Maximum Oscillation Period corresponding to Fundamental Mode Calculator

✖Length of Basin or length of the drainage basin in kilometres.ⓘ Length of Basin [L_b]			+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%

✖Maximum Oscillation Period corresponding to the Fundamental Mode.ⓘ Maximum Oscillation Period corresponding to Fundamental Mode [T₁]

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Formula

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Maximum Oscillation Period corresponding to Fundamental Mode

Formula

`"T"_{"1"} = 2*"L"_{"b"}/sqrt("[g]"*"d")`

Example

`"0.311634min"=2*"30m"/sqrt("[g]"*"1.05m")`

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Maximum Oscillation Period corresponding to Fundamental Mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth)
T₁ = 2*L_b/sqrt([g]*d)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Maximum Oscillation Period - (Measured in Second) - Maximum Oscillation Period corresponding to the Fundamental Mode.
Length of Basin - (Measured in Meter) - Length of Basin or length of the drainage basin in kilometres.
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

Length of Basin: 30 Meter --> 30 Meter No Conversion Required
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T₁ = 2*L_b/sqrt([g]*d) --> 2*30/sqrt([g]*1.05)

Evaluating ... ...

T₁ = 18.6980476870372

STEP 3: Convert Result to Output's Unit

18.6980476870372 Second -->0.311634128117287 Minute (Check conversion here)

FINAL ANSWER

0.311634128117287 ≈ 0.311634 Minute <-- Maximum Oscillation Period

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Maximum Oscillation Period corresponding to Fundamental Mode

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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National Institute of Technology (NIT), Warangal

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< 22 Harbor Oscillations Calculators

Additional Length to account for Mass Outside each end of Channel

Go Additional Length of the Channel = (-Channel Width corresponding to Mean Water Depth/pi)*ln(pi*Channel Width corresponding to Mean Water Depth/(sqrt([g]*Channel Depth)*Resonant Period for Helmholtz Mode))

Resonant Period for Helmholtz Mode

Go Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*Channel Cross-sectional Area))

Channel Cross-sectional Area given Resonant Period for Helmholtz mode

Go Channel Cross-sectional Area = (Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*(Resonant Period for Helmholtz Mode/2*pi)^2)

Basin Surface Area given Resonant Period for Helmholtz mode

Go Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel))

Additional Length accounting for Mass Outside each End of Channel

Go Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length

Channel Length for Resonant Period for Helmholtz Mode

Go Channel Length = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Additional Length of the Channel

Standing Wave Height given Maximum Horizontal Particle Excursion at Node

Go Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth)

Maximum Horizontal Particle Excursion at Node

Go Maximum Horizontal Particle Excursion = (Standing Wave Height*Natural Free Oscillating Period of a Basin/2*pi)*sqrt([g]/Water Depth)

Standing Wave Height for Average Horizontal Velocity at Node

Go Standing Wave Height = (Average Horizontal Velocity at a Node*pi*Water Depth*Natural Free Oscillating Period of a Basin)/Wavelength

Water Depth given Average Horizontal Velocity at Node

Go Water Depth = (Standing Wave Height*Wavelength)/Average Horizontal Velocity at a Node*pi*Natural Free Oscillating Period of a Basin

Wave Length for Average Horizontal Velocity at Node

Go Wavelength = (Average Horizontal Velocity at a Node*pi*Water Depth*Natural Free Oscillating Period of a Basin)/Standing Wave Height

Average Horizontal Velocity at Node

Go Average Horizontal Velocity at a Node = (Standing Wave Height*Wavelength)/pi*Water Depth*Natural Free Oscillating Period of a Basin

Water Depth given Maximum Horizontal Particle Excursion at Node

Go Water Depth = [g]/(2*pi*Maximum Horizontal Particle Excursion/Standing Wave Height*Natural Free Oscillating Period of a Basin)^2

Standing Wave Height given Maximum Horizontal Velocity at Node

Go Standing Wave Height = (Maximum Horizontal Velocity at a Node/sqrt([g]/Water Depth))*2

Maximum Horizontal Velocity at Node

Go Maximum Horizontal Velocity at a Node = (Standing Wave Height/2)*sqrt([g]/Water Depth)

Period for Fundamental Mode

Go Natural Free Oscillating Period of a Basin = (4*Length of Basin)/sqrt([g]*Water Depth)

Basin Length along Axis for given Period of Fundamental Mode

Go Length of Basin = Natural Free Oscillating Period of a Basin*sqrt([g]*Water Depth)/4

Basin Length along axis given Maximum Oscillation Period corresponding to Fundamental Mode

Go Length of Basin = Maximum Oscillation Period*sqrt([g]*Water Depth)/2

Maximum Oscillation Period corresponding to Fundamental Mode

Go Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth)

Water Depth given Maximum Horizontal Velocity at Node

Go Water Depth = [g]/(Maximum Horizontal Velocity at a Node/(Standing Wave Height/2))^2

Water Depth for given Period for Fundamental Mode

Go Water Depth = ((4*Length of Basin/Natural Free Oscillating Period of a Basin)^2)/[g]

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

Go Water Depth = (2*Length of Basin/Natural Free Oscillating Period of a Basin)^2/[g]

Maximum Oscillation Period corresponding to Fundamental Mode Formula

Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth)
T₁ = 2*L_b/sqrt([g]*d)

What is Wave Reflection on Structures?

If there is a change in water depth as a wave propagates forward, a portion of the wave’s energy will be reflected. When a wave hits a vertical, impermeable, rigid surface-piercing wall, essentially all of the wave energy will reflect from the wall. On the other hand, when a wave propagates over a small bottom slope, only a very small portion of the energy will be reflected. The degree of wave reflection is defined by the reflection coefficient Cr = Hr/Hi where Hr and Hi are the reflected and incident wave heights, respectively.

How to Calculate Maximum Oscillation Period corresponding to Fundamental Mode?

Maximum Oscillation Period corresponding to Fundamental Mode calculator uses Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth) to calculate the Maximum Oscillation Period, The Maximum Oscillation Period corresponding to Fundamental Mode for Closed Basin is defined as parameter influencing maximum oscillation period T1 corresponding to fundamental mode is given by setting n = 1. Maximum Oscillation Period is denoted by T₁ symbol.

How to calculate Maximum Oscillation Period corresponding to Fundamental Mode using this online calculator? To use this online calculator for Maximum Oscillation Period corresponding to Fundamental Mode, enter Length of Basin (L_b) & Water Depth (d) and hit the calculate button. Here is how the Maximum Oscillation Period corresponding to Fundamental Mode calculation can be explained with given input values -> 0.005322 = 2*30/sqrt([g]*1.05).

FAQ

What is Maximum Oscillation Period corresponding to Fundamental Mode?

The Maximum Oscillation Period corresponding to Fundamental Mode for Closed Basin is defined as parameter influencing maximum oscillation period T1 corresponding to fundamental mode is given by setting n = 1 and is represented as T₁ = 2*L_b/sqrt([g]*d) or Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth). Length of Basin or length of the drainage basin in kilometres & 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 Maximum Oscillation Period corresponding to Fundamental Mode?

The Maximum Oscillation Period corresponding to Fundamental Mode for Closed Basin is defined as parameter influencing maximum oscillation period T1 corresponding to fundamental mode is given by setting n = 1 is calculated using Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth). To calculate Maximum Oscillation Period corresponding to Fundamental Mode, you need Length of Basin (L_b) & Water Depth (d). With our tool, you need to enter the respective value for Length of Basin & 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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