Mean depth given Ursell number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3)
d = ((Hw*λo^2)/U)^(1/3)
This formula uses 4 Variables
Variables Used
Mean Depth - (Measured in Meter) - Mean Depth for Steady two-dimensional waves.
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, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave.
Ursell Number - Ursell Number indicates the nonlinearity of long surface gravity waves on a fluid layer.
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 = ((Hwo^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 <-- Mean Depth
(Calculation completed in 00.004 seconds)

Credits

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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/Mean Depth)+0.0095721*(Deep-Water Wavelength/Mean Depth)^2+0.0077829*(Deep-Water Wavelength/Mean Depth)^3)/(1+0.078834*(Deep-Water Wavelength/Mean Depth)+0.0317567*(Deep-Water Wavelength/Mean Depth)^2+0.0093407*(Deep-Water Wavelength/Mean Depth)^3)
Mean depth given Ursell number
Go 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*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*Mean Depth^3)/Deep-Water Wavelength^2
Ursell Number
Go Ursell Number = (Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Mean Depth^3
Volume Flow Rate per unit Span Underneath Waves given Second Type of Mean Fluid Speed
Go Rate of Volume Flow = 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/Mean Depth)
Mean Depth given Second Type of Mean Fluid Speed
Go 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/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*Mean Depth
Mean Depth in Stokes' Second Approximation to Wave Speed if there is no Mass Transport
Go 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/Mean Depth

Mean depth given Ursell number Formula

Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3)
d = ((Hw*λo^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 Mean Depth = ((Wave Height for Surface Gravity Waves*Deep-Water Wavelength^2)/Ursell Number)^(1/3) to calculate the 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. 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 (Hw), Deep-Water Wavelength 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 -> 4.108284 = ((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 = ((Hwo^2)/U)^(1/3) or 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, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave & Ursell Number indicates the nonlinearity of long surface gravity waves on a fluid layer.
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 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 (Hw), Deep-Water Wavelength 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 Mean Depth?
In this formula, 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 -
  • Mean Depth = Rate of Volume Flow/(Fluid Stream Velocity-Mean Horizontal Fluid Velocity)
  • Mean Depth = Rate of Volume Flow/Wave Speed
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