Period for Fundamental Mode Solution

STEP 0: Pre-Calculation Summary
Formula Used
Natural Free Oscillating Period of a Basin = (4*Length of Basin)/sqrt([g]*Water Depth)
Tn = (4*Lb)/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
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.
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. 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
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
Tn = (4*Lb)/sqrt([g]*d) --> (4*30)/sqrt([g]*1.05)
Evaluating ... ...
Tn = 37.3960953740745
STEP 3: Convert Result to Output's Unit
37.3960953740745 Second --> No Conversion Required
FINAL ANSWER
37.3960953740745 37.3961 Second <-- Natural Free Oscillating Period of a Basin
(Calculation completed in 00.004 seconds)

Credits

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]

Period for Fundamental Mode Formula

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

What are Open Basins?

Open Basins are Exorheic, or open lakes drain into a river, or other body of water that ultimately drains into the ocean.

What are Closed Basins?

Enclosed basins can experience oscillations due to a variety of causes. Lake oscillations are usually the result of a sudden change, or a series of intermittent-periodic changes, in atmospheric pressure or wind velocity. Oscillations in canals can be initiated by suddenly adding or subtracting large quantities of water. Harbor oscillations are usually initiated by forcing through the entrance; hence, they deviate from a true closed basin. Local seismic activity can also create oscillations in an enclosed basin.

How to Calculate Period for Fundamental Mode?

Period for Fundamental Mode calculator uses Natural Free Oscillating Period of a Basin = (4*Length of Basin)/sqrt([g]*Water Depth) to calculate the Natural Free Oscillating Period of a Basin, The Period for fundamental mode is a parameter defined when the number of nodes in the basin n does not include the node at the entrance. Natural Free Oscillating Period of a Basin is denoted by Tn symbol.

How to calculate Period for Fundamental Mode using this online calculator? To use this online calculator for Period for Fundamental Mode, enter Length of Basin (Lb) & Water Depth (d) and hit the calculate button. Here is how the Period for Fundamental Mode calculation can be explained with given input values -> 38.31959 = (4*30)/sqrt([g]*1.05).

FAQ

What is Period for Fundamental Mode?
The Period for fundamental mode is a parameter defined when the number of nodes in the basin n does not include the node at the entrance and is represented as Tn = (4*Lb)/sqrt([g]*d) or Natural Free Oscillating Period of a Basin = (4*Length of Basin)/sqrt([g]*Water Depth). Length of Basin or length of the drainage basin in kilometres & Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
How to calculate Period for Fundamental Mode?
The Period for fundamental mode is a parameter defined when the number of nodes in the basin n does not include the node at the entrance is calculated using Natural Free Oscillating Period of a Basin = (4*Length of Basin)/sqrt([g]*Water Depth). To calculate Period for Fundamental Mode, you need Length of Basin (Lb) & 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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