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

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✖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.ⓘ Channel Width corresponding to Mean Water Depth [W]			+10% -10%
✖Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit.ⓘ Channel Depth [D_t]			+10% -10%
✖Resonant Period for Helmholtz Mode is the specific time period at which a resonant oscillation occurs in a system exhibiting Helmholtz resonance.ⓘ Resonant Period for Helmholtz Mode [T_H]			+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 to Account for Mass Outside Each End of Channel [l'_c]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
l'_c = (-W/pi)*ln(pi*W/(sqrt([g]*D_t)*T_H))
This formula uses 2 Constants, 2 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., 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., sqrt(Number)

Variables Used

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.
Channel Width corresponding to Mean Water Depth - (Measured in Meter) - 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.
Channel Depth - (Measured in Meter) - Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit.
Resonant Period for Helmholtz Mode - (Measured in Second) - Resonant Period for Helmholtz Mode is the specific time period at which a resonant oscillation occurs in a system exhibiting Helmholtz resonance.

STEP 1: Convert Input(s) to Base Unit

Channel Width corresponding to Mean Water Depth: 52 Meter --> 52 Meter No Conversion Required
Channel Depth: 5.01 Meter --> 5.01 Meter No Conversion Required
Resonant Period for Helmholtz Mode: 50 Second --> 50 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l'_c = (-W/pi)*ln(pi*W/(sqrt([g]*D_t)*T_H)) --> (-52/pi)*ln(pi*52/(sqrt([g]*5.01)*50))

Evaluating ... ...

l'_c = 12.6341909733244

STEP 3: Convert Result to Output's Unit

12.6341909733244 Meter --> No Conversion Required

FINAL ANSWER

12.6341909733244 ≈ 12.63419 Meter <-- Additional Length of the Channel

(Calculation completed in 00.004 seconds)

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< Harbor Oscillations Calculators

Period for Fundamental Mode

LaTeX 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

LaTeX Go Length of Basin along Axis = Maximum Oscillation Period*sqrt([g]*Water Depth)/2

Maximum Oscillation Period corresponding to Fundamental Mode

LaTeX Go Maximum Oscillation Period = 2*Length of Basin along Axis/sqrt([g]*Water Depth)

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

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

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

LaTeX Go

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

Additional Length to Account for Mass Outside Each End of Channel calculator 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 calculate 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 calculate Additional Length to Account for Mass Outside Each End of Channel using this online calculator? To use this online calculator 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. Here is how the Additional Length to Account for Mass Outside Each End of Channel calculation can be explained with given input values -> 12.63419 = (-52/pi)*ln(pi*52/(sqrt([g]*5.01)*50)).

FAQ

What is Additional Length to Account for Mass Outside Each End of 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 and is represented as l'_c = (-W/pi)*ln(pi*W/(sqrt([g]*D_t)*T_H)) or 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)). 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, Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit & Resonant Period for Helmholtz Mode is the specific time period at which a resonant oscillation occurs in a system exhibiting Helmholtz resonance.

How to calculate Additional Length to Account for Mass Outside Each End of 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 is calculated using 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 calculate Additional Length to Account for Mass Outside Each End of Channel, you need Channel Width corresponding to Mean Water Depth (W), Channel Depth (D_t) & Resonant Period for Helmholtz Mode (T_H). With our tool, you need to enter the respective value for Channel Width corresponding to Mean Water Depth, Channel Depth & Resonant Period for Helmholtz Mode and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Additional Length of the Channel?

In this formula, Additional Length of the Channel uses Channel Width corresponding to Mean Water Depth, Channel Depth & Resonant Period for Helmholtz Mode. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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