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Equilibrium Form of PM Spectrum for Fully-Developed Seas Formula

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Frequency Energy Spectrum is typically obtained by performing a Fourier transform of the time history of a ground motion or structural response. Check FAQs

E f = (\frac{0.0081 \cdot {[g]}^{2}}{{(2 \cdot π)}^{4} \cdot f^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot π \cdot U \cdot f}{[g]})}^{- 4})

E_f - Frequency Energy Spectrum?f - Wave Frequency?U - Wind Speed?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Equilibrium Form of PM Spectrum for Fully-Developed Seas Example

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Here is how the Equilibrium Form of PM Spectrum for Fully-Developed Seas equation looks like with Values.

Here is how the Equilibrium Form of PM Spectrum for Fully-Developed Seas equation looks like with Units.

Here is how the Equilibrium Form of PM Spectrum for Fully-Developed Seas equation looks like.

1.5E-8 = (\frac{0.0081 \cdot {9.8066}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot 8^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot 3.1416 \cdot 4 \cdot 8}{9.8066})}^{- 4})

1.5E-8 = (\frac{0.0081 \cdot {9.8066m/s²}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot {8kHz}^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot 3.1416 \cdot 4m/s \cdot 8kHz}{9.8066m/s²})}^{- 4})

1.5E-8 = (\frac{0.0081 \cdot {9.8066}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot 8^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot 3.1416 \cdot 4 \cdot 8}{9.8066})}^{- 4})

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Equilibrium Form of PM Spectrum for Fully-Developed Seas Solution

Follow our step by step solution on how to calculate Equilibrium Form of PM Spectrum for Fully-Developed Seas?

FIRST Step Consider the formula

E f = (\frac{0.0081 \cdot {[g]}^{2}}{{(2 \cdot π)}^{4} \cdot f^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot π \cdot U \cdot f}{[g]})}^{- 4})

Next Step Substitute values of Variables

∴

E f = (\frac{0.0081 \cdot {[g]}^{2}}{{(2 \cdot π)}^{4} \cdot {8kHz}^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot π \cdot 4m/s \cdot 8kHz}{[g]})}^{- 4})

Next Step Substitute values of Constants

∴

E f = (\frac{0.0081 \cdot {9.8066m/s²}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot {8kHz}^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot 3.1416 \cdot 4m/s \cdot 8kHz}{9.8066m/s²})}^{- 4})

Next Step Prepare to Evaluate

∴

E f = (\frac{0.0081 \cdot {9.8066}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot 8^{5}}) \cdot \exp (- 0.24 \cdot {(\frac{2 \cdot 3.1416 \cdot 4 \cdot 8}{9.8066})}^{- 4})

Next Step Evaluate

∴

E f = 1.52530386864411E-08

LAST Step Rounding Answer

∴

E f = 1.5E-8

Equilibrium Form of PM Spectrum for Fully-Developed Seas Formula Elements

Variables

Constants

Functions

Frequency Energy Spectrum

Frequency Energy Spectrum is typically obtained by performing a Fourier transform of the time history of a ground motion or structural response.

Symbol: E_f

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Frequency Energy Spectrum

Wave Frequency

Wave Frequency is the number of waves that pass a fixed point in a given amount of time.

Symbol: f

Measurement: FrequencyUnit: kHz

Note: Value should be greater than 0.

Formulas to find Wave Frequency

Wind Speed

Wind Speed is a fundamental atmospheric quantity caused by air moving from high to low pressure, usually due to changes in temperature.

Symbol: U

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Wind Speed

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

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other formulas in Wave Period Distribution and Wave Spectrum category

Go Probability Density of Wave Period

p = 2.7 \cdot (\frac{P^{3}}{T'}) \cdot \exp (- 0.675 \cdot {(\frac{P}{T'})}^{4})

Go Mean Zero-upcrossing Period

T' Z = 2 \cdot π \cdot \sqrt{\frac{m 0}{m 2}}

Go Mean Crest Period

T c = 2 \cdot π \cdot (\frac{m 2}{m 4})

Go Most Probable Maximum Wave Period

T max = 2 \cdot \frac{\sqrt{1 + v^{2}}}{1} + \sqrt{1 + (16 \cdot \frac{v^{2}}{π} \cdot H^{2})}

How to Evaluate Equilibrium Form of PM Spectrum for Fully-Developed Seas?

Equilibrium Form of PM Spectrum for Fully-Developed Seas evaluator uses Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4) to evaluate the Frequency Energy Spectrum, The Equilibrium Form of PM Spectrum for Fully-Developed Seas spectrum describes the distribution of wave energy in fully developed seas, where the wind has been blowing over a sufficiently long distance and time to fully develop the wave field. In this state, the energy input from the wind is balanced by the energy dissipation due to wave breaking and other processes, leading to a stationary wave spectrum. Frequency Energy Spectrum is denoted by E_f symbol.

How to evaluate Equilibrium Form of PM Spectrum for Fully-Developed Seas using this online evaluator? To use this online evaluator for Equilibrium Form of PM Spectrum for Fully-Developed Seas, enter Wave Frequency (f) & Wind Speed (U) and hit the calculate button.

FAQs on Equilibrium Form of PM Spectrum for Fully-Developed Seas

What is the formula to find Equilibrium Form of PM Spectrum for Fully-Developed Seas?

The formula of Equilibrium Form of PM Spectrum for Fully-Developed Seas is expressed as Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4). Here is an example- 1.5E-8 = ((0.0081*[g]^2)/((2*pi)^4*8000^5))*exp(-0.24*((2*pi*4*8000)/[g])^-4).

How to calculate Equilibrium Form of PM Spectrum for Fully-Developed Seas?

With Wave Frequency (f) & Wind Speed (U) we can find Equilibrium Form of PM Spectrum for Fully-Developed Seas using the formula - Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth, Archimedes' constant and Exponential Growth (exp) function(s).

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