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King's Dimensionless Velocity Formula

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King’s Dimensionless Velocity is measure of fluid flow independent of scale, expressed as the ratio of velocity to a characteristic speed. Check FAQs

V' m = \frac{A avg \cdot T \cdot V m}{2 \cdot π \cdot a o \cdot A b}

V'_m - King’s Dimensionless Velocity?A_avg - Average Area over the Channel Length?T - Tidal Period?V_m - Maximum Cross Sectional Average Velocity?a_o - Ocean Tide Amplitude?A_b - Surface Area of Bay?π - Archimedes' constant?

King's Dimensionless Velocity Example

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Here is how the King's Dimensionless Velocity equation looks like with Values.

Here is how the King's Dimensionless Velocity equation looks like with Units.

Here is how the King's Dimensionless Velocity equation looks like.

113.0986 = \frac{8 \cdot 130 \cdot 4.1}{2 \cdot 3.1416 \cdot 4 \cdot 1.5001}

113.0986 = \frac{8m² \cdot 130s \cdot 4.1m/s}{2 \cdot 3.1416 \cdot 4m \cdot 1.5001m²}

113.0986 = \frac{8 \cdot 130 \cdot 4.1}{2 \cdot 3.1416 \cdot 4 \cdot 1.5001}

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King's Dimensionless Velocity Solution

Follow our step by step solution on how to calculate King's Dimensionless Velocity?

FIRST Step Consider the formula

V' m = \frac{A avg \cdot T \cdot V m}{2 \cdot π \cdot a o \cdot A b}

Next Step Substitute values of Variables

∴

V' m = \frac{8m² \cdot 130s \cdot 4.1m/s}{2 \cdot π \cdot 4m \cdot 1.5001m²}

Next Step Substitute values of Constants

∴

V' m = \frac{8m² \cdot 130s \cdot 4.1m/s}{2 \cdot 3.1416 \cdot 4m \cdot 1.5001m²}

Next Step Prepare to Evaluate

∴

V' m = \frac{8 \cdot 130 \cdot 4.1}{2 \cdot 3.1416 \cdot 4 \cdot 1.5001}

Next Step Evaluate

∴

V' m = 113.098572985775

LAST Step Rounding Answer

∴

V' m = 113.0986

King's Dimensionless Velocity Formula Elements

Variables

Constants

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.

Symbol: V'_m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find King’s Dimensionless Velocity

Average Area over the Channel Length

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.

Symbol: A_avg

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Average Area over the Channel Length

Tidal Period

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.

Symbol: T

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Tidal Period

Maximum Cross Sectional Average Velocity

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.

Symbol: V_m

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Maximum Cross Sectional Average Velocity

Ocean Tide Amplitude

Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.

Symbol: a_o

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Ocean Tide Amplitude

Surface Area of Bay

Surface Area of Bay is defined as a small body of water set off from the main body.

Symbol: A_b

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Surface Area of Bay

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 Inlet Currents and Tidal Elevations category

Go Average Velocity in Channel for Flow through Inlet into Bay

V avg = \frac{A b \cdot d Bay}{A avg}

Go Average Area over Channel Length for Flow through Inlet into Bay

A avg = \frac{A b \cdot d Bay}{V avg}

Go Surface Area of Bay for Flow through Inlet into Bay

A b = \frac{V avg \cdot A avg}{d Bay}

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

d Bay = \frac{A avg \cdot V avg}{A b}

How to Evaluate King's Dimensionless Velocity?

King's Dimensionless Velocity evaluator 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 evaluate 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 evaluate King's Dimensionless Velocity using this online evaluator? To use this online evaluator 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.

FAQs on King's Dimensionless Velocity

What is the formula to find King's Dimensionless Velocity?

The formula of King's Dimensionless Velocity is expressed as 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). Here is an example- 113.1061 = (8*130*4.1)/(2*pi*4*1.5001).

How to calculate King's Dimensionless Velocity?

With 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) we can find King's Dimensionless Velocity using the formula - 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). This formula also uses Archimedes' constant .

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King's Dimensionless Velocity Formula

King's Dimensionless Velocity Example

King's Dimensionless Velocity Solution

King's Dimensionless Velocity Formula Elements

Other formulas in Inlet Currents and Tidal Elevations category

How to Evaluate King's Dimensionless Velocity?

FAQs on King's Dimensionless Velocity

Variable Name