Pressure taken as Gauge Pressure relative to Wave Mechanics Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sub Surface Pressure = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))-(Mass Density*[g]*Seabed Elevation)
p = (ρ*[g]*H*cosh(2*pi*(DZ+d)/λ))*cos(θ)/(2*cosh(2*pi*d/λ))-(ρ*[g]*Z)
This formula uses 2 Constants, 2 Functions, 8 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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)
cosh - The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2., cosh(Number)
Variables Used
Sub Surface Pressure - (Measured in Pascal) - Sub Surface Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Mass Density - (Measured in Kilogram per Cubic Meter) - The Mass Density of a substance is its mass per unit volume.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom expressing the local fluid velocity component.
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Phase Angle - (Measured in Radian) - Phase Angle characteristic of a periodic wave. The angular component periodic wave is known as the phase angle. It is a complex quantity measured by angular units like radians or degrees.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
Seabed Elevation - Seabed Elevation of the catchment under consideration. Seabed is the bottom of the ocean.
STEP 1: Convert Input(s) to Base Unit
Mass Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Wave Height: 3 Meter --> 3 Meter No Conversion Required
Distance above the Bottom: 2 Meter --> 2 Meter No Conversion Required
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Phase Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required
Seabed Elevation: 0.8 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
p = (ρ*[g]*H*cosh(2*pi*(DZ+d)/λ))*cos(θ)/(2*cosh(2*pi*d/λ))-(ρ*[g]*Z) --> (997*[g]*3*cosh(2*pi*(2)/26.8))*cos(0.5235987755982)/(2*cosh(2*pi*1.05/26.8))-(997*[g]*0.8)
Evaluating ... ...
p = 5883.83510991116
STEP 3: Convert Result to Output's Unit
5883.83510991116 Pascal -->5.88383510991116 Kilopascal (Check conversion here)
FINAL ANSWER
5.88383510991116 5.883835 Kilopascal <-- Sub Surface Pressure
(Calculation completed in 00.020 seconds)

Credits

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Coorg Institute of Technology (CIT), Coorg
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7 Pressure Reference Factor Calculators

Pressure taken as Gauge Pressure relative to Wave Mechanics
Go Sub Surface Pressure = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))-(Mass Density*[g]*Seabed Elevation)
Pressure Reference Factor given Height of Surface Waves based on Subsurface Measurements
Go Pressure Factor = Correction Factor*(Sub Surface Pressure+(Mass Density*[g]*Depth below the SWL of Pressure Gauge))/(Elevation of Water Surface*Mass Density*[g])
Pressure given Height of Surface Waves based on Subsurface Measurements
Go Sub Surface Pressure = ((Elevation of Water Surface*Mass Density*[g]*Pressure Factor)/Correction Factor)-(Mass Density*[g]*Depth below the SWL of Pressure Gauge)
Pressure Reference Factor
Go Pressure Factor = cosh(2*pi*(Distance above the Bottom)/Wavelength)/(cosh(2*pi*Water Depth/Wavelength))
Pressure given Pressure Response Factor
Go Sub Surface Pressure = Mass Density*[g]*(((Wave Height/2)*cos(Phase Angle)*Pressure Factor)-Seabed Elevation)
Wavelength for Pressure Response Factor at bottom
Go Wavelength = 2*pi*Water Depth/(acosh(1/Pressure Factor))
Pressure response factor at bottom
Go Pressure Factor = 1/cosh(2*pi*Water Depth/Wavelength)

Pressure taken as Gauge Pressure relative to Wave Mechanics Formula

Sub Surface Pressure = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))-(Mass Density*[g]*Seabed Elevation)
p = (ρ*[g]*H*cosh(2*pi*(DZ+d)/λ))*cos(θ)/(2*cosh(2*pi*d/λ))-(ρ*[g]*Z)

What is Wavelength?

Wavelength, distance between corresponding points of two consecutive waves. “Corresponding points” refers to two points or particles in the same phase i.e., points that have completed identical fractions of their periodic motion.

How to Calculate Pressure taken as Gauge Pressure relative to Wave Mechanics?

Pressure taken as Gauge Pressure relative to Wave Mechanics calculator uses Sub Surface Pressure = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))-(Mass Density*[g]*Seabed Elevation) to calculate the Sub Surface Pressure, The Pressure taken as Gauge Pressure relative to Wave Mechanics is the pressure relative to atmospheric pressure. Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below it. Sub Surface Pressure is denoted by p symbol.

How to calculate Pressure taken as Gauge Pressure relative to Wave Mechanics using this online calculator? To use this online calculator for Pressure taken as Gauge Pressure relative to Wave Mechanics, enter Mass Density (ρ), Wave Height (H), Distance above the Bottom (DZ+d), Wavelength (λ), Phase Angle (θ), Water Depth (d) & Seabed Elevation (Z) and hit the calculate button. Here is how the Pressure taken as Gauge Pressure relative to Wave Mechanics calculation can be explained with given input values -> 0.005922 = (997*[g]*3*cosh(2*pi*(2)/26.8))*cos(0.5235987755982)/(2*cosh(2*pi*1.05/26.8))-(997*[g]*0.8).

FAQ

What is Pressure taken as Gauge Pressure relative to Wave Mechanics?
The Pressure taken as Gauge Pressure relative to Wave Mechanics is the pressure relative to atmospheric pressure. Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below it and is represented as p = (ρ*[g]*H*cosh(2*pi*(DZ+d)/λ))*cos(θ)/(2*cosh(2*pi*d/λ))-(ρ*[g]*Z) or Sub Surface Pressure = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))-(Mass Density*[g]*Seabed Elevation). The Mass Density of a substance is its mass per unit volume, Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough, Distance above the Bottom expressing the local fluid velocity component, Wavelength can be defined as the distance between two successive crests or troughs of a wave, Phase Angle characteristic of a periodic wave. The angular component periodic wave is known as the phase angle. It is a complex quantity measured by angular units like radians or degrees, Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body & Seabed Elevation of the catchment under consideration. Seabed is the bottom of the ocean.
How to calculate Pressure taken as Gauge Pressure relative to Wave Mechanics?
The Pressure taken as Gauge Pressure relative to Wave Mechanics is the pressure relative to atmospheric pressure. Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below it is calculated using Sub Surface Pressure = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))-(Mass Density*[g]*Seabed Elevation). To calculate Pressure taken as Gauge Pressure relative to Wave Mechanics, you need Mass Density (ρ), Wave Height (H), Distance above the Bottom (DZ+d), Wavelength (λ), Phase Angle (θ), Water Depth (d) & Seabed Elevation (Z). With our tool, you need to enter the respective value for Mass Density, Wave Height, Distance above the Bottom, Wavelength, Phase Angle, Water Depth & Seabed Elevation 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 Sub Surface Pressure?
In this formula, Sub Surface Pressure uses Mass Density, Wave Height, Distance above the Bottom, Wavelength, Phase Angle, Water Depth & Seabed Elevation. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Sub Surface Pressure = Mass Density*[g]*(((Wave Height/2)*cos(Phase Angle)*Pressure Factor)-Seabed Elevation)
  • Sub Surface Pressure = ((Elevation of Water Surface*Mass Density*[g]*Pressure Factor)/Correction Factor)-(Mass Density*[g]*Depth below the SWL of Pressure Gauge)
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