✖Basin Length is the horizontal distance or extent of a water body, such as a bay, estuary, or lagoon. It is an important parameter in the design and analysis of coastal structures.ⓘ Basin Length [L_B]			+10% -10%
✖Number of Nodes along the Axis of a Basin refers to specific points or segments along a central line (axis) of a coastal basin or water body.ⓘ Number of Nodes along the Axis of a Basin [N]			+10% -10%
✖Depth of Water is the depth as measured from the water level to the bottom of the considered water body.ⓘ Depth of Water [D_w]			+10% -10%

✖Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again.ⓘ Natural Free Oscillation Period for Closed Basin [T_n]

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Formula

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Natural Free Oscillation Period for Closed Basin

Formula

`"T"_{"n"} = (2*"L"_{"B"})/("N"*sqrt("[g]"*"D"_{"w"}))`

Example

`"8.613477s"=(2*"180m")/("1.3"*sqrt("[g]"*"105.4m"))`

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Natural Free Oscillation Period for Closed Basin Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water))
T_n = (2*L_B)/(N*sqrt([g]*D_w))
This formula uses 1 Constants, 1 Functions, 4 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

Natural Free Oscillating Period of a Basin - (Measured in Second) - Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again.
Basin Length - (Measured in Meter) - Basin Length is the horizontal distance or extent of a water body, such as a bay, estuary, or lagoon. It is an important parameter in the design and analysis of coastal structures.
Number of Nodes along the Axis of a Basin - Number of Nodes along the Axis of a Basin refers to specific points or segments along a central line (axis) of a coastal basin or water body.
Depth of Water - (Measured in Meter) - Depth of Water 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

Basin Length: 180 Meter --> 180 Meter No Conversion Required
Number of Nodes along the Axis of a Basin: 1.3 --> No Conversion Required
Depth of Water: 105.4 Meter --> 105.4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = (2*L_B)/(N*sqrt([g]*D_w)) --> (2*180)/(1.3*sqrt([g]*105.4))

Evaluating ... ...

T_n = 8.61347713579559

STEP 3: Convert Result to Output's Unit

8.61347713579559 Second --> No Conversion Required

FINAL ANSWER

8.61347713579559 ≈ 8.613477 Second <-- Natural Free Oscillating Period of a Basin

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Free Oscillation Period » Natural Free Oscillation Period for Closed Basin

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< 6 Free Oscillation Period Calculators

Natural Free Oscillation Period

Go Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth at Harbor))*((Number of Nodes along the X-axis of Basin/Basin Dimensions along the X-axis)^2+(Number of Nodes along the Y-axis of Basin/Basin Dimensions along the Y-axis)^2)^-0.5

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node

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

Natural Free Oscillation Period for Open Basin

Go Natural Free Oscillating Period of a Basin = 4*Basin Length/((1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))

Natural Free Oscillation Period for Average Horizontal Velocity at Node

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

Natural Free Oscillation Period for Closed Basin

Go Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water))

Water Depth given Natural Free Oscillation Period

Go Water Depth = (((2*Harbor Basin Length)/(Natural Free Oscillating Period of a Basin*Number of Nodes along the Axis of a Basin))^2)/[g]

< 11 Important Formulas of Harbor Oscillation Calculators

Natural Free Oscillation Period

Resonant Period for Helmholtz Mode

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

Additional Length

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

Basin Length along Axis in Open Basin

Go Length of Open Basin along Axis = (Natural Free Oscillating Period of a Basin*(1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))/4

Average Horizontal Velocity at Node

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

Natural Free Oscillation Period for Open Basin

Go Natural Free Oscillating Period of a Basin = 4*Basin Length/((1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))

Natural Free Oscillation Period for Closed Basin

Go Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water))

Standing Wave Height given Maximum Horizontal Velocity at Node

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

Maximum Horizontal Velocity at Node

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

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

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

Water Depth given Maximum Horizontal Velocity at Node

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

Natural Free Oscillation Period for Closed Basin Formula

Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water))
T_n = (2*L_B)/(N*sqrt([g]*D_w))

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 Natural Free Oscillation Period for Closed Basin?

Natural Free Oscillation Period for Closed Basin calculator uses Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water)) to calculate the Natural Free Oscillating Period of a Basin, The Natural Free Oscillation Period for Closed Basin formula is defined as the time it takes for a waterbody within a closed or semi-enclosed basin, like a bay or a lagoon, to undergo a complete cycle of oscillation when disturbed from its equilibrium state. Natural Free Oscillating Period of a Basin is denoted by T_n symbol.

How to calculate Natural Free Oscillation Period for Closed Basin using this online calculator? To use this online calculator for Natural Free Oscillation Period for Closed Basin, enter Basin Length (L_B), Number of Nodes along the Axis of a Basin (N) & Depth of Water (D_w) and hit the calculate button. Here is how the Natural Free Oscillation Period for Closed Basin calculation can be explained with given input values -> 5.59876 = (2*180)/(1.3*sqrt([g]*105.4)).

FAQ

What is Natural Free Oscillation Period for Closed Basin?

The Natural Free Oscillation Period for Closed Basin formula is defined as the time it takes for a waterbody within a closed or semi-enclosed basin, like a bay or a lagoon, to undergo a complete cycle of oscillation when disturbed from its equilibrium state and is represented as T_n = (2*L_B)/(N*sqrt([g]*D_w)) or Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water)). Basin Length is the horizontal distance or extent of a water body, such as a bay, estuary, or lagoon. It is an important parameter in the design and analysis of coastal structures, Number of Nodes along the Axis of a Basin refers to specific points or segments along a central line (axis) of a coastal basin or water body & Depth of Water is the depth as measured from the water level to the bottom of the considered water body.

How to calculate Natural Free Oscillation Period for Closed Basin?

The Natural Free Oscillation Period for Closed Basin formula is defined as the time it takes for a waterbody within a closed or semi-enclosed basin, like a bay or a lagoon, to undergo a complete cycle of oscillation when disturbed from its equilibrium state is calculated using Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water)). To calculate Natural Free Oscillation Period for Closed Basin, you need Basin Length (L_B), Number of Nodes along the Axis of a Basin (N) & Depth of Water (D_w). With our tool, you need to enter the respective value for Basin Length, Number of Nodes along the Axis of a Basin & Depth of Water 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 Natural Free Oscillating Period of a Basin?

In this formula, Natural Free Oscillating Period of a Basin uses Basin Length, Number of Nodes along the Axis of a Basin & Depth of Water. We can use 6 other way(s) to calculate the same, which is/are as follows -

Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth at Harbor))*((Number of Nodes along the X-axis of Basin/Basin Dimensions along the X-axis)^2+(Number of Nodes along the Y-axis of Basin/Basin Dimensions along the Y-axis)^2)^-0.5
Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water))
Natural Free Oscillating Period of a Basin = (Wave Height*Wavelength)/(Average Horizontal Velocity at a Node*pi*Water Depth at Harbor)
Natural Free Oscillating Period of a Basin = 4*Basin Length/((1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))
Natural Free Oscillating Period of a Basin = 4*Basin Length/((1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))
Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth at Harbor))*((Number of Nodes along the X-axis of Basin/Basin Dimensions along the X-axis)^2+(Number of Nodes along the Y-axis of Basin/Basin Dimensions along the Y-axis)^2)^-0.5

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