Average Per Cycle Exchange Coefficient Calculator

Average Per Cycle Exchange Coefficient Equation:

\[ E = 1 - \left( \frac{C_i}{C_o} \right)^{\frac{1}{i}} \]

Concentration of Substance after i Tidal Cycles (C_i):

mg/L

Initial Concentration (C_o):

mg/L

Tidal Cycles (i):

cycles

Average Per Cycle Exchange Coefficient (E):

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1. What is the Average Per Cycle Exchange Coefficient?

The Average Per Cycle Exchange Coefficient is the average fraction of water exchanged between a confined water body and the adjacent sea over a complete tidal cycle. It quantifies the efficiency of water exchange in coastal systems.

2. How Does the Calculator Work?

The calculator uses the exchange coefficient equation:

\[ E = 1 - \left( \frac{C_i}{C_o} \right)^{\frac{1}{i}} \]

Where:

\( E \) — Average per Cycle Exchange Coefficient
\( C_i \) — Concentration of substance after i tidal cycles (mg/L)
\( C_o \) — Initial concentration of substance (mg/L)
\( i \) — Number of tidal cycles

Explanation: The equation calculates the average fraction of water exchanged per tidal cycle based on the dilution of a tracer substance over multiple tidal cycles.

3. Importance of Exchange Coefficient Calculation

Details: Accurate exchange coefficient calculation is crucial for understanding water renewal rates in harbors, estuaries, and coastal basins, which affects water quality management and pollution control.

4. Using the Calculator

Tips: Enter concentration values in mg/L and the number of tidal cycles. All values must be valid (concentrations ≥ 0, initial concentration > 0, tidal cycles ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for exchange coefficients?
A: Exchange coefficients typically range from 0.1 to 0.9, with higher values indicating more efficient water exchange.

Q2: How many tidal cycles should be used for accurate calculation?
A: Generally, 3-10 tidal cycles provide reliable results, but this depends on the specific water body and tidal characteristics.

Q3: What substances are commonly used as tracers?
A: Conservative tracers like salinity, fluorescent dyes, or specific ions that don't react with the environment are commonly used.

Q4: Are there limitations to this method?
A: The method assumes complete mixing and conservative behavior of the tracer, which may not hold true in all environments.

Q5: How does this relate to water quality management?
A: Higher exchange coefficients indicate better flushing and dilution capacity, which is important for managing pollutant loads.