King's Dimensionless Velocity Calculator

King's Dimensionless Velocity Formula:

\[ V'm = \frac{A_{avg} \times T \times V_m}{2\pi \times a_o \times A_b} \]

Average Area over the Channel Length (Aavg):

m²

Tidal Period (T):

Maximum Cross Sectional Average Velocity (Vm):

m/s

Ocean Tide Amplitude (ao):

Surface Area of Bay (Ab):

m²

King's Dimensionless Velocity (V'm):

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1. What is 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. It's particularly useful in tidal hydraulics and coastal engineering applications.

2. How Does the Calculator Work?

The calculator uses King's Dimensionless Velocity formula:

\[ V'm = \frac{A_{avg} \times T \times V_m}{2\pi \times a_o \times A_b} \]

Where:

\( A_{avg} \) — Average Area over the Channel Length (m²)
\( T \) — Tidal Period (s)
\( V_m \) — Maximum Cross Sectional Average Velocity (m/s)
\( a_o \) — Ocean Tide Amplitude (m)
\( A_b \) — Surface Area of Bay (m²)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: This dimensionless parameter characterizes tidal flow behavior and helps in scaling hydraulic models for coastal and estuarine systems.

3. Importance of King's Dimensionless Velocity

Details: King's Dimensionless Velocity is crucial for understanding tidal dynamics, designing coastal structures, and predicting sediment transport in estuaries and bays. It provides a scale-independent measure of flow characteristics.

4. Using the Calculator

Tips: Enter all values in the specified units. Average Area over the Channel Length, Tidal Period, Maximum Cross Sectional Average Velocity, Ocean Tide Amplitude, and Surface Area of Bay must all be positive values for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of King's Dimensionless Velocity?
A: Values typically range from 0.1 to 10, with lower values indicating more restricted flow and higher values indicating more efficient tidal exchange.

Q2: How does this parameter relate to tidal prism?
A: King's Dimensionless Velocity incorporates both geometric characteristics (areas) and dynamic characteristics (velocity, period, amplitude) of the tidal system.

Q3: When is this parameter most useful?
A: Particularly valuable for comparative studies of different tidal inlets and for scaling hydraulic models of coastal systems.

Q4: Are there limitations to this equation?
A: The formula assumes simplified tidal dynamics and may need adjustment for complex geometries or non-sinusoidal tidal forcing.

Q5: Can this be used for river systems?
A: Primarily designed for tidal systems with well-defined tidal characteristics, though similar principles may apply to some river-estuary interactions.