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

Formula

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

Example

`"0.199709m²"=("40.0m"+"20.0m")*"30m²"/("[g]"*("19.3s"/2*pi)^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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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Channel Cross-sectional Area given Resonant Period for Helmholtz Mode

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< 21 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 (Helmholtz Mode)+Additional Length of the Channel)*Surface Area of Bay/([g]*Cross Sectional Area))

Maximum Horizontal Particle Excursion at Node

Go Maximum Horizontal Particle Excursion = (Standing Wave Height of Ocean*Natural Free Oscillating Period of a Basin/2*pi)*sqrt([g]/Water Depth)

Standing Wave Height given Maximum Horizontal Particle Excursion at Node

Go Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth at Harbor)

Channel Cross-sectional Area given Resonant Period for Helmholtz Mode

Go Cross Sectional Area = (Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area/([g]*(Resonant Period/2*pi)^2)

Basin Surface Area given Resonant Period for Helmholtz Mode

Go Surface Area = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/(Channel Length (Helmholtz Mode)+Additional Length of the Channel))

Channel Length for Resonant Period for Helmholtz Mode

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

Additional Length

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

Basin Length along Axis in Open Basin

Go Length of Open Basin along Axis = (Natural Free Oscillating Period of a Basin*(1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))/4

Average Horizontal Velocity at Node

Go Average Horizontal Velocity at a Node = (Standing Wave Height of Ocean*Wavelength)/pi*Water Depth at Harbor*Natural Free Oscillating Period of a Basin

Water Depth given Average Horizontal Velocity at Node

Go Water Depth = (Standing Wave Height of Ocean*Wavelength)/Average Horizontal Velocity at a Node*pi*Natural Free Oscillating Period of a Basin

Standing Wave Height for Average Horizontal Velocity at Node

Go Wave Height = (Average Horizontal Velocity at a Node*pi*Water Depth at Harbor*Natural Free Oscillating Period of a Basin)/Wavelength

Wave Length for Average Horizontal Velocity at Node

Go Wavelength = (Average Horizontal Velocity at a Node*pi*Water Depth at Harbor*Natural Free Oscillating Period of a Basin)/Wave Height

Water Depth given Maximum Horizontal Particle Excursion at Node

Go Water Depth at Harbor = [g]/(2*pi*Maximum Horizontal Particle Excursion/Wave Height*Natural Free Oscillating Period of a Basin)^2

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 for given Period of Fundamental Mode

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

Maximum Horizontal Velocity at Node

Go Maximum Horizontal Velocity at a Node = (Standing Wave Height of Ocean/2)*sqrt([g]/Depth of Water)

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 for given Period for Fundamental Mode

Go Water Depth at Harbor = ((4*Length of Basin along Axis/Natural Free Oscillating Period of a Basin)^2)/[g]

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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