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Phase Angle for Total or Absolute Pressure Formula

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Phase Angle is the angular displacement between the oscillations of water level and pore water pressure within the seabed or coastal structures. Check FAQs

θ = a \cos (\frac{P abs + (ρ \cdot [g] \cdot Z) - (P atm)}{\frac{ρ \cdot [g] \cdot H \cdot \cosh (2 \cdot π \cdot \frac{D Z+d}{λ})}{2 \cdot \cosh (2 \cdot π \cdot \frac{d}{λ})}})

θ - Phase Angle?P_abs - Absolute Pressure?ρ - Mass Density?Z - Seabed Elevation?P_atm - Atmospheric Pressure?H - Wave Height?D_Z+d - Distance above the Bottom?λ - Wavelength?d - Water Depth?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Phase Angle for Total or Absolute Pressure Example

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Here is how the Phase Angle for Total or Absolute Pressure equation looks like with Values.

Here is how the Phase Angle for Total or Absolute Pressure equation looks like with Units.

Here is how the Phase Angle for Total or Absolute Pressure equation looks like.

55.8208 = a \cos (\frac{100000 + (997 \cdot 9.8066 \cdot 0.908) - (99987)}{\frac{997 \cdot 9.8066 \cdot 3 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8})}{2 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.05}{26.8})}})

55.8208° = a \cos (\frac{100000Pa + (997kg/m³ \cdot 9.8066m/s² \cdot 0.908) - (99987Pa)}{\frac{997kg/m³ \cdot 9.8066m/s² \cdot 3m \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m})}{2 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.05m}{26.8m})}})

55.8208 = a \cos (\frac{100000 + (997 \cdot 9.8066 \cdot 0.908) - (99987)}{\frac{997 \cdot 9.8066 \cdot 3 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8})}{2 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.05}{26.8})}})

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Phase Angle for Total or Absolute Pressure Solution

Follow our step by step solution on how to calculate Phase Angle for Total or Absolute Pressure?

FIRST Step Consider the formula

θ = a \cos (\frac{P abs + (ρ \cdot [g] \cdot Z) - (P atm)}{\frac{ρ \cdot [g] \cdot H \cdot \cosh (2 \cdot π \cdot \frac{D Z+d}{λ})}{2 \cdot \cosh (2 \cdot π \cdot \frac{d}{λ})}})

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{100000Pa + (997kg/m³ \cdot [g] \cdot 0.908) - (99987Pa)}{\frac{997kg/m³ \cdot [g] \cdot 3m \cdot \cosh (2 \cdot π \cdot \frac{2m}{26.8m})}{2 \cdot \cosh (2 \cdot π \cdot \frac{1.05m}{26.8m})}})

Next Step Substitute values of Constants

∴

θ = a \cos (\frac{100000Pa + (997kg/m³ \cdot 9.8066m/s² \cdot 0.908) - (99987Pa)}{\frac{997kg/m³ \cdot 9.8066m/s² \cdot 3m \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2m}{26.8m})}{2 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.05m}{26.8m})}})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{100000 + (997 \cdot 9.8066 \cdot 0.908) - (99987)}{\frac{997 \cdot 9.8066 \cdot 3 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{2}{26.8})}{2 \cdot \cosh (2 \cdot 3.1416 \cdot \frac{1.05}{26.8})}})

Next Step Evaluate

∴

θ = 0.97425599496585rad

Next Step Convert to Output's Unit

∴

θ = 55.8207566768725°

LAST Step Rounding Answer

∴

θ = 55.8208°

Phase Angle for Total or Absolute Pressure Formula Elements

Variables

Constants

Functions

Phase Angle

Phase Angle is the angular displacement between the oscillations of water level and pore water pressure within the seabed or coastal structures.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Phase Angle

Absolute Pressure

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.

Symbol: P_abs

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Absolute Pressure

Mass Density

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.

Symbol: ρ

Measurement: Mass ConcentrationUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Mass Density

Seabed Elevation

Seabed Elevation impact on the distribution of subsurface pressures in coastal areas. Variations in seabed elevation can affect the flow of groundwater.

Symbol: Z

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Seabed Elevation

Atmospheric Pressure

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.

Symbol: P_atm

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Atmospheric Pressure

Wave Height

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.

Symbol: H

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wave Height

Distance above the Bottom

Distance above the Bottom directly influences the magnitude of pressure exerted by the overlying water column on submerged structures or sediments.

Symbol: D_Z+d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance above the Bottom

Wavelength

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.

Symbol: λ

Measurement: WavelengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength

Water Depth

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.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Water Depth

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: cosh(Number)

Other formulas in Pressure Component category

Go Total or Absolute Pressure

P abs = (ρ \cdot [g] \cdot H \cdot \cosh (2 \cdot π \cdot \frac{D Z+d}{λ}) \cdot \frac{\cos (θ)}{2} \cdot \cosh (2 \cdot π \cdot \frac{d}{λ})) - (ρ \cdot [g] \cdot Z) + P atm

Go Atmospheric Pressure given Total or Absolute Pressure

P atm = P abs - (ρ \cdot [g] \cdot H \cdot \cosh (2 \cdot π \cdot \frac{D Z+d}{λ})) \cdot \frac{\cos (θ)}{2 \cdot \cosh (2 \cdot π \cdot \frac{d}{λ})} + (ρ \cdot [g] \cdot Z)

How to Evaluate Phase Angle for Total or Absolute Pressure?

Phase Angle for Total or Absolute Pressure evaluator 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 evaluate 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 evaluate Phase Angle for Total or Absolute Pressure using this online evaluator? To use this online evaluator 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.

FAQs on Phase Angle for Total or Absolute Pressure

What is the formula to find Phase Angle for Total or Absolute Pressure?

The formula of Phase Angle for Total or Absolute Pressure is expressed as 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)))). Here is an example- 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)))).

How to calculate Phase Angle for Total or Absolute Pressure?

With 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) we can find Phase Angle for Total or Absolute Pressure using the formula - 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)))). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth, Archimedes' constant and , Cosine (cos), Inverse Cosine (acos), Hyperbolic Cosine (cosh) function(s).

Can the Phase Angle for Total or Absolute Pressure be negative?

Yes, the Phase Angle for Total or Absolute Pressure, measured in Angle can be negative.

Which unit is used to measure Phase Angle for Total or Absolute Pressure?

Phase Angle for Total or Absolute Pressure is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Phase Angle for Total or Absolute Pressure can be measured.

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Phase Angle for Total or Absolute Pressure Formula

Phase Angle for Total or Absolute Pressure Example

Phase Angle for Total or Absolute Pressure Solution

Phase Angle for Total or Absolute Pressure Formula Elements

Other formulas in Pressure Component category

How to Evaluate Phase Angle for Total or Absolute Pressure?

FAQs on Phase Angle for Total or Absolute Pressure

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