Maximum Velocity of Solitary Wave Calculator

✖Celerity of the Wave refers to the speed at which a wave propagates through a medium.ⓘ Celerity of The Wave [C]			+10% -10%
✖Function of H/d as N obtained from the graph of functions M and N in Solitary Wave Theory (Munk, 1949).ⓘ Function of H/d as N [N]			+10% -10%
✖Function of H/d as M obtained from the graph of functions M and N in Solitary Wave Theory (Munk, 1949).ⓘ Function of H/d as M [M]			+10% -10%
✖Elevation above the Bottom refers to the height or depth of an object or feature above the seabed or ocean floor.ⓘ Elevation above the Bottom [y]			+10% -10%
✖Water depth from bed means the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth from Bed [D_w]			+10% -10%

✖Maximum Velocity of Solitary Wave is the rate of change of its position with respect to a frame of reference, and is a function of time.ⓘ Maximum Velocity of Solitary Wave [u_max]

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Formula

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Maximum Velocity of Solitary Wave

Formula

`"u"_{"max"} = ("C"*"N")/(1+cos("M"*"y"/"D"_{"w"}))`

Example

`"6.024014m/s"=("24.05m/s"*"0.5")/(1+cos("0.8"*"4.92m"/"45m"))`

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Maximum Velocity of Solitary Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Velocity of Solitary Wave = (Celerity of The Wave*Function of H/d as N)/(1+cos(Function of H/d as M*Elevation above the Bottom/Water Depth from Bed))
u_max = (C*N)/(1+cos(M*y/D_w))
This formula uses 1 Functions, 6 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Maximum Velocity of Solitary Wave - (Measured in Meter per Second) - Maximum Velocity of Solitary Wave is the rate of change of its position with respect to a frame of reference, and is a function of time.
Celerity of The Wave - (Measured in Meter per Second) - Celerity of the Wave refers to the speed at which a wave propagates through a medium.
Function of H/d as N - Function of H/d as N obtained from the graph of functions M and N in Solitary Wave Theory (Munk, 1949).
Function of H/d as M - Function of H/d as M obtained from the graph of functions M and N in Solitary Wave Theory (Munk, 1949).
Elevation above the Bottom - (Measured in Meter) - Elevation above the Bottom refers to the height or depth of an object or feature above the seabed or ocean floor.
Water Depth from Bed - (Measured in Meter) - Water depth from bed means the depth as measured from the water level to the bottom of the considered water body.

STEP 1: Convert Input(s) to Base Unit

Celerity of The Wave: 24.05 Meter per Second --> 24.05 Meter per Second No Conversion Required
Function of H/d as N: 0.5 --> No Conversion Required
Function of H/d as M: 0.8 --> No Conversion Required
Elevation above the Bottom: 4.92 Meter --> 4.92 Meter No Conversion Required
Water Depth from Bed: 45 Meter --> 45 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

u_max = (C*N)/(1+cos(M*y/D_w)) --> (24.05*0.5)/(1+cos(0.8*4.92/45))

Evaluating ... ...

u_max = 6.02401421283649

STEP 3: Convert Result to Output's Unit

6.02401421283649 Meter per Second --> No Conversion Required

FINAL ANSWER

6.02401421283649 ≈ 6.024014 Meter per Second <-- Maximum Velocity of Solitary Wave

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Solitary Wave » Maximum Velocity of Solitary Wave

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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!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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< 17 Solitary Wave Calculators

Wave Height of Unbroken Wave in Water of Finite Depth

Go Height of The Wave = Water Depth from Bed*(((0.141063*(Length of Water Wave/Water Depth from Bed))+(0.0095721*(Length of Water Wave/Water Depth from Bed)^2)+(0.0077829*(Length of Water Wave/Water Depth from Bed)^3))/(1+(0.078834*(Length of Water Wave/Water Depth from Bed))+(0.0317567*(Length of Water Wave/Water Depth from Bed)^2)+(0.0093407*(Length of Water Wave/Water Depth from Bed)^3)))*Solitary Wave Amplitude

Water Surface above Bottom

Go Water Surface Ordinate = Water Depth from Bed+Height of The Wave*(sech(sqrt((3/4)*(Height of The Wave/Water Depth from Bed^3))*(Spatial (Progressive Wave)-(Celerity of The Wave*Temporal (Progressive Wave)))))^2

Maximum Velocity of Solitary Wave

Go Maximum Velocity of Solitary Wave = (Celerity of The Wave*Function of H/d as N)/(1+cos(Function of H/d as M*Elevation above the Bottom/Water Depth from Bed))

Water Depth Given Total Wave Energy per Unit Crest Width of Solitary Wave

Go Water Depth from Bed = (Total Wave Energy per Unit Crest Width/((8/(3*sqrt(3)))*Density of Salt Water*[g]*Height of The Wave^(3/2)))^(2/3)

Wave Height for Total Wave Energy per Unit Crest Width of Solitary Wave

Go Height of The Wave = (Total Wave Energy per Unit Crest Width/((8/(3*sqrt(3)))*Density of Salt Water*[g]*Water Depth from Bed^(3/2)))^(2/3)

Total Wave Energy per Unit Crest Width of Solitary Wave

Go Total Wave Energy per Unit Crest Width = (8/(3*sqrt(3)))*Density of Salt Water*[g]*Height of The Wave^(3/2)*Water Depth from Bed^(3/2)

