King's Dimensionless Velocity Calculator

✖Average Area over the Channel Length is calculated with surface area of bay, change of bay elevation with time and average velocity in channel for flow.ⓘ Average Area over the Channel Length [A_avg]			+10% -10%
✖Tidal Period is the time taken for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day.ⓘ Tidal Period [T]			+10% -10%
✖Maximum Cross Sectional Average Velocity during a tidal cycle which is the periodic rise and fall of the waters of the ocean and its inlets.ⓘ Maximum Cross Sectional Average Velocity [V_m]			+10% -10%
✖Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.ⓘ Ocean Tide Amplitude [a_o]			+10% -10%
✖Surface Area of Bay is defined as a small body of water set off from the main body.ⓘ Surface Area of Bay [A_b]			+10% -10%

✖King’s Dimensionless Velocity is measure of fluid flow independent of scale, expressed as the ratio of velocity to a characteristic speed.ⓘ King's Dimensionless Velocity [V'_m]

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King's Dimensionless Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

King’s Dimensionless Velocity = (Average Area over the Channel Length*Tidal Period*Maximum Cross Sectional Average Velocity)/(2*pi*Ocean Tide Amplitude*Surface Area of Bay)
V'_m = (A_avg*T*V_m)/(2*pi*a_o*A_b)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

King’s Dimensionless Velocity - King’s Dimensionless Velocity is measure of fluid flow independent of scale, expressed as the ratio of velocity to a characteristic speed.
Average Area over the Channel Length - (Measured in Square Meter) - Average Area over the Channel Length is calculated with surface area of bay, change of bay elevation with time and average velocity in channel for flow.
Tidal Period - (Measured in Second) - Tidal Period is the time taken for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day.
Maximum Cross Sectional Average Velocity - (Measured in Meter per Second) - Maximum Cross Sectional Average Velocity during a tidal cycle which is the periodic rise and fall of the waters of the ocean and its inlets.
Ocean Tide Amplitude - (Measured in Meter) - Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.
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.

STEP 1: Convert Input(s) to Base Unit

Average Area over the Channel Length: 8 Square Meter --> 8 Square Meter No Conversion Required
Tidal Period: 130 Second --> 130 Second No Conversion Required
Maximum Cross Sectional Average Velocity: 4.1 Meter per Second --> 4.1 Meter per Second No Conversion Required
Ocean Tide Amplitude: 4 Meter --> 4 Meter No Conversion Required
Surface Area of Bay: 1.5001 Square Meter --> 1.5001 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V'_m = (A_avg*T*V_m)/(2*pi*a_o*A_b) --> (8*130*4.1)/(2*pi*4*1.5001)

Evaluating ... ...

V'_m = 113.098572985775

STEP 3: Convert Result to Output's Unit

113.098572985775 --> No Conversion Required

FINAL ANSWER

113.098572985775 ≈ 113.0986 <-- King’s Dimensionless Velocity

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Hydrodynamics of Tidal Inlets 1 » Inlet Hydrodynamics » Inlet Currents and Tidal Elevations » King's Dimensionless Velocity

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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< Inlet Currents and Tidal Elevations Calculators

Change of Bay Elevation with Time for Flow through Inlet into Bay

LaTeX Go Change of Bay Elevation with Time = (Average Area over the Channel Length*Average Velocity in Channel for Flow)/Surface Area of Bay

Average Area over Channel Length for Flow through Inlet into Bay

LaTeX Go Average Area over the Channel Length = (Surface Area of Bay*Change of Bay Elevation with Time)/Average Velocity in Channel for Flow

Average Velocity in Channel for Flow through Inlet into Bay

LaTeX Go Average Velocity in Channel for Flow = (Surface Area of Bay*Change of Bay Elevation with Time)/Average Area over the Channel Length

Surface Area of Bay for Flow through Inlet into Bay

LaTeX Go Surface Area of Bay = (Average Velocity in Channel for Flow*Average Area over the Channel Length)/Change of Bay Elevation with Time

King's Dimensionless Velocity Formula

LaTeX Go

What is Inlet flow patterns?

An Inlet has a "gorge" where flows converge before they expand again on the opposite side. Shoal (shallow) areas that extend bayward and oceanward from the gorge depend on inlet hydraulics, wave conditions, and general geomorphology. All these interact to determine flow patterns in and around the inlet and locations where flow channels occur.

How to Calculate King's Dimensionless Velocity?

King's Dimensionless Velocity calculator uses King’s Dimensionless Velocity = (Average Area over the Channel Length*Tidal Period*Maximum Cross Sectional Average Velocity)/(2*pi*Ocean Tide Amplitude*Surface Area of Bay) to calculate the King’s Dimensionless Velocity, King's Dimensionless Velocity, solved the same equations but included the effect of inertia; the possibility exists that the inlet system could have a Helmholtz frequency (or pumping mode, where the basin oscillates uniformly) that is tuned to the forcing ocean tide and amplification of the bay tide could occur. King’s Dimensionless Velocity is denoted by V'_m symbol.

How to calculate King's Dimensionless Velocity using this online calculator? To use this online calculator for King's Dimensionless Velocity, enter Average Area over the Channel Length (A_avg), Tidal Period (T), Maximum Cross Sectional Average Velocity (V_m), Ocean Tide Amplitude (a_o) & Surface Area of Bay (A_b) and hit the calculate button. Here is how the King's Dimensionless Velocity calculation can be explained with given input values -> 113.1061 = (8*130*4.1)/(2*pi*4*1.5001).

FAQ

What is King's Dimensionless Velocity?

King's Dimensionless Velocity, solved the same equations but included the effect of inertia; the possibility exists that the inlet system could have a Helmholtz frequency (or pumping mode, where the basin oscillates uniformly) that is tuned to the forcing ocean tide and amplification of the bay tide could occur and is represented as V'_m = (A_avg*T*V_m)/(2*pi*a_o*A_b) or King’s Dimensionless Velocity = (Average Area over the Channel Length*Tidal Period*Maximum Cross Sectional Average Velocity)/(2*pi*Ocean Tide Amplitude*Surface Area of Bay). Average Area over the Channel Length is calculated with surface area of bay, change of bay elevation with time and average velocity in channel for flow, Tidal Period is the time taken for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day, Maximum Cross Sectional Average Velocity during a tidal cycle which is the periodic rise and fall of the waters of the ocean and its inlets, Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun & Surface Area of Bay is defined as a small body of water set off from the main body.

How to calculate King's Dimensionless Velocity?

King's Dimensionless Velocity, solved the same equations but included the effect of inertia; the possibility exists that the inlet system could have a Helmholtz frequency (or pumping mode, where the basin oscillates uniformly) that is tuned to the forcing ocean tide and amplification of the bay tide could occur is calculated using King’s Dimensionless Velocity = (Average Area over the Channel Length*Tidal Period*Maximum Cross Sectional Average Velocity)/(2*pi*Ocean Tide Amplitude*Surface Area of Bay). To calculate King's Dimensionless Velocity, you need Average Area over the Channel Length (A_avg), Tidal Period (T), Maximum Cross Sectional Average Velocity (V_m), Ocean Tide Amplitude (a_o) & Surface Area of Bay (A_b). With our tool, you need to enter the respective value for Average Area over the Channel Length, Tidal Period, Maximum Cross Sectional Average Velocity, Ocean Tide Amplitude & Surface Area of Bay and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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