Natural Free Oscillation Period for Closed Basins Solution

STEP 0: Pre-Calculation Summary
Formula Used
Natural Free Oscillating Period of a Basin = (2*Harbour Basin Length)/(Number of nodes along the Axis of a Basin*sqrt([g]*Water Depth))
Tn = (2*LB)/(N*sqrt([g]*D))
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 have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.
Harbour Basin Length - (Measured in Meter) - Harbour Basin Length or Length of Basin is defined as the length of the drainage basin.
Number of nodes along the Axis of a Basin - Number of nodes along the Axis of a Basin where Basin axis is the lowest point on the basement surface.
Water Depth - (Measured in Meter) - Water depth means the depth as measured from the water level to the bottom of the considered water body.
STEP 1: Convert Input(s) to Base Unit
Harbour Basin Length: 40 Meter --> 40 Meter No Conversion Required
Number of nodes along the Axis of a Basin: 1.3 --> No Conversion Required
Water Depth: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tn = (2*LB)/(N*sqrt([g]*D)) --> (2*40)/(1.3*sqrt([g]*12))
Evaluating ... ...
Tn = 5.67277650793402
STEP 3: Convert Result to Output's Unit
5.67277650793402 Second --> No Conversion Required
FINAL ANSWER
5.67277650793402 5.672777 Second <-- Natural Free Oscillating Period of a Basin
(Calculation completed in 00.004 seconds)

Credits

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Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has created this Calculator and 2000+ more calculators!
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Verified by M Naveen
National Institute of Technology (NIT), Warangal
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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))*((Number of Nodes along the x-axes of Basin/Basin Dimensions along the x-axis)^2+(Number of Nodes along the y-axes 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)/(Standing Wave Height*sqrt([g]/Water Depth))
Natural Free Oscillation Period for Open Basin
​ Go Natural Free Oscillating Period of a Basin = 4*Harbour Basin Length/((1+(2*Number of nodes along the Axis of a Basin))*sqrt([g]*Water Depth))
Natural Free Oscillation Period for Closed Basins
​ Go Natural Free Oscillating Period of a Basin = (2*Harbour Basin Length)/(Number of nodes along the Axis of a Basin*sqrt([g]*Water Depth))
Natural Free Oscillation Period for Average Horizontal Velocity at Node
​ Go Natural Free Oscillating Period of a Basin = (Standing Wave Height*Wavelength)/(Average Horizontal Velocity at a Node*pi*Water Depth)
Water Depth given Natural Free Oscillation Period
​ Go Water Depth = (((2*Harbour Basin Length)/(Natural Free Oscillating Period of a Basin*Number of nodes along the Axis of a Basin))^2)/[g]

Natural Free Oscillation Period for Closed Basins Formula

Natural Free Oscillating Period of a Basin = (2*Harbour Basin Length)/(Number of nodes along the Axis of a Basin*sqrt([g]*Water Depth))
Tn = (2*LB)/(N*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 Natural Free Oscillation Period for Closed Basins?

Natural Free Oscillation Period for Closed Basins calculator uses Natural Free Oscillating Period of a Basin = (2*Harbour Basin Length)/(Number of nodes along the Axis of a Basin*sqrt([g]*Water Depth)) to calculate the Natural Free Oscillating Period of a Basin, The Natural Free Oscillation Period for Closed Basins, assuming water is inviscid and incompressible basin oscillations involve standing waves in shallow water. The simplest basin geometry is a narrow rectangular basin with vertical sides and uniform depth. Natural Free Oscillating Period of a Basin is denoted by Tn symbol.

How to calculate Natural Free Oscillation Period for Closed Basins using this online calculator? To use this online calculator for Natural Free Oscillation Period for Closed Basins, enter Harbour Basin Length (LB), Number of nodes along the Axis of a Basin (N) & Water Depth (D) and hit the calculate button. Here is how the Natural Free Oscillation Period for Closed Basins calculation can be explained with given input values -> 5.672777 = (2*40)/(1.3*sqrt([g]*12)).

FAQ

What is Natural Free Oscillation Period for Closed Basins?
The Natural Free Oscillation Period for Closed Basins, assuming water is inviscid and incompressible basin oscillations involve standing waves in shallow water. The simplest basin geometry is a narrow rectangular basin with vertical sides and uniform depth and is represented as Tn = (2*LB)/(N*sqrt([g]*D)) or Natural Free Oscillating Period of a Basin = (2*Harbour Basin Length)/(Number of nodes along the Axis of a Basin*sqrt([g]*Water Depth)). Harbour Basin Length or Length of Basin is defined as the length of the drainage basin, Number of nodes along the Axis of a Basin where Basin axis is the lowest point on the basement surface & Water depth means 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 Basins?
The Natural Free Oscillation Period for Closed Basins, assuming water is inviscid and incompressible basin oscillations involve standing waves in shallow water. The simplest basin geometry is a narrow rectangular basin with vertical sides and uniform depth is calculated using Natural Free Oscillating Period of a Basin = (2*Harbour Basin Length)/(Number of nodes along the Axis of a Basin*sqrt([g]*Water Depth)). To calculate Natural Free Oscillation Period for Closed Basins, you need Harbour Basin Length (LB), Number of nodes along the Axis of a Basin (N) & Water Depth (D). With our tool, you need to enter the respective value for Harbour Basin Length, Number of nodes along the Axis of a Basin & Water Depth 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 Harbour Basin Length, Number of nodes along the Axis of a Basin & Water Depth. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth))*((Number of Nodes along the x-axes of Basin/Basin Dimensions along the x-axis)^2+(Number of Nodes along the y-axes of Basin/Basin Dimensions along the y-axis)^2)^-0.5
  • Natural Free Oscillating Period of a Basin = 4*Harbour Basin Length/((1+(2*Number of nodes along the Axis of a Basin))*sqrt([g]*Water Depth))
  • Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Standing Wave Height*sqrt([g]/Water Depth))
  • Natural Free Oscillating Period of a Basin = (Standing Wave Height*Wavelength)/(Average Horizontal Velocity at a Node*pi*Water Depth)
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