Water Surface above Bottom given Pressure Beneath Solitary Wave

Go Ordinate of the Water Surface = (Pressure Under Wave/(Density of Salt Water*[g]))+Elevation above the Bottom

Elevation above Bottom given Pressure Beneath Solitary Wave

Go Elevation above the Bottom = Ordinate of the Water Surface-(Pressure Under Wave/(Density of Salt Water*[g]))

Pressure Beneath Solitary Wave

Go Pressure Under Wave = Density of Salt Water*[g]*(Ordinate of the Water Surface-Elevation above the Bottom)

Wavelength of Regions of Validity Stokes and Cnoidal Wave Theory

Go Water Wave Length = Water Depth from Bed*(21.5*exp(-1.87*(Height of The Wave/Water Depth from Bed)))

Celerity of Solitary Wave

Go Celerity of The Wave = sqrt([g]*(Height of The Wave+Water Depth from Bed))

Empirical Relationship between Slope and Breaker Height-to-Water Depth Ratio

Go Breaker Height-to-Water Depth Ratio = 0.75+(25*Wave Slope)-(112*Wave Slope^2)+(3870*Wave Slope^3)

Wave Height given Celerity of Solitary Wave

Go Height of The Wave = (Celerity of The Wave^2/[g])-Water Depth from Bed

Water Depth Given Celerity of Solitary Wave

Go Water Depth from Bed = (Celerity of The Wave^2/[g])-Height of The Wave

Water Depth Given Volume of Water within Wave above Still Water Level

Go Water Depth from Bed = ((Volume of Water per Unit Crest Width)^2/((16/3)*Height of The Wave))^(1/3)

Volume of Water above Still Water Level per Unit Crest Width

Go Volume of Water per Unit Crest Width = ((16/3)*Water Depth from Bed^3*Height of The Wave)^0.5

Wave Height Given Volume of Water within Wave above Still Water Level

Go Height of The Wave = Volume of Water per Unit Crest Width^2/((16/3)*Water Depth from Bed^3)

Maximum Velocity of Solitary Wave Formula

Maximum Velocity of Solitary Wave = (Celerity of The Wave*Function of H/d as N)/(1+cos(Function of H/d as M*Elevation above the Bottom/Water Depth from Bed))
u_max = (C*N)/(1+cos(M*y/D_w))

What is Solitary Wave?

A solitary wave is a wave which propagates without any temporal evolution in shape or size when viewed in the reference frame moving with the group velocity of the wave. For example, two solitons propagating in opposite directions effectively pass through each other without breaking.

How to Calculate Maximum Velocity of Solitary Wave?

Maximum Velocity of Solitary Wave calculator uses Maximum Velocity of Solitary Wave = (Celerity of The Wave*Function of H/d as N)/(1+cos(Function of H/d as M*Elevation above the Bottom/Water Depth from Bed)) to calculate the Maximum Velocity of Solitary Wave, The Maximum Velocity of Solitary Wave is defined as the velocity of a wave, equal to the product of its wavelength and frequency (number of vibrations per second) and is independent of its intensity. Maximum Velocity of Solitary Wave is denoted by u_max symbol.

How to calculate Maximum Velocity of Solitary Wave using this online calculator? To use this online calculator for Maximum Velocity of Solitary Wave, enter Celerity of The Wave (C), Function of H/d as N (N), Function of H/d as M (M), Elevation above the Bottom (y) & Water Depth from Bed (D_w) and hit the calculate button. Here is how the Maximum Velocity of Solitary Wave calculation can be explained with given input values -> 6.024014 = (24.05*0.5)/(1+cos(0.8*4.92/45)).

FAQ

What is Maximum Velocity of Solitary Wave?

The Maximum Velocity of Solitary Wave is defined as the velocity of a wave, equal to the product of its wavelength and frequency (number of vibrations per second) and is independent of its intensity and is represented as u_max = (C*N)/(1+cos(M*y/D_w)) or Maximum Velocity of Solitary Wave = (Celerity of The Wave*Function of H/d as N)/(1+cos(Function of H/d as M*Elevation above the Bottom/Water Depth from Bed)). Celerity of the Wave refers to the speed at which a wave propagates through a medium, Function of H/d as N obtained from the graph of functions M and N in Solitary Wave Theory (Munk, 1949), Function of H/d as M obtained from the graph of functions M and N in Solitary Wave Theory (Munk, 1949), Elevation above the Bottom refers to the height or depth of an object or feature above the seabed or ocean floor & Water depth from bed means the depth as measured from the water level to the bottom of the considered water body.

How to calculate Maximum Velocity of Solitary Wave?

The Maximum Velocity of Solitary Wave is defined as the velocity of a wave, equal to the product of its wavelength and frequency (number of vibrations per second) and is independent of its intensity is calculated using Maximum Velocity of Solitary Wave = (Celerity of The Wave*Function of H/d as N)/(1+cos(Function of H/d as M*Elevation above the Bottom/Water Depth from Bed)). To calculate Maximum Velocity of Solitary Wave, you need Celerity of The Wave (C), Function of H/d as N (N), Function of H/d as M (M), Elevation above the Bottom (y) & Water Depth from Bed (D_w). With our tool, you need to enter the respective value for Celerity of The Wave, Function of H/d as N, Function of H/d as M, Elevation above the Bottom & Water Depth from Bed and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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