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Basin Surface Area given Resonant Period for Helmholtz Mode Calculator

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✖Cross Sectional Area is the area of the channel when viewed in a plane perpendicular to the direction of flow.ⓘ Cross Sectional Area [A_C]			+10% -10%
✖Resonant Period is the natural period of oscillation at which a body of water or a structure responds most strongly to external forcing.ⓘ Resonant Period [T_r2]			+10% -10%
✖Channel Length (Helmholtz Mode) is the specific length of a coastal channel at which the natural frequency of the channel matches the frequency of incoming waves, leading to resonance.ⓘ Channel Length (Helmholtz Mode) [L_ch]			+10% -10%
✖Additional Length of the Channel refers to the extra distance required in a channel or conduit to accommodate certain flow characteristics or conditions.ⓘ Additional Length of the Channel [l'_c]			+10% -10%

✖Surface Area is the extent of a two-dimensional surface within a three-dimensional space. This surface can pertain to various natural and man-made structures and phenomena.ⓘ Basin Surface Area given Resonant Period for Helmholtz Mode [A_s]

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Basin Surface Area given Resonant Period for Helmholtz Mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface Area = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/(Channel Length (Helmholtz Mode)+Additional Length of the Channel))
A_s = ([g]*A_C*(T_r2/2*pi)^2/(L_ch+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 - (Measured in Square Meter) - Surface Area is the extent of a two-dimensional surface within a three-dimensional space. This surface can pertain to various natural and man-made structures and phenomena.
Cross Sectional Area - (Measured in Square Meter) - Cross Sectional Area is the area of the channel when viewed in a plane perpendicular to the direction of flow.
Resonant Period - (Measured in Second) - Resonant Period is the natural period of oscillation at which a body of water or a structure responds most strongly to external forcing.
Channel Length (Helmholtz Mode) - (Measured in Meter) - Channel Length (Helmholtz Mode) is the specific length of a coastal channel at which the natural frequency of the channel matches the frequency of incoming waves, leading to resonance.
Additional Length of the Channel - (Measured in Meter) - Additional Length of the Channel refers to the extra distance required in a channel or conduit to accommodate certain flow characteristics or conditions.

STEP 1: Convert Input(s) to Base Unit

Cross Sectional Area: 0.2 Square Meter --> 0.2 Square Meter No Conversion Required
Resonant Period: 19.3 Second --> 19.3 Second No Conversion Required
Channel Length (Helmholtz Mode): 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_s = ([g]*A_C*(T_r2/2*pi)^2/(L_ch+l'_c)) --> ([g]*0.2*(19.3/2*pi)^2/(40+20))

Evaluating ... ...

A_s = 30.0437260270156

STEP 3: Convert Result to Output's Unit

30.0437260270156 Square Meter --> No Conversion Required

FINAL ANSWER

30.0437260270156 ≈ 30.04373 Square Meter <-- Surface Area

(Calculation completed in 00.020 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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< Harbor Oscillations Calculators

Period for Fundamental Mode

LaTeX Go Natural Free Oscillating Period of a Basin = (4*Length of Basin along Axis)/sqrt([g]*Water Depth at Harbor)

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

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

Maximum Oscillation Period corresponding to Fundamental Mode

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

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

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

Basin Surface Area given Resonant Period for Helmholtz Mode Formula

LaTeX Go

Surface Area = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/(Channel Length (Helmholtz Mode)+Additional Length of the Channel))
A_s = ([g]*A_C*(T_r2/2*pi)^2/(L_ch+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 = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/(Channel Length (Helmholtz Mode)+Additional Length of the Channel)) to calculate the Surface Area, The Basin Surface Area given Resonant Period for Helmholtz Mode formula is defined as the relationship between the surface area of a basin (such as a bay, harbor, or estuary) and its natural resonant period for Helmholtz oscillations. Surface Area is denoted by A_s 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 Cross Sectional Area (A_C), Resonant Period (T_r2), Channel Length (Helmholtz Mode) (L_ch) & 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 -> 30.04373 = ([g]*0.2*(19.3/2*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 formula is defined as the relationship between the surface area of a basin (such as a bay, harbor, or estuary) and its natural resonant period for Helmholtz oscillations and is represented as A_s = ([g]*A_C*(T_r2/2*pi)^2/(L_ch+l'_c)) or Surface Area = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/(Channel Length (Helmholtz Mode)+Additional Length of the Channel)). Cross Sectional Area is the area of the channel when viewed in a plane perpendicular to the direction of flow, Resonant Period is the natural period of oscillation at which a body of water or a structure responds most strongly to external forcing, Channel Length (Helmholtz Mode) is the specific length of a coastal channel at which the natural frequency of the channel matches the frequency of incoming waves, leading to resonance & Additional Length of the Channel refers to the extra distance required in a channel or conduit to accommodate certain flow characteristics or conditions.

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

The Basin Surface Area given Resonant Period for Helmholtz Mode formula is defined as the relationship between the surface area of a basin (such as a bay, harbor, or estuary) and its natural resonant period for Helmholtz oscillations is calculated using Surface Area = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/(Channel Length (Helmholtz Mode)+Additional Length of the Channel)). To calculate Basin Surface Area given Resonant Period for Helmholtz Mode, you need Cross Sectional Area (A_C), Resonant Period (T_r2), Channel Length (Helmholtz Mode) (L_ch) & Additional Length of the Channel (l'_c). With our tool, you need to enter the respective value for Cross Sectional Area, Resonant Period, Channel Length (Helmholtz Mode) & 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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