Water Surface above Bottom Calculator

✖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%
✖Height of The Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Height of The Wave [H_w]			+10% -10%
✖Spatial (Progressive Wave) is a wave that continuously travels in a medium in the same direction minus the changes.ⓘ Spatial (Progressive Wave) [x]			+10% -10%
✖Celerity of the Wave refers to the speed at which a wave propagates through a medium.ⓘ Celerity of The Wave [C]			+10% -10%
✖Temporal (Progressive Wave) is a wave which generally travels continuously in a medium of the same direction without the change in its amplitude.ⓘ Temporal (Progressive Wave) [t]			+10% -10%

✖Ordinate of the Water Surface is defined as the vertical distance between two points on the water plane.ⓘ Water Surface above Bottom [y_s]

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Formula

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Water Surface above Bottom

Formula

`"y"_{"s"} = "D"_{"w"}+"H"_{"w"}*(sech(sqrt((3/4)*("H"_{"w"}/"D"_{"w"}^3))*("x"-("C"*"t"))))^2`

Example

`"45.00041"="45m"+"14m"*(sech(sqrt((3/4)*("14m"/("45m")^3))*("50"-("24.05m/s"*"25"))))^2`

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Water Surface above Bottom Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ordinate of the Water Surface = 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
y_s = D_w+H_w*(sech(sqrt((3/4)*(H_w/D_w^3))*(x-(C*t))))^2
This formula uses 2 Functions, 6 Variables

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)
sech - The hyperbolic secant function is a hyperbolic function that is the reciprocal of the hyperbolic cosine function., sech(Number)

Variables Used

Ordinate of the Water Surface - Ordinate of the Water Surface is defined as the vertical distance between two points on the water plane.
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.
Height of The Wave - (Measured in Meter) - Height of The Wave is the difference between the elevations of a crest and a neighboring trough.
Spatial (Progressive Wave) - Spatial (Progressive Wave) is a wave that continuously travels in a medium in the same direction minus the changes.
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.
Temporal (Progressive Wave) - Temporal (Progressive Wave) is a wave which generally travels continuously in a medium of the same direction without the change in its amplitude.

STEP 1: Convert Input(s) to Base Unit

Water Depth from Bed: 45 Meter --> 45 Meter No Conversion Required
Height of The Wave: 14 Meter --> 14 Meter No Conversion Required
Spatial (Progressive Wave): 50 --> No Conversion Required
Celerity of The Wave: 24.05 Meter per Second --> 24.05 Meter per Second No Conversion Required
Temporal (Progressive Wave): 25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_s = D_w+H_w*(sech(sqrt((3/4)*(H_w/D_w^3))*(x-(C*t))))^2 --> 45+14*(sech(sqrt((3/4)*(14/45^3))*(50-(24.05*25))))^2

Evaluating ... ...

y_s = 45.0004059473241

STEP 3: Convert Result to Output's Unit

45.0004059473241 --> No Conversion Required

FINAL ANSWER

45.0004059473241 ≈ 45.00041 <-- Ordinate of the Water Surface

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Solitary Wave » Water Surface above Bottom

Credits

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)))*Wave Amplitude

Water Surface above Bottom

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

Any Elevation above Bottom given Pressure beneath Solitary Wave

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

Pressure beneath Solitary Wave

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

Wavelength of Regions of Validity Stokes and Cnoidal Wave Theory

Go Length of Water Wave = Water Depth from Bed*(21.5*exp(-1.87*(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*Slope for Waves)-(112*Slope for Waves^2)+(3870*Slope for Waves^3)

Celerity of Solitary Wave

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

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)

Water Surface above Bottom Formula

What are the characteristics of progressive waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

How to Calculate Water Surface above Bottom?

Water Surface above Bottom calculator uses Ordinate of the Water Surface = 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 to calculate the Ordinate of the Water Surface, The Water Surface above Bottom means height above bottom, in relation to mean sea level, of floods of various magnitudes and frequencies in floodplains of coastal or riverine areas. Ordinate of the Water Surface is denoted by y_s symbol.

How to calculate Water Surface above Bottom using this online calculator? To use this online calculator for Water Surface above Bottom, enter Water Depth from Bed (D_w), Height of The Wave (H_w), Spatial (Progressive Wave) (x), Celerity of The Wave (C) & Temporal (Progressive Wave) (t) and hit the calculate button. Here is how the Water Surface above Bottom calculation can be explained with given input values -> 45.00041 = 45+14*(sech(sqrt((3/4)*(14/45^3))*(50-(24.05*25))))^2.

FAQ

What is Water Surface above Bottom?

The Water Surface above Bottom means height above bottom, in relation to mean sea level, of floods of various magnitudes and frequencies in floodplains of coastal or riverine areas and is represented as y_s = D_w+H_w*(sech(sqrt((3/4)*(H_w/D_w^3))*(x-(C*t))))^2 or Ordinate of the Water Surface = 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. Water depth from bed means the depth as measured from the water level to the bottom of the considered water body, Height of The Wave is the difference between the elevations of a crest and a neighboring trough, Spatial (Progressive Wave) is a wave that continuously travels in a medium in the same direction minus the changes, Celerity of the Wave refers to the speed at which a wave propagates through a medium & Temporal (Progressive Wave) is a wave which generally travels continuously in a medium of the same direction without the change in its amplitude.

How to calculate Water Surface above Bottom?

The Water Surface above Bottom means height above bottom, in relation to mean sea level, of floods of various magnitudes and frequencies in floodplains of coastal or riverine areas is calculated using Ordinate of the Water Surface = 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. To calculate Water Surface above Bottom, you need Water Depth from Bed (D_w), Height of The Wave (H_w), Spatial (Progressive Wave) (x), Celerity of The Wave (C) & Temporal (Progressive Wave) (t). With our tool, you need to enter the respective value for Water Depth from Bed, Height of The Wave, Spatial (Progressive Wave), Celerity of The Wave & Temporal (Progressive Wave) 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 Ordinate of the Water Surface?

In this formula, Ordinate of the Water Surface uses Water Depth from Bed, Height of The Wave, Spatial (Progressive Wave), Celerity of The Wave & Temporal (Progressive Wave). We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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