Fetch Length given Frequency at Spectral Peak Solution

STEP 0: Pre-Calculation Summary
Formula Used
Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2
Fl = ((V10^3)*((fp/3.5)^-(1/0.33)))/[g]^2
This formula uses 1 Constants, 3 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Variables Used
Fetch Length - (Measured in Meter) - Fetch Length is the length of water over which a given wind has blown without obstruction.
Wind Speed at Height of 10 m - (Measured in Meter per Second) - Wind Speed at Height of 10 m is the ten-meter wind speed measured ten meters above the top of the datum of consideration.
Frequency at Spectral Peak - (Measured in Hertz) - Frequency at Spectral Peak is the number of occurrences of a repeating event per unit of time.
STEP 1: Convert Input(s) to Base Unit
Wind Speed at Height of 10 m: 22 Meter per Second --> 22 Meter per Second No Conversion Required
Frequency at Spectral Peak: 0.013162 Kilohertz --> 13.162 Hertz (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fl = ((V10^3)*((fp/3.5)^-(1/0.33)))/[g]^2 --> ((22^3)*((13.162/3.5)^-(1/0.33)))/[g]^2
Evaluating ... ...
Fl = 2.00001489638791
STEP 3: Convert Result to Output's Unit
2.00001489638791 Meter --> No Conversion Required
FINAL ANSWER
2.00001489638791 2.000015 Meter <-- Fetch Length
(Calculation completed in 00.004 seconds)

Credits

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Coorg Institute of Technology (CIT), Coorg
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19 Parametric Spectrum Models Calculators

JONSWAP Spectrum for Fetch-limited Seas
Go Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2))
Frequency of Spectral Peak
Go Frequency at Spectral Peak = ([g]*18.8*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.33)/(2*pi*Wind Speed at Height of 10 m)
Frequency of Spectral Peak Given Wind Speed
Go Frequency at Spectral Peak = ([g]*(Controlling Parameter for the Angular Distribution/11.5)^(-1/2.5))/(2*pi*Wind Speed at Height of 10 m)
Wind Speed given Maximum Controlling Parameter for Angular Distribution
Go Wind Speed at Height of 10 m = [g]*(Controlling Parameter for the Angular Distribution/11.5)^(-1/2.5)/(2*pi*Frequency at Spectral Peak)
Maximum Controlling Parameter for Angular Distribution
Go Controlling Parameter for the Angular Distribution = 11.5*((2*pi*Frequency at Spectral Peak*Wind Speed at Height of 10 m)/[g])^-2.5
Wind Speed at Elevation 10m above Sea Surface given Scaling Parameter
Go Wind Speed at Height of 10 m = ((Fetch Length*[g])/(Dimensionless Scaling Parameter/0.076)^(-1/0.22))^0.5
Fetch Length given Scaling Parameter
Go Fetch Length = (Wind Speed at Height of 10 m^2*((Dimensionless Scaling Parameter/0.076)^-(1/0.22)))/[g]
Scaling Parameter
Go Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22
Dimensionless Time
Go Dimensionless Time = ([g]*Time for Dimensionless Parameter Calculation)/Friction Velocity
Significant Wave Height given Significant Wave Height of Lower and Higher frequency Components
Go Significant Wave Height = sqrt(Significant Wave Height 1^2+Significant Wave Height 2^2)
Significant Wave Height of Higher frequency Component
Go Significant Wave Height 2 = sqrt(Significant Wave Height^2-Significant Wave Height 1^2)
Significant Wave Height of Lower frequency Component
Go Significant Wave Height 1 = sqrt(Significant Wave Height^2-Significant Wave Height 2^2)
Wind Speed at Elevation 10m above Sea Surface given Frequency at Spectral Peak
Go Wind Speed at Height of 10 m = ((Fetch Length*[g]^2)/(Frequency at Spectral Peak/3.5)^-(1/0.33))^(1/3)
Fetch Length given Frequency at Spectral Peak
Go Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2
Frequency at Spectral Peak
Go Frequency at Spectral Peak = 3.5*(([g]^2*Fetch Length)/Wind Speed at Height of 10 m^3)^-0.33
Shape Factor for Higher Frequency Component
Go Shape Factor for Higher Frequency Component = 1.82*exp(-0.027*Significant Wave Height)
Phillip's equilibrium range of spectrum for fully developed sea in deep water
Go Phillip's Equilibrium Range of Spectrum = Constant B*[g]^2*Wave Angular Frequency^-5
Weighing Factor for Angular Frequency greater than One
Go Weighing Factor = 1-0.5*(2-Wave Angular Frequency)^2
Weighing Factor for angular frequency lesser than or equal to one
Go Weighing Factor = 0.5*Wave Angular Frequency^2

Fetch Length given Frequency at Spectral Peak Formula

Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2
Fl = ((V10^3)*((fp/3.5)^-(1/0.33)))/[g]^2

What are the characteristics of progressive waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

How to Calculate Fetch Length given Frequency at Spectral Peak?

Fetch Length given Frequency at Spectral Peak calculator uses Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2 to calculate the Fetch Length, The Fetch length given frequency at spectral peak is defined as the length of water over which a given wind has blown without obstruction. Fetch Length is denoted by Fl symbol.

How to calculate Fetch Length given Frequency at Spectral Peak using this online calculator? To use this online calculator for Fetch Length given Frequency at Spectral Peak, enter Wind Speed at Height of 10 m (V10) & Frequency at Spectral Peak (fp) and hit the calculate button. Here is how the Fetch Length given Frequency at Spectral Peak calculation can be explained with given input values -> 2.000015 = ((22^3)*((13.162/3.5)^-(1/0.33)))/[g]^2.

FAQ

What is Fetch Length given Frequency at Spectral Peak?
The Fetch length given frequency at spectral peak is defined as the length of water over which a given wind has blown without obstruction and is represented as Fl = ((V10^3)*((fp/3.5)^-(1/0.33)))/[g]^2 or Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2. Wind Speed at Height of 10 m is the ten-meter wind speed measured ten meters above the top of the datum of consideration & Frequency at Spectral Peak is the number of occurrences of a repeating event per unit of time.
How to calculate Fetch Length given Frequency at Spectral Peak?
The Fetch length given frequency at spectral peak is defined as the length of water over which a given wind has blown without obstruction is calculated using Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2. To calculate Fetch Length given Frequency at Spectral Peak, you need Wind Speed at Height of 10 m (V10) & Frequency at Spectral Peak (fp). With our tool, you need to enter the respective value for Wind Speed at Height of 10 m & Frequency at Spectral Peak 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 Fetch Length?
In this formula, Fetch Length uses Wind Speed at Height of 10 m & Frequency at Spectral Peak. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Fetch Length = (Wind Speed at Height of 10 m^2*((Dimensionless Scaling Parameter/0.076)^-(1/0.22)))/[g]
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