✖Absolute Pressure is the total pressure measured with respect to absolute zero, which is a perfect vacuum. It is the sum of the gauge pressure and the atmospheric pressure.ⓘ Absolute Pressure [P_abs]			+10% -10%
✖Mass Density is crucial for understanding the distribution of pressures exerted by overlying soil or water layers on underground structures like foundations, tunnels, or pipelines.ⓘ Mass Density [ρ]			+10% -10%
✖Seabed Elevation impact on the distribution of subsurface pressures in coastal areas. Variations in seabed elevation can affect the flow of groundwater.ⓘ Seabed Elevation [Z]			+10% -10%
✖Atmospheric Pressure is the force per unit area exerted against a surface by the weight of air above that surface in the Earth’s atmosphere.ⓘ Atmospheric Pressure [P_atm]			+10% -10%
✖Wave Height is the vertical distance between the crest and the trough of a wave. Higher wave heights correspond to greater wave forces, which leads to increased structural loading.ⓘ Wave Height [H]			+10% -10%
✖Distance above the Bottom directly influences the magnitude of pressure exerted by the overlying water column on submerged structures or sediments.ⓘ Distance above the Bottom [D_Z+d]			+10% -10%
✖Wavelength is the distance between successive peaks or troughs of a wave. It is crucial in understanding the behavior of waves, particularly in relation to subsurface pressure.ⓘ Wavelength [λ]			+10% -10%
✖Water Depth is vertical distance from the surface of a body of water to its bottom, it is a critical parameter for understanding the characteristics and behaviors of the marine environment.ⓘ Water Depth [d]			+10% -10%

✖Phase Angle is the angular displacement between the oscillations of water level and pore water pressure within the seabed or coastal structures.ⓘ Phase Angle for Total or Absolute Pressure [θ]

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Formula

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Phase Angle for Total or Absolute Pressure

Formula

`"θ" = acos(("P"_{"abs"}+("ρ"*"[g]"*"Z")-("P"_{"atm"}))/(("ρ"*"[g]"*"H"*cosh(2*pi*("D"_{"Z+d"})/"λ"))/(2*cosh(2*pi*"d"/"λ"))))`

Example

`"55.82076°"=acos(("100000Pa"+("997kg/m³"*"[g]"*"0.908")-("99987Pa"))/(("997kg/m³"*"[g]"*"3m"*cosh(2*pi*("2m")/"26.8m"))/(2*cosh(2*pi*"1.05m"/"26.8m"))))`

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Phase Angle for Total or Absolute Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Angle = acos((Absolute Pressure+(Mass Density*[g]*Seabed Elevation)-(Atmospheric Pressure))/((Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))/(2*cosh(2*pi*Water Depth/Wavelength))))
θ = acos((P_abs+(ρ*[g]*Z)-(P_atm))/((ρ*[g]*H*cosh(2*pi*(D_Z+d)/λ))/(2*cosh(2*pi*d/λ))))
This formula uses 2 Constants, 3 Functions, 9 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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)
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

Phase Angle - (Measured in Radian) - Phase Angle is the angular displacement between the oscillations of water level and pore water pressure within the seabed or coastal structures.
Absolute Pressure - (Measured in Pascal) - Absolute Pressure is the total pressure measured with respect to absolute zero, which is a perfect vacuum. It is the sum of the gauge pressure and the atmospheric pressure.
Mass Density - (Measured in Kilogram per Cubic Meter) - Mass Density is crucial for understanding the distribution of pressures exerted by overlying soil or water layers on underground structures like foundations, tunnels, or pipelines.
Seabed Elevation - Seabed Elevation impact on the distribution of subsurface pressures in coastal areas. Variations in seabed elevation can affect the flow of groundwater.
Atmospheric Pressure - (Measured in Pascal) - Atmospheric Pressure is the force per unit area exerted against a surface by the weight of air above that surface in the Earth’s atmosphere.
Wave Height - (Measured in Meter) - Wave Height is the vertical distance between the crest and the trough of a wave. Higher wave heights correspond to greater wave forces, which leads to increased structural loading.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom directly influences the magnitude of pressure exerted by the overlying water column on submerged structures or sediments.
Wavelength - (Measured in Meter) - Wavelength is the distance between successive peaks or troughs of a wave. It is crucial in understanding the behavior of waves, particularly in relation to subsurface pressure.
Water Depth - (Measured in Meter) - Water Depth is vertical distance from the surface of a body of water to its bottom, it is a critical parameter for understanding the characteristics and behaviors of the marine environment.

STEP 1: Convert Input(s) to Base Unit

Absolute Pressure: 100000 Pascal --> 100000 Pascal No Conversion Required
Mass Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Seabed Elevation: 0.908 --> No Conversion Required
Atmospheric Pressure: 99987 Pascal --> 99987 Pascal 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
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos((P_abs+(ρ*[g]*Z)-(P_atm))/((ρ*[g]*H*cosh(2*pi*(D_Z+d)/λ))/(2*cosh(2*pi*d/λ)))) --> acos((100000+(997*[g]*0.908)-(99987))/((997*[g]*3*cosh(2*pi*(2)/26.8))/(2*cosh(2*pi*1.05/26.8))))

Evaluating ... ...

