Celerity of Wave given Two Depths Calculator

✖Depth of Point 2 is the depth of point below the free surface in a static mass of liquid.ⓘ Depth of Point 2 [D₂]			+10% -10%
✖Depth of Point 1 is the depth of point below the free surface in a static mass of liquid.ⓘ Depth of Point 1 [h ₁]			+10% -10%

✖Celerity of Wave is the addition to the normal water velocity of the channels.ⓘ Celerity of Wave given Two Depths [C_w]

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Formula

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Celerity of Wave given Two Depths

Formula

`"C"_{"w"} = sqrt(("[g]"*"D"_{"2"}*("D"_{"2"}+"h "_{"1"}))/(2*"h "_{"1"}))`

Example

`"13.56004m/s"=sqrt(("[g]"*"15m"*("15m"+"10m"))/(2*"10m"))`

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Download Non-uniform Flow in Channels Formula PDF

Celerity of Wave given Two Depths Solution

STEP 0: Pre-Calculation Summary

Formula Used

Celerity of Wave = sqrt(([g]*Depth of Point 2*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1))
C_w = sqrt(([g]*D₂*(D₂+h ₁))/(2*h ₁))
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

Celerity of Wave - (Measured in Meter per Second) - Celerity of Wave is the addition to the normal water velocity of the channels.
Depth of Point 2 - (Measured in Meter) - Depth of Point 2 is the depth of point below the free surface in a static mass of liquid.
Depth of Point 1 - (Measured in Meter) - Depth of Point 1 is the depth of point below the free surface in a static mass of liquid.

STEP 1: Convert Input(s) to Base Unit

Depth of Point 2: 15 Meter --> 15 Meter No Conversion Required
Depth of Point 1: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_w = sqrt(([g]*D₂*(D₂+h ₁))/(2*h ₁)) --> sqrt(([g]*15*(15+10))/(2*10))

Evaluating ... ...

C_w = 13.5600400994982

STEP 3: Convert Result to Output's Unit

13.5600400994982 Meter per Second --> No Conversion Required

FINAL ANSWER

13.5600400994982 ≈ 13.56004 Meter per Second <-- Celerity of Wave

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Non-uniform Flow in Channels » Surges in Open Channel Flow » Surge due to Sudden Increase of Flow » Celerity of Wave given Two Depths

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 9 Surge due to Sudden Increase of Flow Calculators

Celerity of Wave in Non Uniform Flow

Go Celerity of Wave = sqrt([g]*Depth of Point 1*(1+1.5*(Height of Channel/Depth of Point 1)+0.5*(Height of Channel/Depth of Point 1)*(Height of Channel/Depth of Point 1)))

Heights of Surge given Celerity of Wave

Go Height of Channel = (Velocity of Fluid at 1-Velocity of Fluid at 2)/(((([g]*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1))/Celerity of Wave))

Absolute Velocity of Surge Moving towards Right in Negative Surges

Go Absolute Velocity of Issuing Jet = Velocity of Fluid at 1+sqrt(([g]*Depth of Point 2*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1))

Absolute Velocity of Surge Moving towards Right

Go Absolute Velocity of Issuing Jet = (Velocity of Fluid at 1*Depth of Point 1-Velocity of Fluid at 2*Depth of Point 2)/(Depth of Point 1-Depth of Point 2)

Depth of Flow given Absolute Velocity of Surge Moving towards Right with Depth

Go Depth of Point 1 = ((Absolute Velocity of Issuing Jet-Velocity of Fluid at 2)/(Absolute Velocity of Issuing Jet-Velocity of Fluid at 1))*Depth of Point 2

Depth of Flow at Point given Absolute Velocity of Surge Moving towards Right

Go Depth of Point 2 = Depth of Point 1/((Absolute Velocity of Issuing Jet-Velocity of Fluid at 2)/(Absolute Velocity of Issuing Jet-Velocity of Fluid at 1))

Celerity of Wave given Two Depths

Go Celerity of Wave = sqrt(([g]*Depth of Point 2*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1))

Celerity of Wave from Lagrange's Celerity Equation

Go Celerity of Wave = sqrt([g]*Depth of Point 1)

Depth of Flow given Celerity of Wave from Lagrange's Celerity Equation

Go Velocity of Fluid at 2 = (Celerity of Wave/[g])^2

Celerity of Wave given Two Depths Formula

Celerity of Wave = sqrt(([g]*Depth of Point 2*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1))
C_w = sqrt(([g]*D₂*(D₂+h ₁))/(2*h ₁))

What is Celerity of the Wave?

The open channel Surges due to sudden changes of flow depth creates Celerity (Wave Velocity) in the flow in addition to the normal water velocity of the channels. These waves travel in the downstream and sometimes upstream of the channels depending on the various situations.

What is a Jet Flow?

A jet is the flow of a fluid that exits a nozzle into an ambient fluid of different velocity. The nozzle is used to increase the pressure which in turn will increase the velocity of the jet. If the surrounding ambient fluid is at rest then the jet is called a free jet.

How to Calculate Celerity of Wave given Two Depths?

Celerity of Wave given Two Depths calculator uses Celerity of Wave = sqrt(([g]*Depth of Point 2*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1)) to calculate the Celerity of Wave, The Celerity of Wave given Two Depths is defined as the addition to the normal water velocity of the channels in open channel flow. Celerity of Wave is denoted by C_w symbol.

How to calculate Celerity of Wave given Two Depths using this online calculator? To use this online calculator for Celerity of Wave given Two Depths, enter Depth of Point 2 (D₂) & Depth of Point 1 (h ₁) and hit the calculate button. Here is how the Celerity of Wave given Two Depths calculation can be explained with given input values -> 13.56004 = sqrt(([g]*15*(15+10))/(2*10)).

FAQ

What is Celerity of Wave given Two Depths?

The Celerity of Wave given Two Depths is defined as the addition to the normal water velocity of the channels in open channel flow and is represented as C_w = sqrt(([g]*D₂*(D₂+h ₁))/(2*h ₁)) or Celerity of Wave = sqrt(([g]*Depth of Point 2*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1)). Depth of Point 2 is the depth of point below the free surface in a static mass of liquid & Depth of Point 1 is the depth of point below the free surface in a static mass of liquid.

How to calculate Celerity of Wave given Two Depths?

The Celerity of Wave given Two Depths is defined as the addition to the normal water velocity of the channels in open channel flow is calculated using Celerity of Wave = sqrt(([g]*Depth of Point 2*(Depth of Point 2+Depth of Point 1))/(2*Depth of Point 1)). To calculate Celerity of Wave given Two Depths, you need Depth of Point 2 (D₂) & Depth of Point 1 (h ₁). With our tool, you need to enter the respective value for Depth of Point 2 & Depth of Point 1 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 Celerity of Wave?

In this formula, Celerity of Wave uses Depth of Point 2 & Depth of Point 1. We can use 2 other way(s) to calculate the same, which is/are as follows -

Celerity of Wave = sqrt([g]*Depth of Point 1*(1+1.5*(Height of Channel/Depth of Point 1)+0.5*(Height of Channel/Depth of Point 1)*(Height of Channel/Depth of Point 1)))
Celerity of Wave = sqrt([g]*Depth of Point 1)

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