Basin Surface Area given Resonant Period for Helmholtz mode Calculator

✖Channel Cross-sectional Area [length^2] is the cross sectional area of the channel.ⓘ Channel Cross-sectional Area [A_C]			+10% -10%
✖Resonant Period for Helmholtz Mode [time], Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity.ⓘ Resonant Period for Helmholtz Mode [T_H]			+10% -10%
✖Channel Length is the measurement or extent of water wider than a strait, joining two larger areas of water.ⓘ Channel Length [L_c]			+10% -10%
✖Additional Length of the Channel to account for Mass Outside each end of the Channel.ⓘ Additional Length of the Channel [l'_c]			+10% -10%

✖Surface Area of Bay is defined as a small body of water set off from the main body.ⓘ Basin Surface Area given Resonant Period for Helmholtz mode [A_b]

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Basin Surface Area given Resonant Period for Helmholtz mode

Formula

`"A"_{"b"} = ("[g]"*"A"_{"C"}*("T"_{"H"}/2*pi)^2/("L"_{"c"}+"l'"_{"c"}))`

Example

`"10082.06m²"=("[g]"*"10m²"*("50s"/2*pi)^2/("40m"+"20m"))`

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Basin Surface Area given Resonant Period for Helmholtz mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel))
A_b = ([g]*A_C*(T_H/2*pi)^2/(L_c+l'_c))
This formula uses 2 Constants, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Surface Area of Bay - (Measured in Square Meter) - Surface Area of Bay is defined as a small body of water set off from the main body.
Channel Cross-sectional Area - (Measured in Square Meter) - Channel Cross-sectional Area [length^2] is the cross sectional area of the channel.
Resonant Period for Helmholtz Mode - (Measured in Second) - Resonant Period for Helmholtz Mode [time], Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity.
Channel Length - (Measured in Meter) - Channel Length is the measurement or extent of water wider than a strait, joining two larger areas of water.
Additional Length of the Channel - (Measured in Meter) - Additional Length of the Channel to account for Mass Outside each end of the Channel.

STEP 1: Convert Input(s) to Base Unit

Channel Cross-sectional Area: 10 Square Meter --> 10 Square Meter No Conversion Required
Resonant Period for Helmholtz Mode: 50 Second --> 50 Second No Conversion Required
Channel Length: 40 Meter --> 40 Meter No Conversion Required
Additional Length of the Channel: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_b = ([g]*A_C*(T_H/2*pi)^2/(L_c+l'_c)) --> ([g]*10*(50/2*pi)^2/(40+20))

Evaluating ... ...

A_b = 10082.0579166607

STEP 3: Convert Result to Output's Unit

10082.0579166607 Square Meter --> No Conversion Required

FINAL ANSWER

10082.0579166607 ≈ 10082.06 Square Meter <-- Surface Area of Bay

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Basin Surface Area given Resonant Period for Helmholtz mode

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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]

Basin Surface Area given Resonant Period for Helmholtz mode Formula

Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel))
A_b = ([g]*A_C*(T_H/2*pi)^2/(L_c+l'_c))

What are Open basins - Helmholtz resonance?

A harbor basin open to the sea through an inlet can resonate in a mode referred to as the Helmholtz or grave mode (Sorensen 1986b). This very long period mode appears to be particularly significant for harbors responding to tsunami energy and for several harbors on the Great Lakes that respond to long-wave energy spectra generated by storms (Miles 1974; Sorensen 1986; Sorensen and Seelig 1976).

How to Calculate Basin Surface Area given Resonant Period for Helmholtz mode?

Basin Surface Area given Resonant Period for Helmholtz mode calculator uses Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel)) to calculate the Surface Area of Bay, The Basin Surface Area given Resonant Period for Helmholtz mode is defined as the area of a small body of water set off from the main body. Surface Area of Bay is denoted by A_b symbol.

How to calculate Basin Surface Area given Resonant Period for Helmholtz mode using this online calculator? To use this online calculator for Basin Surface Area given Resonant Period for Helmholtz mode, enter Channel Cross-sectional Area (A_C), Resonant Period for Helmholtz Mode (T_H), Channel Length (L_c) & Additional Length of the Channel (l'_c) and hit the calculate button. Here is how the Basin Surface Area given Resonant Period for Helmholtz mode calculation can be explained with given input values -> 10082.06 = ([g]*10*(50/2*pi)^2/(40+20)).

FAQ

What is Basin Surface Area given Resonant Period for Helmholtz mode?

The Basin Surface Area given Resonant Period for Helmholtz mode is defined as the area of a small body of water set off from the main body and is represented as A_b = ([g]*A_C*(T_H/2*pi)^2/(L_c+l'_c)) or Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel)). Channel Cross-sectional Area [length^2] is the cross sectional area of the channel, Resonant Period for Helmholtz Mode [time], Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity, Channel Length is the measurement or extent of water wider than a strait, joining two larger areas of water & Additional Length of the Channel to account for Mass Outside each end of the Channel.

How to calculate Basin Surface Area given Resonant Period for Helmholtz mode?

The Basin Surface Area given Resonant Period for Helmholtz mode is defined as the area of a small body of water set off from the main body is calculated using Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel)). To calculate Basin Surface Area given Resonant Period for Helmholtz mode, you need Channel Cross-sectional Area (A_C), Resonant Period for Helmholtz Mode (T_H), Channel Length (L_c) & Additional Length of the Channel (l'_c). With our tool, you need to enter the respective value for Channel Cross-sectional Area, Resonant Period for Helmholtz Mode, Channel Length & Additional Length of the Channel 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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