Phase Angle for Total or Absolute Pressure Calculator

✖Absolute Pressure is labeled when any pressure is detected above the absolute zero of pressure.ⓘ Absolute Pressure [P_abs]			+10% -10%
✖Mass Density is a physical quantity that represents the mass of a substance per unit volume.ⓘ Mass Density [ρ]			+10% -10%
✖Seabed Elevation of the catchment under consideration. Seabed is the bottom of the ocean.ⓘ Seabed Elevation [Z]			+10% -10%
✖Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth.ⓘ Atmospheric Pressure [P_atm]			+10% -10%
✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height [H]			+10% -10%
✖Distance above the Bottom expressing the local fluid velocity component.ⓘ Distance above the Bottom [D_Z+d]			+10% -10%
✖Wavelength can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength [λ]			+10% -10%
✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%

✖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.ⓘ 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

`"65.76273°"=acos(("100000Pa"+("997kg/m³"*"[g]"*"0.8")-("101325Pa"))/(("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 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.
Absolute Pressure - (Measured in Pascal) - Absolute Pressure is labeled when any pressure is detected above the absolute zero of pressure.
Mass Density - (Measured in Kilogram per Cubic Meter) - Mass Density is a physical quantity that represents the mass of a substance per unit volume.
Seabed Elevation - Seabed Elevation of the catchment under consideration. Seabed is the bottom of the ocean.
Atmospheric Pressure - (Measured in Pascal) - Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth.
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.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

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: 0.8 --> No Conversion Required
Atmospheric Pressure: 101325 Pascal --> 101325 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]*0.8)-(101325))/((997*[g]*3*cosh(2*pi*(2)/26.8))/(2*cosh(2*pi*1.05/26.8))))

Evaluating ... ...

θ = 1.14777613048906

STEP 3: Convert Result to Output's Unit

1.14777613048906 Radian -->65.7627281028926 Degree (Check conversion here)

FINAL ANSWER

65.7627281028926 ≈ 65.76273 Degree <-- Phase Angle

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Subsurface Pressure » Pressure Component » Phase Angle for Total or Absolute Pressure

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< 16 Pressure Component Calculators

Water Surface Elevation of Two Sinusoidal Wave

Go Elevation of Water Surface = (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

Dynamic Component due to Acceleration from Absolute Pressure Equation

Go Dynamic Component due to Acceleration = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))

Height of Surface Waves based on Subsurface Measurements

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

Correction Factor given Height of Surface Waves based on Subsurface Measurements

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

Depth below SWL of Pressure Gauge

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

Friction Velocity given Dimensionless Time

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

Water Surface Elevation

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

Wave celerity for shallow water given water depth

Go Celerity of the Wave = 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 = (Celerity of the Wave^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, Phase Angle for Total or Absolute Pressure is the characteristic of a periodic wave. It is synonymous to Phase in many contexts. In phasors, a wave exhibits twofold characteristics: Magnitude and Phase. The phase angle refers to the angular component of a periodic wave. 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 -> 3772.005 = acos((100000+(997*[g]*0.8)-(101325))/((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?

Phase Angle for Total or Absolute Pressure is the characteristic of a periodic wave. It is synonymous to Phase in many contexts. In phasors, a wave exhibits twofold characteristics: Magnitude and Phase. The phase angle refers to the angular component of a periodic wave 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 labeled when any pressure is detected above the absolute zero of pressure, Mass Density is a physical quantity that represents the mass of a substance per unit volume, Seabed Elevation of the catchment under consideration. Seabed is the bottom of the ocean, Atmospheric pressure, also known as barometric pressure, is the pressure within the atmosphere of Earth, 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 & Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

How to calculate Phase Angle for Total or Absolute Pressure?

Phase Angle for Total or Absolute Pressure is the characteristic of a periodic wave. It is synonymous to Phase in many contexts. In phasors, a wave exhibits twofold characteristics: Magnitude and Phase. The phase angle refers to the angular component of a periodic wave is calculated using 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 Phase Angle for Total or Absolute Pressure, you need 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). With our tool, you need to enter the respective value for Absolute Pressure, Mass Density, Seabed Elevation, Atmospheric Pressure, Wave Height, Distance above the Bottom, Wavelength & Water Depth 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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