King's Dimensionless Variable Calculator

King's Dimensionless Variable Formula:

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

River or Freshwater Inflow to a Bay (Qr):

m³/s

Tidal Period (T):

seconds

Ocean Tide Amplitude (ao):

meters

Surface Area of Bay (Ab):

m²

King's Dimensionless Variable (Qr'):

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1. What is King's Dimensionless Variable?

King's Dimensionless Variable for Freshwater is a metric used in fluid dynamics to characterize flow patterns in freshwater environments succinctly. It helps in understanding the interaction between river inflow and tidal forces in bay systems.

2. How Does the Calculator Work?

The calculator uses King's Dimensionless Variable formula:

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

Where:

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

Explanation: This dimensionless variable quantifies the relative importance of freshwater inflow compared to tidal forcing in estuarine systems.

3. Importance of King's Dimensionless Variable

Details: This parameter is crucial for understanding estuarine circulation patterns, salt intrusion, and mixing processes in coastal environments. It helps in predicting how freshwater inflows affect tidal dynamics and water quality in bays and estuaries.

4. Using the Calculator

Tips: Enter all values in the specified units. River inflow in cubic meters per second, tidal period in seconds, tide amplitude in meters, and surface area in square meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Qr' value indicate?
A: A high Qr' value indicates that freshwater inflow dominates over tidal forcing in the bay system.

Q2: What does a low Qr' value indicate?
A: A low Qr' value suggests that tidal forces are more significant compared to freshwater inflow in the system.

Q3: What are typical ranges for Qr'?
A: Values typically range from 0.001 to 10, with lower values indicating tide-dominated systems and higher values indicating river-dominated systems.

Q4: How is tidal period measured?
A: Tidal period is typically measured as the time between successive high tides, approximately 12 hours and 25 minutes for semi-diurnal tides.

Q5: Can this formula be used for saltwater systems?
A: While primarily designed for freshwater inflow analysis, the formula can be adapted for various estuarine and coastal systems with appropriate modifications.