Surface Area of Bay or Basin using King's Dimensionless Variable Calculator

King's Formula:

\[ Ab = \frac{Qr \times T}{Qr' \times 2 \times \pi \times ao} \]

River or Freshwater Inflow to a Bay (Qr):

m³/s

Tidal Period (T):

seconds

King's Dimensionless Variable for Freshwater (Qr'):

Ocean Tide Amplitude (ao):

meters

Surface Area of Bay (Ab):

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1. What is King's Dimensionless Variable Formula?

King's Dimensionless Variable Formula calculates the surface area of a bay or basin using freshwater inflow, tidal period, King's dimensionless variable, and ocean tide amplitude. It provides a hydrodynamic approach to estimate bay surface areas in coastal engineering studies.

2. How Does the Calculator Work?

The calculator uses King's formula:

\[ Ab = \frac{Qr \times T}{Qr' \times 2 \times \pi \times ao} \]

Where:

\( Ab \) — Surface Area of Bay (m²)
\( Qr \) — River or Freshwater Inflow to a Bay (m³/s)
\( T \) — Tidal Period (seconds)
\( Qr' \) — King's Dimensionless Variable for Freshwater
\( \pi \) — Mathematical constant pi (≈3.14159)
\( ao \) — Ocean Tide Amplitude (meters)

Explanation: The formula relates freshwater inflow and tidal characteristics to determine the surface area of coastal basins and bays.

3. Importance of Surface Area Calculation

Details: Accurate surface area estimation is crucial for coastal management, tidal flushing studies, sediment transport analysis, and environmental impact assessments of bays and basins.

4. Using the Calculator

Tips: Enter freshwater inflow in m³/s, tidal period in seconds, King's dimensionless variable, and ocean tide amplitude in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is King's Dimensionless Variable?
A: King's dimensionless variable is a parameter that characterizes the freshwater influence on tidal hydrodynamics in coastal systems, typically ranging between 0.5-0.7 for most natural bays.

Q2: How is tidal period determined?
A: Tidal period is typically 12.42 hours (44712 seconds) for semi-diurnal tides or 24.84 hours (89424 seconds) for diurnal tides, based on lunar cycles.

Q3: What are typical values for freshwater inflow?
A: Freshwater inflow varies greatly by location, from less than 1 m³/s for small bays to hundreds of m³/s for major river estuaries.

Q4: When is this formula most accurate?
A: The formula works best for well-mixed bays with relatively constant freshwater inflow and regular tidal patterns.

Q5: Are there limitations to this equation?
A: The formula assumes steady-state conditions and may be less accurate for highly stratified systems or during extreme weather events.