 \cdot (- 1 + \sqrt{1 + (8 \cdot ({Fr}^{2}))}))

How to Evaluate Conjugate Depth y1 given Discharge per Unit Width of Channel?

Conjugate Depth y1 given Discharge per Unit Width of Channel evaluator 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 evaluate 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 evaluate Conjugate Depth y1 given Discharge per Unit Width of Channel using this online evaluator? To use this online evaluator 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.

FAQs on Conjugate Depth y1 given Discharge per Unit Width of Channel

What is the formula to find Conjugate Depth y1 given Discharge per Unit Width of Channel?

The formula of Conjugate Depth y1 given Discharge per Unit Width of Channel is expressed as 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))). Here is an example- 3.574125 = 0.5*1.2*(-1+sqrt(1+(8*(10.02^2))/([g]*1.2*1.2*1.2))).

How to calculate Conjugate Depth y1 given Discharge per Unit Width of Channel?

With Depth of Point 2 for Rectangular Channel (d_2R) & Discharge per Unit Width (q) we can find Conjugate Depth y1 given Discharge per Unit Width of Channel using the formula - 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))). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root Function function(s).

What are the other ways to Calculate Depth of Point 1 for Rectangular Channel?

Here are the different ways to Calculate Depth of Point 1 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)))))
Depth of Point 1 for Rectangular Channel=Depth of Point 2 for Rectangular Channel*(0.5*(-1+sqrt(1+(8*(Froude Number^2)))))

Can the Conjugate Depth y1 given Discharge per Unit Width of Channel be negative?

No, the Conjugate Depth y1 given Discharge per Unit Width of Channel, measured in Length cannot be negative.

Which unit is used to measure Conjugate Depth y1 given Discharge per Unit Width of Channel?

Conjugate Depth y1 given Discharge per Unit Width of Channel is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Conjugate Depth y1 given Discharge per Unit Width of Channel can be measured.

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