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Additional Length Formula

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

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

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

Additional Length Example

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Here is how the Additional Length equation looks like with Values.

Here is how the Additional Length equation looks like with Units.

Here is how the Additional Length equation looks like.

20.0875 = (9.8066 \cdot 0.2 \cdot \frac{{(\frac{19.3}{2} \cdot 3.1416)}^{2}}{30}) - 40

20.0875m = (9.8066m/s² \cdot 0.2m² \cdot \frac{{(\frac{19.3s}{2} \cdot 3.1416)}^{2}}{30m²}) - 40m

20.0875 = (9.8066 \cdot 0.2 \cdot \frac{{(\frac{19.3}{2} \cdot 3.1416)}^{2}}{30}) - 40

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Additional Length Solution

Follow our step by step solution on how to calculate Additional Length?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l' c = ([g] \cdot 0.2m² \cdot \frac{{(\frac{19.3s}{2} \cdot π)}^{2}}{30m²}) - 40m

Next Step Substitute values of Constants

∴

l' c = (9.8066m/s² \cdot 0.2m² \cdot \frac{{(\frac{19.3s}{2} \cdot 3.1416)}^{2}}{30m²}) - 40m

Next Step Prepare to Evaluate

∴

l' c = (9.8066 \cdot 0.2 \cdot \frac{{(\frac{19.3}{2} \cdot 3.1416)}^{2}}{30}) - 40

Next Step Evaluate

∴

l' c = 20.0874520540313m

LAST Step Rounding Answer

∴

l' c = 20.0875m

Additional Length Formula Elements

Variables

Constants

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

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

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

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

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)

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 Horizontal Velocity at Node

V max = (\frac{H w}{2}) \cdot \sqrt{\frac{[g]}{D w}}

Go Standing Wave Height given Maximum Horizontal Velocity at Node

H w = (\frac{V max}{\sqrt{\frac{[g]}{D w}}}) \cdot 2

Go Water Depth given Maximum Horizontal Velocity at Node

D w = \frac{[g]}{{(\frac{V max}{\frac{H w}{2}})}^{2}}

Go Resonant Period for Helmholtz Mode

T H = (2 \cdot π) \cdot \sqrt{(L ch + l' c) \cdot \frac{A b}{[g] \cdot A C}}

How to Evaluate Additional Length?

Additional Length evaluator uses Additional Length of the Channel = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Channel Length (Helmholtz Mode) to evaluate the Additional Length of the Channel, The Additional Length formula is defined as the extended length of a structure or an element beyond its primary or original design length. This concept can apply to various aspects such as pipelines, breakwaters, groynes, jetties, or any coastal defense structure. Additional Length of the Channel is denoted by l'_c symbol.

How to evaluate Additional Length using this online evaluator? To use this online evaluator for Additional Length, enter Cross Sectional Area (A_C), Resonant Period (T_r2), Surface Area (A_s) & Channel Length (Helmholtz Mode) (L_ch) and hit the calculate button.

FAQs on Additional Length

What is the formula to find Additional Length?

The formula of Additional Length is expressed as Additional Length of the Channel = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Channel Length (Helmholtz Mode). Here is an example- 1161.669 = ([g]*0.2*(19.3/2*pi)^2/30)-40.

How to calculate Additional Length?

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

Can the Additional Length be negative?

No, the Additional Length, measured in Length cannot be negative.

Which unit is used to measure Additional Length?

Additional Length is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Additional Length can be measured.

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Additional Length Formula

Additional Length Example

Additional Length Solution

Additional Length Formula Elements

Other formulas in Harbor Oscillations category

How to Evaluate Additional Length?

FAQs on Additional Length

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