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Channel Cross-sectional Area given Resonant Period for Helmholtz Mode Calculator

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✖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.ⓘ Surface Area [A_s]			+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%

✖Cross Sectional Area is the area of the channel when viewed in a plane perpendicular to the direction of flow.ⓘ Channel Cross-sectional Area given Resonant Period for Helmholtz Mode [A_C]

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Formula

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Channel Cross-sectional Area given Resonant Period for Helmholtz Mode

Formula

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

Example

0.199709 m² = (40.0 m + 20.0 m) \cdot \frac{30 m²}{[g] \cdot {(\frac{19.3 s}{2} \cdot π)}^{2}}

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Channel Cross-sectional Area given Resonant Period for Helmholtz Mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Channel Length (Helmholtz Mode): 40 Meter --> 40 Meter No Conversion Required
Additional Length of the Channel: 20 Meter --> 20 Meter No Conversion Required
Surface Area: 30 Square Meter --> 30 Square Meter No Conversion Required
Resonant Period: 19.3 Second --> 19.3 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_C = (L_ch+l'_c)*A_s/([g]*(T_r2/2*pi)^2) --> (40+20)*30/([g]*(19.3/2*pi)^2)

Evaluating ... ...

A_C = 0.19970891741606

STEP 3: Convert Result to Output's Unit

0.19970891741606 Square Meter --> No Conversion Required

FINAL ANSWER

0.19970891741606 ≈ 0.199709 Square Meter <-- Cross Sectional Area

(Calculation completed in 00.004 seconds)

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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 Cross-sectional Area given Resonant Period for Helmholtz Mode Formula

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

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 Cross-sectional Area given Resonant Period for Helmholtz Mode?

Channel Cross-sectional Area given Resonant Period for Helmholtz Mode calculator uses Cross Sectional Area = (Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area/([g]*(Resonant Period/2*pi)^2) to calculate the Cross Sectional Area, The Channel Cross-sectional Area given Resonant Period for Helmholtz Mode formula is defined as the specific area of a channel's cross-section that correlates with a particular resonant period, specifically in the context of the Helmholtz mode. The Helmholtz mode, in this context, is a fundamental oscillatory mode where the water in a coastal or ocean channel oscillates back and forth, often influenced by the geometry of the channel and the properties of the water. Cross Sectional Area is denoted by A_C symbol.

How to calculate Channel Cross-sectional Area given Resonant Period for Helmholtz Mode using this online calculator? To use this online calculator for Channel Cross-sectional Area given Resonant Period for Helmholtz Mode, enter Channel Length (Helmholtz Mode) (L_ch), Additional Length of the Channel (l'_c), Surface Area (A_s) & Resonant Period (T_r2) and hit the calculate button. Here is how the Channel Cross-sectional Area given Resonant Period for Helmholtz Mode calculation can be explained with given input values -> 0.199709 = (40+20)*30/([g]*(19.3/2*pi)^2).

FAQ

What is Channel Cross-sectional Area given Resonant Period for Helmholtz Mode?

The Channel Cross-sectional Area given Resonant Period for Helmholtz Mode formula is defined as the specific area of a channel's cross-section that correlates with a particular resonant period, specifically in the context of the Helmholtz mode. The Helmholtz mode, in this context, is a fundamental oscillatory mode where the water in a coastal or ocean channel oscillates back and forth, often influenced by the geometry of the channel and the properties of the water and is represented as A_C = (L_ch+l'_c)*A_s/([g]*(T_r2/2*pi)^2) or Cross Sectional Area = (Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area/([g]*(Resonant Period/2*pi)^2). 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, 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 & Resonant Period is the natural period of oscillation at which a body of water or a structure responds most strongly to external forcing.

How to calculate Channel Cross-sectional Area given Resonant Period for Helmholtz Mode?

The Channel Cross-sectional Area given Resonant Period for Helmholtz Mode formula is defined as the specific area of a channel's cross-section that correlates with a particular resonant period, specifically in the context of the Helmholtz mode. The Helmholtz mode, in this context, is a fundamental oscillatory mode where the water in a coastal or ocean channel oscillates back and forth, often influenced by the geometry of the channel and the properties of the water is calculated using Cross Sectional Area = (Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area/([g]*(Resonant Period/2*pi)^2). To calculate Channel Cross-sectional Area given Resonant Period for Helmholtz Mode, you need Channel Length (Helmholtz Mode) (L_ch), Additional Length of the Channel (l'_c), Surface Area (A_s) & Resonant Period (T_r2). With our tool, you need to enter the respective value for Channel Length (Helmholtz Mode), Additional Length of the Channel, Surface Area & Resonant Period 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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