θ = 0.97425599496585

STEP 3: Convert Result to Output's Unit

0.97425599496585 Radian -->55.8207566768725 Degree (Check conversion here)

FINAL ANSWER

55.8207566768725 ≈ 55.82076 Degree <-- Phase Angle

(Calculation completed in 00.004 seconds)

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< 14 Pressure Component Calculators

Water Surface Elevation of Two Sinusoidal Wave

Go Water Elevation = (Wave Height/2)*cos((2*pi*Spatial Progressive Wave/Wavelength of Component Wave 1)-(2*pi*Temporal Progressive Wave/Wave Period of Component Wave 1))+(Wave Height/2)*cos((2*pi*Spatial Progressive Wave/Wavelength of Component Wave 2)-(2*pi*Temporal Progressive Wave/Wave Period of Component Wave 2))

Phase Angle for Total or Absolute Pressure

Go Phase Angle = acos((Absolute Pressure+(Mass Density*[g]*Seabed Elevation)-(Atmospheric Pressure))/((Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))/(2*cosh(2*pi*Water Depth/Wavelength))))

Atmospheric Pressure given Total or Absolute Pressure

Go Atmospheric Pressure = Absolute 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)

Total or Absolute Pressure

Go Absolute 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)+Atmospheric Pressure

Depth below SWL of Pressure Gauge

Go Depth below the SWL of Pressure Gauge = ((Water Surface Elevation*Mass Density*[g]*Pressure Response Factor/Correction Factor)-Pressure)/(Mass Density*[g])

Correction Factor given Height of Surface Waves based on Subsurface Measurements

Go Correction Factor = Water Surface Elevation*Mass Density*[g]*Pressure Response Factor/(Pressure+(Mass Density*[g]*Depth below the SWL of Pressure Gauge))

Friction Velocity given Dimensionless Time

Go Friction Velocity = ([g]*Time for Dimensionless Parameter Calculation)/Dimensionless Time

Water Surface Elevation

Go Water Elevation = (Wave Height/2)*cos(Phase Angle)

Wave celerity for shallow water given water depth

Go Wave Celerity = sqrt([g]*Water Depth)

Atmospheric Pressure given Gauge Pressure

Go Atmospheric Pressure = Absolute Pressure-Gauge Pressure

Total Pressure given Gauge Pressure

Go Total Pressure = Gauge Pressure+Atmospheric Pressure

Water Depth given Wave Celerity for Shallow Water

Go Water Depth = (Wave Celerity^2)/[g]

Radian Frequency given Wave Period

Go Wave Angular Frequency = 1/Mean Wave Period

Wave Period given Average Frequency

Go Wave Period = 1/Wave Angular Frequency

Phase Angle for Total or Absolute Pressure Formula

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 Phase Angle for Total or Absolute Pressure?

Phase Angle for Total or Absolute Pressure calculator uses Phase Angle = acos((Absolute Pressure+(Mass Density*[g]*Seabed Elevation)-(Atmospheric Pressure))/((Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))/(2*cosh(2*pi*Water Depth/Wavelength)))) to calculate the Phase Angle, The Phase Angle for Total or Absolute Pressure Formula is defined as the angular difference between the total or absolute pressure and the corresponding tidal elevation. It helps in analyzing the behavior of waves and tides by providing insights into the timing and magnitude of pressure changes beneath the water surface. Phase Angle is denoted by θ symbol.

How to calculate Phase Angle for Total or Absolute Pressure using this online calculator? To use this online calculator for Phase Angle for Total or Absolute Pressure, enter Absolute Pressure (P_abs), Mass Density (ρ), Seabed Elevation (Z), Atmospheric Pressure (P_atm), Wave Height (H), Distance above the Bottom (D_Z+d), Wavelength (λ) & Water Depth (d) and hit the calculate button. Here is how the Phase Angle for Total or Absolute Pressure calculation can be explained with given input values -> 3456.437 = acos((100000+(997*[g]*0.908)-(99987))/((997*[g]*3*cosh(2*pi*(2)/26.8))/(2*cosh(2*pi*1.05/26.8)))).

FAQ

What is Phase Angle for Total or Absolute Pressure?

The Phase Angle for Total or Absolute Pressure Formula is defined as the angular difference between the total or absolute pressure and the corresponding tidal elevation. It helps in analyzing the behavior of waves and tides by providing insights into the timing and magnitude of pressure changes beneath the water surface and is represented as θ = acos((P_abs+(ρ*[g]*Z)-(P_atm))/((ρ*[g]*H*cosh(2*pi*(D_Z+d)/λ))/(2*cosh(2*pi*d/λ)))) or Phase Angle = acos((Absolute Pressure+(Mass Density*[g]*Seabed Elevation)-(Atmospheric Pressure))/((Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))/(2*cosh(2*pi*Water Depth/Wavelength)))). Absolute Pressure is the total pressure measured with respect to absolute zero, which is a perfect vacuum. It is the sum of the gauge pressure and the atmospheric pressure, Mass Density is crucial for understanding the distribution of pressures exerted by overlying soil or water layers on underground structures like foundations, tunnels, or pipelines, Seabed Elevation impact on the distribution of subsurface pressures in coastal areas. Variations in seabed elevation can affect the flow of groundwater, Atmospheric Pressure is the force per unit area exerted against a surface by the weight of air above that surface in the Earth’s atmosphere, Wave Height is the vertical distance between the crest and the trough of a wave. Higher wave heights correspond to greater wave forces, which leads to increased structural loading, Distance above the Bottom directly influences the magnitude of pressure exerted by the overlying water column on submerged structures or sediments, Wavelength is the distance between successive peaks or troughs of a wave. It is crucial in understanding the behavior of waves, particularly in relation to subsurface pressure & Water Depth is vertical distance from the surface of a body of water to its bottom, it is a critical parameter for understanding the characteristics and behaviors of the marine environment.

How to calculate Phase Angle for Total or Absolute Pressure?

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