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

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Cross Sectional Area is the area of the channel when viewed in a plane perpendicular to the direction of flow. Check FAQs

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

A_C - Cross Sectional Area?L_ch - Channel Length (Helmholtz Mode)?l'_c - Additional Length of the Channel?A_s - Surface Area?T_r2 - Resonant Period?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

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

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Here is how the Channel Cross-sectional Area given Resonant Period for Helmholtz Mode equation looks like with Values.

Here is how the Channel Cross-sectional Area given Resonant Period for Helmholtz Mode equation looks like with Units.

Here is how the Channel Cross-sectional Area given Resonant Period for Helmholtz Mode equation looks like.

0.1997 = (40 + 20) \cdot \frac{30}{9.8066 \cdot {(\frac{19.3}{2} \cdot 3.1416)}^{2}}

0.1997m² = (40m + 20m) \cdot \frac{30m²}{9.8066m/s² \cdot {(\frac{19.3s}{2} \cdot 3.1416)}^{2}}

0.1997 = (40 + 20) \cdot \frac{30}{9.8066 \cdot {(\frac{19.3}{2} \cdot 3.1416)}^{2}}

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

Follow our step by step solution on how to calculate Channel Cross-sectional Area given Resonant Period for Helmholtz Mode?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A C = (40m + 20m) \cdot \frac{30m²}{[g] \cdot {(\frac{19.3s}{2} \cdot π)}^{2}}

Next Step Substitute values of Constants

∴

A C = (40m + 20m) \cdot \frac{30m²}{9.8066m/s² \cdot {(\frac{19.3s}{2} \cdot 3.1416)}^{2}}

Next Step Prepare to Evaluate

∴

A C = (40 + 20) \cdot \frac{30}{9.8066 \cdot {(\frac{19.3}{2} \cdot 3.1416)}^{2}}

Next Step Evaluate

∴

A C = 0.19970891741606m²

LAST Step Rounding Answer

∴

A C = 0.1997m²

Channel Cross-sectional Area given Resonant Period for Helmholtz Mode Formula Elements

Variables

Constants

Cross Sectional Area

Cross Sectional Area is the area of the channel when viewed in a plane perpendicular to the direction of flow.

Symbol: A_C

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Cross Sectional Area

Channel Length (Helmholtz Mode)

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.

Symbol: L_ch

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Channel Length (Helmholtz Mode)

Additional Length of the Channel

Additional Length of the Channel refers to the extra distance required in a channel or conduit to accommodate certain flow characteristics or conditions.

Symbol: l'_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Additional Length of the Channel

Surface Area

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.

Symbol: A_s

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Surface Area

Resonant Period

Resonant Period is the natural period of oscillation at which a body of water or a structure responds most strongly to external forcing.

Symbol: T_r2

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Resonant Period

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Harbor Oscillations category

Go Maximum Oscillation Period corresponding to Fundamental Mode

T 1 = 2 \cdot \frac{L ba}{\sqrt{[g] \cdot D}}

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

L ba = T 1 \cdot \frac{\sqrt{[g] \cdot D}}{2}

Go Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

d = \frac{{(2 \cdot \frac{L ba}{T n})}^{2}}{[g]}

Go Period for Fundamental Mode

T n = \frac{4 \cdot L ba}{\sqrt{[g] \cdot d}}

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

Channel Cross-sectional Area given Resonant Period for Helmholtz Mode evaluator uses Cross Sectional Area = (Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area/([g]*(Resonant Period/2*pi)^2) to evaluate 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 evaluate Channel Cross-sectional Area given Resonant Period for Helmholtz Mode using this online evaluator? To use this online evaluator 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.

FAQs on Channel Cross-sectional Area given Resonant Period for Helmholtz Mode

What is the formula to find Channel Cross-sectional Area given Resonant Period for Helmholtz Mode?

The formula of Channel Cross-sectional Area given Resonant Period for Helmholtz Mode is expressed as Cross Sectional Area = (Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area/([g]*(Resonant Period/2*pi)^2). Here is an example- 0.199709 = (40+20)*30/([g]*(19.3/2*pi)^2).

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

With Channel Length (Helmholtz Mode) (L_ch), Additional Length of the Channel (l'_c), Surface Area (A_s) & Resonant Period (T_r2) we can find Channel Cross-sectional Area given Resonant Period for Helmholtz Mode using the formula - Cross Sectional Area = (Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area/([g]*(Resonant Period/2*pi)^2). This formula also uses Gravitational acceleration on Earth, Archimedes' constant .

Can the Channel Cross-sectional Area given Resonant Period for Helmholtz Mode be negative?

Yes, the Channel Cross-sectional Area given Resonant Period for Helmholtz Mode, measured in Area can be negative.

Which unit is used to measure Channel Cross-sectional Area given Resonant Period for Helmholtz Mode?

Channel Cross-sectional Area given Resonant Period for Helmholtz Mode is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Channel Cross-sectional Area given Resonant Period for Helmholtz Mode can be measured.

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

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

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

Channel Cross-sectional Area given Resonant Period for Helmholtz Mode Formula Elements

Other formulas in Harbor Oscillations category

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

FAQs on Channel Cross-sectional Area given Resonant Period for Helmholtz Mode

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