Additional Length accounting for Mass Outside each End of Channel Solution

STEP 0: Pre-Calculation Summary
Formula Used
Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length
l'c = ([g]*AC*(TH/2*pi)^2/Ab)-Lc
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
Additional Length of the Channel - (Measured in Meter) - Additional Length of the Channel to account for Mass Outside each end of the Channel.
Channel Cross-sectional Area - (Measured in Square Meter) - Channel Cross-sectional Area [length^2] is the cross sectional area of the channel.
Resonant Period for Helmholtz Mode - (Measured in Second) - Resonant Period for Helmholtz Mode [time], Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity.
Surface Area of Bay - (Measured in Square Meter) - Surface Area of Bay is defined as a small body of water set off from the main body.
Channel Length - (Measured in Meter) - Channel Length is the measurement or extent of water wider than a strait, joining two larger areas of water.
STEP 1: Convert Input(s) to Base Unit
Channel Cross-sectional Area: 10 Square Meter --> 10 Square Meter No Conversion Required
Resonant Period for Helmholtz Mode: 50 Second --> 50 Second No Conversion Required
Surface Area of Bay: 1.5001 Square Meter --> 1.5001 Square Meter No Conversion Required
Channel Length: 40 Meter --> 40 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l'c = ([g]*AC*(TH/2*pi)^2/Ab)-Lc --> ([g]*10*(50/2*pi)^2/1.5001)-40
Evaluating ... ...
l'c = 403215.432970898
STEP 3: Convert Result to Output's Unit
403215.432970898 Meter --> No Conversion Required
FINAL ANSWER
403215.432970898 403215.4 Meter <-- Additional Length of the Channel
(Calculation completed in 00.004 seconds)

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22 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+Additional Length of the Channel)*Surface Area of Bay/([g]*Channel Cross-sectional Area))
Channel Cross-sectional Area given Resonant Period for Helmholtz mode
Go Channel Cross-sectional Area = (Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*(Resonant Period for Helmholtz Mode/2*pi)^2)
Basin Surface Area given Resonant Period for Helmholtz mode
Go Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel))
Additional Length accounting for Mass Outside each End of Channel
Go Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length
Channel Length for Resonant Period for Helmholtz Mode
Go Channel Length = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Additional Length of the Channel
Standing Wave Height given Maximum Horizontal Particle Excursion at Node
Go Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth)
Maximum Horizontal Particle Excursion at Node
Go Maximum Horizontal Particle Excursion = (Standing Wave Height*Natural Free Oscillating Period of a Basin/2*pi)*sqrt([g]/Water Depth)
Standing Wave Height for Average Horizontal Velocity at Node
Go Standing Wave Height = (Average Horizontal Velocity at a Node*pi*Water Depth*Natural Free Oscillating Period of a Basin)/Wavelength
Water Depth given Average Horizontal Velocity at Node
Go Water Depth = (Standing Wave Height*Wavelength)/Average Horizontal Velocity at a Node*pi*Natural Free Oscillating Period of a Basin
Wave Length for Average Horizontal Velocity at Node
Go Wavelength = (Average Horizontal Velocity at a Node*pi*Water Depth*Natural Free Oscillating Period of a Basin)/Standing Wave Height
Average Horizontal Velocity at Node
Go Average Horizontal Velocity at a Node = (Standing Wave Height*Wavelength)/pi*Water Depth*Natural Free Oscillating Period of a Basin
Water Depth given Maximum Horizontal Particle Excursion at Node
Go Water Depth = [g]/(2*pi*Maximum Horizontal Particle Excursion/Standing Wave Height*Natural Free Oscillating Period of a Basin)^2
Standing Wave Height given Maximum Horizontal Velocity at Node
Go Standing Wave Height = (Maximum Horizontal Velocity at a Node/sqrt([g]/Water Depth))*2
Maximum Horizontal Velocity at Node
Go Maximum Horizontal Velocity at a Node = (Standing Wave Height/2)*sqrt([g]/Water Depth)
Period for Fundamental Mode
Go Natural Free Oscillating Period of a Basin = (4*Length of Basin)/sqrt([g]*Water Depth)
Basin Length along Axis for given Period of Fundamental Mode
Go Length of Basin = Natural Free Oscillating Period of a Basin*sqrt([g]*Water Depth)/4
Basin Length along axis given Maximum Oscillation Period corresponding to Fundamental Mode
Go Length of Basin = Maximum Oscillation Period*sqrt([g]*Water Depth)/2
Maximum Oscillation Period corresponding to Fundamental Mode
Go Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth)
Water Depth given Maximum Horizontal Velocity at Node
Go Water Depth = [g]/(Maximum Horizontal Velocity at a Node/(Standing Wave Height/2))^2
Water Depth for given Period for Fundamental Mode
Go Water Depth = ((4*Length of Basin/Natural Free Oscillating Period of a Basin)^2)/[g]
Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode
Go Water Depth = (2*Length of Basin/Natural Free Oscillating Period of a Basin)^2/[g]

Additional Length accounting for Mass Outside each End of Channel Formula

Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length
l'c = ([g]*AC*(TH/2*pi)^2/Ab)-Lc

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 accounting for Mass Outside each End of Channel?

Additional Length accounting for Mass Outside each End of Channel calculator uses Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length to calculate the Additional Length of the Channel, The Additional Length accounting for Mass Outside each End of Channel is defined as the additional 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 accounting for Mass Outside each End of Channel using this online calculator? To use this online calculator for Additional Length accounting for Mass Outside each End of Channel, enter Channel Cross-sectional Area (AC), Resonant Period for Helmholtz Mode (TH), Surface Area of Bay (Ab) & Channel Length (Lc) and hit the calculate button. Here is how the Additional Length accounting for Mass Outside each End of Channel calculation can be explained with given input values -> 403242.3 = ([g]*10*(50/2*pi)^2/1.5001)-40.

FAQ

What is Additional Length accounting for Mass Outside each End of Channel?
The Additional Length accounting for Mass Outside each End of Channel is defined as the additional length parameter influencing the resonant period for Helmholtz mode and is represented as l'c = ([g]*AC*(TH/2*pi)^2/Ab)-Lc or Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length. Channel Cross-sectional Area [length^2] is the cross sectional area of the channel, Resonant Period for Helmholtz Mode [time], Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity, Surface Area of Bay is defined as a small body of water set off from the main body & Channel Length is the measurement or extent of water wider than a strait, joining two larger areas of water.
How to calculate Additional Length accounting for Mass Outside each End of Channel?
The Additional Length accounting for Mass Outside each End of Channel is defined as the additional length parameter influencing the resonant period for Helmholtz mode is calculated using Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length. To calculate Additional Length accounting for Mass Outside each End of Channel, you need Channel Cross-sectional Area (AC), Resonant Period for Helmholtz Mode (TH), Surface Area of Bay (Ab) & Channel Length (Lc). With our tool, you need to enter the respective value for Channel Cross-sectional Area, Resonant Period for Helmholtz Mode, Surface Area of Bay & Channel Length 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 Cross-sectional Area, Resonant Period for Helmholtz Mode, Surface Area of Bay & Channel Length. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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))
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