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Additional Length to Account for Mass Outside Each End of Channel 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 = (- \frac{W}{π}) \cdot \ln (π \cdot \frac{W}{\sqrt{[g] \cdot D t} \cdot T H})

l'_c - Additional Length of the Channel?W - Channel Width corresponding to Mean Water Depth?D_t - Channel Depth?T_H - Resonant Period for Helmholtz Mode?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Additional Length to Account for Mass Outside Each End of Channel Example

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Here is how the Additional Length to Account for Mass Outside Each End of Channel equation looks like with Values.

Here is how the Additional Length to Account for Mass Outside Each End of Channel equation looks like with Units.

Here is how the Additional Length to Account for Mass Outside Each End of Channel equation looks like.

12.6342 = (- \frac{52}{3.1416}) \cdot \ln (3.1416 \cdot \frac{52}{\sqrt{9.8066 \cdot 5.01} \cdot 50})

12.6342m = (- \frac{52m}{3.1416}) \cdot \ln (3.1416 \cdot \frac{52m}{\sqrt{9.8066m/s² \cdot 5.01m} \cdot 50s})

12.6342 = (- \frac{52}{3.1416}) \cdot \ln (3.1416 \cdot \frac{52}{\sqrt{9.8066 \cdot 5.01} \cdot 50})

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Additional Length to Account for Mass Outside Each End of Channel Solution

Follow our step by step solution on how to calculate Additional Length to Account for Mass Outside Each End of Channel?

FIRST Step Consider the formula

l' c = (- \frac{W}{π}) \cdot \ln (π \cdot \frac{W}{\sqrt{[g] \cdot D t} \cdot T H})

Next Step Substitute values of Variables

∴

l' c = (- \frac{52m}{π}) \cdot \ln (π \cdot \frac{52m}{\sqrt{[g] \cdot 5.01m} \cdot 50s})

Next Step Substitute values of Constants

∴

l' c = (- \frac{52m}{3.1416}) \cdot \ln (3.1416 \cdot \frac{52m}{\sqrt{9.8066m/s² \cdot 5.01m} \cdot 50s})

Next Step Prepare to Evaluate

∴

l' c = (- \frac{52}{3.1416}) \cdot \ln (3.1416 \cdot \frac{52}{\sqrt{9.8066 \cdot 5.01} \cdot 50})

Next Step Evaluate

∴

l' c = 12.6341909733244m

LAST Step Rounding Answer

∴

l' c = 12.6342m

Additional Length to Account for Mass Outside Each End of Channel Formula Elements

Variables

Constants

Functions

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

Channel Width corresponding to Mean Water Depth

Channel Width corresponding to Mean Water Depth is the width of a natural or engineered channel where the average depth of the water is taken into consideration.

Symbol: W

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Channel Width corresponding to Mean Water Depth

Channel Depth

Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit.

Symbol: D_t

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Channel Depth

Resonant Period for Helmholtz Mode

Resonant Period for Helmholtz Mode is the specific time period at which a resonant oscillation occurs in a system exhibiting Helmholtz resonance.

Symbol: T_H

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Resonant Period for 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

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Additional Length of the Channel

Go Additional Length

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

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 Additional Length to Account for Mass Outside Each End of Channel?

Additional Length to Account for Mass Outside Each End of Channel evaluator uses 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)) to evaluate the Additional Length of the Channel, The Additional Length to Account for Mass Outside Each End of Channel formula is defined as a length parameter influencing the resonant period for Helmholtz mode. Additional Length of the Channel is denoted by l'_c symbol.

How to evaluate Additional Length to Account for Mass Outside Each End of Channel using this online evaluator? To use this online evaluator for Additional Length to Account for Mass Outside Each End of Channel, enter Channel Width corresponding to Mean Water Depth (W), Channel Depth (D_t) & Resonant Period for Helmholtz Mode (T_H) and hit the calculate button.

FAQs on Additional Length to Account for Mass Outside Each End of Channel

What is the formula to find Additional Length to Account for Mass Outside Each End of Channel?

The formula of Additional Length to Account for Mass Outside Each End of Channel is expressed as 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)). Here is an example- 12.63419 = (-52/pi)*ln(pi*52/(sqrt([g]*5.01)*50)).

How to calculate Additional Length to Account for Mass Outside Each End of Channel?

With Channel Width corresponding to Mean Water Depth (W), Channel Depth (D_t) & Resonant Period for Helmholtz Mode (T_H) we can find Additional Length to Account for Mass Outside Each End of Channel using the formula - 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)). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and , Natural Logarithm (ln), Square Root (sqrt) function(s).

What are the other ways to Calculate Additional Length of the Channel?

Here are the different ways to Calculate Additional Length of the Channel-

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

Can the Additional Length to Account for Mass Outside Each End of Channel be negative?

No, the Additional Length to Account for Mass Outside Each End of Channel, measured in Length cannot be negative.

Which unit is used to measure Additional Length to Account for Mass Outside Each End of Channel?

Additional Length to Account for Mass Outside Each End of Channel is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Additional Length to Account for Mass Outside Each End of Channel can be measured.

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Additional Length to Account for Mass Outside Each End of Channel Formula

​GoAdditional Length Formula

Additional Length to Account for Mass Outside Each End of Channel Example

Additional Length to Account for Mass Outside Each End of Channel Solution

Additional Length to Account for Mass Outside Each End of Channel Formula Elements

Other Formulas to find Additional Length of the Channel

Other formulas in Harbor Oscillations category

How to Evaluate Additional Length to Account for Mass Outside Each End of Channel?

FAQs on Additional Length to Account for Mass Outside Each End of Channel

Variable Name

GoAdditional Length Formula