Water Depth given 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%
✖Natural Free Oscillating Period of a Basin have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.ⓘ Natural Free Oscillating Period of a Basin [T_n]			+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 given Maximum Oscillation Period corresponding to Fundamental Mode [d]

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Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

Formula

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

Example

`"12.13547m"=(2*"30m"/"5.5s")^2/"[g]"`

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Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

Water Depth = (2*Length of Basin/Natural Free Oscillating Period of a Basin)^2/[g]
d = (2*L_b/T_n)^2/[g]
This formula uses 1 Constants, 3 Variables

Constants Used

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

Variables Used

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.
Length of Basin - (Measured in Meter) - Length of Basin or length of the drainage basin in kilometres.
Natural Free Oscillating Period of a Basin - (Measured in Second) - Natural Free Oscillating Period of a Basin have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.

STEP 1: Convert Input(s) to Base Unit

Length of Basin: 30 Meter --> 30 Meter No Conversion Required
Natural Free Oscillating Period of a Basin: 5.5 Second --> 5.5 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = (2*L_b/T_n)^2/[g] --> (2*30/5.5)^2/[g]

Evaluating ... ...

d = 12.1354656751092

STEP 3: Convert Result to Output's Unit

12.1354656751092 Meter --> No Conversion Required

FINAL ANSWER

12.1354656751092 ≈ 12.13547 Meter <-- Water Depth

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Water Depth given 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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< 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]

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode Formula

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

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 Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode?

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode calculator uses Water Depth = (2*Length of Basin/Natural Free Oscillating Period of a Basin)^2/[g] to calculate the Water Depth, The Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode is defined as depth parameter influencing the natural free oscillation period involve standing waves in shallow water. Water Depth is denoted by d symbol.

How to calculate Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode using this online calculator? To use this online calculator for Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode, enter Length of Basin (L_b) & Natural Free Oscillating Period of a Basin (T_n) and hit the calculate button. Here is how the Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode calculation can be explained with given input values -> 12.13547 = (2*30/5.5)^2/[g].

FAQ

What is Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode?

The Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode is defined as depth parameter influencing the natural free oscillation period involve standing waves in shallow water and is represented as d = (2*L_b/T_n)^2/[g] or Water Depth = (2*Length of Basin/Natural Free Oscillating Period of a Basin)^2/[g]. Length of Basin or length of the drainage basin in kilometres & Natural Free Oscillating Period of a Basin have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.

How to calculate Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode?

The Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode is defined as depth parameter influencing the natural free oscillation period involve standing waves in shallow water is calculated using Water Depth = (2*Length of Basin/Natural Free Oscillating Period of a Basin)^2/[g]. To calculate Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode, you need Length of Basin (L_b) & Natural Free Oscillating Period of a Basin (T_n). With our tool, you need to enter the respective value for Length of Basin & Natural Free Oscillating Period of a Basin 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 Water Depth?

In this formula, Water Depth uses Length of Basin & Natural Free Oscillating Period of a Basin. We can use 4 other way(s) to calculate the same, which is/are as follows -

Water Depth = ((4*Length of Basin/Natural Free Oscillating Period of a Basin)^2)/[g]
Water Depth = [g]/(Maximum Horizontal Velocity at a Node/(Standing Wave Height/2))^2
Water Depth = [g]/(2*pi*Maximum Horizontal Particle Excursion/Standing Wave Height*Natural Free Oscillating Period of a Basin)^2
Water Depth = (Standing Wave Height*Wavelength)/Average Horizontal Velocity at a Node*pi*Natural Free Oscillating Period of a Basin

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