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Channel Length for 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%
✖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.ⓘ Surface Area [A_s]			+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%

✖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 for Resonant Period for Helmholtz Mode [L_ch]

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Formula

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Channel Length for Resonant Period for Helmholtz Mode

Formula

L ch = ([g] \cdot A C \cdot \frac{{(\frac{T r 2}{2} \cdot π)}^{2}}{A s}) - l' c

Example

40.08745 m = ([g] \cdot 0.20 m² \cdot \frac{{(\frac{19.3 s}{2} \cdot π)}^{2}}{30 m²}) - 20.0 m

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Channel Length for Resonant Period for Helmholtz Mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

Channel Length (Helmholtz Mode) = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Additional Length of the Channel
L_ch = ([g]*A_C*(T_r2/2*pi)^2/A_s)-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

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.
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.
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.
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
Surface Area: 30 Square Meter --> 30 Square 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

L_ch = ([g]*A_C*(T_r2/2*pi)^2/A_s)-l'_c --> ([g]*0.2*(19.3/2*pi)^2/30)-20

Evaluating ... ...

L_ch = 40.0874520540313

STEP 3: Convert Result to Output's Unit

40.0874520540313 Meter --> No Conversion Required

FINAL ANSWER

40.0874520540313 ≈ 40.08745 Meter <-- Channel Length (Helmholtz Mode)

(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< Harbor Oscillations Calculators

Period for Fundamental Mode

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

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

Maximum Oscillation Period corresponding to Fundamental Mode

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

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

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

Channel Length for Resonant Period for Helmholtz Mode Formula

Channel Length (Helmholtz Mode) = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Additional Length of the Channel
L_ch = ([g]*A_C*(T_r2/2*pi)^2/A_s)-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 Channel Length for Resonant Period for Helmholtz Mode?

Channel Length for Resonant Period for Helmholtz Mode calculator uses Channel Length (Helmholtz Mode) = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Additional Length of the Channel to calculate the Channel Length (Helmholtz Mode), The Channel Length for Resonant Period for Helmholtz Mode formula is defined as the number of intermediaries in a particular distribution channel between the source & channel end point. Channel Length (Helmholtz Mode) is denoted by L_ch symbol.

How to calculate Channel Length for Resonant Period for Helmholtz Mode using this online calculator? To use this online calculator for Channel Length for Resonant Period for Helmholtz Mode, enter Cross Sectional Area (A_C), Resonant Period (T_r2), Surface Area (A_s) & Additional Length of the Channel (l'_c) and hit the calculate button. Here is how the Channel Length for Resonant Period for Helmholtz Mode calculation can be explained with given input values -> 40.08745 = ([g]*0.2*(19.3/2*pi)^2/30)-20.

FAQ

What is Channel Length for Resonant Period for Helmholtz Mode?

The Channel Length for Resonant Period for Helmholtz Mode formula is defined as the number of intermediaries in a particular distribution channel between the source & channel end point and is represented as L_ch = ([g]*A_C*(T_r2/2*pi)^2/A_s)-l'_c or Channel Length (Helmholtz Mode) = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-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, 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 & 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 Channel Length for Resonant Period for Helmholtz Mode?

The Channel Length for Resonant Period for Helmholtz Mode formula is defined as the number of intermediaries in a particular distribution channel between the source & channel end point is calculated using Channel Length (Helmholtz Mode) = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Additional Length of the Channel. To calculate Channel Length for Resonant Period for Helmholtz Mode, you need Cross Sectional Area (A_C), Resonant Period (T_r2), Surface Area (A_s) & Additional Length of the Channel (l'_c). With our tool, you need to enter the respective value for Cross Sectional Area, Resonant Period, Surface Area & 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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