Ocean Tide Amplitude using King's Dimensionless Velocity Calculator

King's Formula:

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

Average Area over the Channel Length (A_avg):

m²

Maximum Cross Sectional Average Velocity (V_m):

m/s

Tidal Period (T):

King's Dimensionless Velocity (V'_m):

Surface Area of Bay (A_b):

m²

Ocean Tide Amplitude (a_o):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is King's Dimensionless Velocity Formula?

King's Dimensionless Velocity Formula calculates ocean tide amplitude by considering the relationship between average channel area, maximum velocity, tidal period, dimensionless velocity, and bay surface area. It provides a theoretical framework for understanding tidal dynamics in coastal systems.

2. How Does the Calculator Work?

The calculator uses King's formula:

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

Where:

\( a_o \) — Ocean Tide Amplitude (m)
\( A_{avg} \) — Average Area over the Channel Length (m²)
\( V_m \) — Maximum Cross Sectional Average Velocity (m/s)
\( T \) — Tidal Period (s)
\( V'_m \) — King's Dimensionless Velocity
\( A_b \) — Surface Area of Bay (m²)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: The equation models how tidal energy propagates through channels into bays, with the dimensionless velocity serving as a scaling parameter that accounts for flow characteristics independent of system size.

3. Importance of Ocean Tide Amplitude Calculation

Details: Accurate tide amplitude prediction is crucial for coastal engineering, navigation, flood risk assessment, and understanding sediment transport processes in estuaries and bays.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters, seconds, square meters). Ensure all inputs are positive values. The dimensionless velocity is a unitless parameter typically derived from empirical studies or theoretical models.

5. Frequently Asked Questions (FAQ)

Q1: What is King's Dimensionless Velocity?
A: It's a scaling parameter that represents the ratio of actual flow velocity to a characteristic velocity, allowing the formula to be applied to various tidal systems regardless of scale.

Q2: How is Average Area over the Channel Length determined?
A: This is typically calculated by integrating the cross-sectional area along the channel length or using averaged measurements from multiple cross-sections.

Q3: What are typical values for King's Dimensionless Velocity?
A: Values typically range between 0.1-10, depending on the specific tidal system characteristics, with common values around 0.5-2.0 for many natural channels.

Q4: Can this formula be used for storm surge prediction?
A: While based on similar principles, storm surges involve additional meteorological factors that may require more complex modeling approaches.

Q5: What are the limitations of this formula?
A: The formula assumes simplified channel geometry and may not account for complex bathymetry, friction effects, or non-linear interactions in highly dynamic tidal systems.