Mean Depth given Ursell Number Calculator

✖The Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level.ⓘ Wave Height for Surface Gravity Waves [H_w]			+10% -10%
✖Deep-Water Wavelength is the wavelength of a wave when the water depth is greater than half of its wavelength.ⓘ Deep-Water Wavelength [λ_o]			+10% -10%
✖Ursell Number is defined as the ratio of the square of the wave height to the product of the wavelength and the water depth.ⓘ Ursell Number [U]			+10% -10%

✖Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.ⓘ Mean Depth given Ursell Number [d]

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Formula

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Mean Depth given Ursell Number

Formula

`"d" = (("H"_{"w"}*"λ"_{"o"}^2)/"U")^(1/3)`

Example

`"10m"=(("3m"*("7m")^2)/"0.147")^(1/3)`

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Mean Depth given Ursell Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Coastal Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3)
d = ((H_w*λ_o^2)/U)^(1/3)
This formula uses 4 Variables

Variables Used

Coastal Mean Depth - (Measured in Meter) - Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.
Wave Height for Surface Gravity Waves - (Measured in Meter) - The Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level.
Deep-Water Wavelength - (Measured in Meter) - Deep-Water Wavelength is the wavelength of a wave when the water depth is greater than half of its wavelength.
Ursell Number - Ursell Number is defined as the ratio of the square of the wave height to the product of the wavelength and the water depth.

STEP 1: Convert Input(s) to Base Unit

Wave Height for Surface Gravity Waves: 3 Meter --> 3 Meter No Conversion Required
Deep-Water Wavelength: 7 Meter --> 7 Meter No Conversion Required
Ursell Number: 0.147 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = ((H_w*λ_o^2)/U)^(1/3) --> ((3*7^2)/0.147)^(1/3)

Evaluating ... ...

d = 10

STEP 3: Convert Result to Output's Unit

10 Meter --> No Conversion Required

FINAL ANSWER

10 Meter <-- Coastal Mean Depth

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

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NSS College of Engineering (NSSCE), Palakkad

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< 14 Non-Linear Wave Theory Calculators

Relative Height of Highest Wave as Function of Wavelength Obtained by Fenton

Go Relative Height as a function of Wavelength = (0.141063*(Deep-Water Wavelength/Coastal Mean Depth)+0.0095721*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0077829*(Deep-Water Wavelength/Coastal Mean Depth)^3)/(1+0.078834*(Deep-Water Wavelength/Coastal Mean Depth)+0.0317567*(Deep-Water Wavelength/Coastal Mean Depth)^2+0.0093407*(Deep-Water Wavelength/Coastal Mean Depth)^3)

Mean Depth given Ursell Number

Go Coastal Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3)

Wavelength given Ursell Number

Go Deep-Water Wavelength = ((Ursell Number*Coastal Mean Depth^3)/Wave Height for Surface Gravity Waves)^0.5

Wave Height given Ursell Number

Go Wave Height for Surface Gravity Waves = (Ursell Number*Coastal Mean Depth^3)/Deep-Water Wavelength^2

Ursell Number

Go Ursell Number = (Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Coastal Mean Depth^3

Volume Flow Rate per unit Span Underneath Waves given Second Type of Mean Fluid Speed

Go Rate of Volume Flow = Coastal Mean Depth*(Fluid Stream Velocity-Mean Horizontal Fluid Velocity)

Wave Speed given Second First Type of Mean Fluid Speed

Go Fluid Stream Velocity = Mean Horizontal Fluid Velocity+(Rate of Volume Flow/Coastal Mean Depth)

Mean Depth given Second Type of Mean Fluid Speed

Go Coastal Mean Depth = Rate of Volume Flow/(Fluid Stream Velocity-Mean Horizontal Fluid Velocity)

Second Type of Mean Fluid Speed

Go Mean Horizontal Fluid Velocity = Fluid Stream Velocity-(Rate of Volume Flow/Coastal Mean Depth)

Wave Speed given First Type of Mean Fluid Speed

Go Wave Speed = Fluid Stream Velocity-Mean Horizontal Fluid Velocity

First Type of Mean Fluid Speed

Go Mean Horizontal Fluid Velocity = Fluid Stream Velocity-Wave Speed

Volume Flow Rate in Stokes' Second Approximation to Wave Speed if there is no Mass Transport

Go Rate of Volume Flow = Wave Speed*Coastal Mean Depth

Mean Depth in Stokes' Second Approximation to Wave Speed if there is no Mass Transport

Go Coastal Mean Depth = Rate of Volume Flow/Wave Speed

Stokes' Second Approximation to Wave Speed if there is no Mass Transport

Go Wave Speed = Rate of Volume Flow/Coastal Mean Depth

Mean Depth given Ursell Number Formula

Coastal Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3)
d = ((H_w*λ_o^2)/U)^(1/3)

What is Ursell Number?

In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953.

How to Calculate Mean Depth given Ursell Number?

Mean Depth given Ursell Number calculator uses Coastal Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3) to calculate the Coastal Mean Depth, The Mean Depth given Ursell Number is defined as a depth parameter influencing the nonlinearity of long surface gravity waves on a fluid layer. Coastal Mean Depth is denoted by d symbol.

How to calculate Mean Depth given Ursell Number using this online calculator? To use this online calculator for Mean Depth given Ursell Number, enter Wave Height for Surface Gravity Waves (H_w), Deep-Water Wavelength (λ_o) & Ursell Number (U) and hit the calculate button. Here is how the Mean Depth given Ursell Number calculation can be explained with given input values -> 10 = ((3*7^2)/0.147)^(1/3).

FAQ

What is Mean Depth given Ursell Number?

The Mean Depth given Ursell Number is defined as a depth parameter influencing the nonlinearity of long surface gravity waves on a fluid layer and is represented as d = ((H_w*λ_o^2)/U)^(1/3) or Coastal Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3). The Wave Height for Surface Gravity Waves refers to the vertical distance between the trough (bottom) and crest (top) of a wave, measured from sea level, Deep-Water Wavelength is the wavelength of a wave when the water depth is greater than half of its wavelength & Ursell Number is defined as the ratio of the square of the wave height to the product of the wavelength and the water depth.

How to calculate Mean Depth given Ursell Number?

The Mean Depth given Ursell Number is defined as a depth parameter influencing the nonlinearity of long surface gravity waves on a fluid layer is calculated using Coastal Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3). To calculate Mean Depth given Ursell Number, you need Wave Height for Surface Gravity Waves (H_w), Deep-Water Wavelength (λ_o) & Ursell Number (U). With our tool, you need to enter the respective value for Wave Height for Surface Gravity Waves, Deep-Water Wavelength & Ursell Number 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 Coastal Mean Depth?

In this formula, Coastal Mean Depth uses Wave Height for Surface Gravity Waves, Deep-Water Wavelength & Ursell Number. We can use 2 other way(s) to calculate the same, which is/are as follows -

Coastal Mean Depth = Rate of Volume Flow/(Fluid Stream Velocity-Mean Horizontal Fluid Velocity)
Coastal Mean Depth = Rate of Volume Flow/Wave Speed

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