Dispersion Coefficient Based On Variance Of Spread Of Tracer At Small Extents Of Dispersion Calculator

Formula Used:

\[ D_p = \frac{\sigma^2 \cdot u^3}{2 \cdot L} \]

Variance of Spread for Dispersion Number <0.01:

m²

Velocity of Pulse:

m/s

Length of Spread for Small Extents:

Dispersion Coefficient at Dispersion Number < 0.01:

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1. What is Dispersion Coefficient?

The Dispersion Coefficient at Dispersion Number < 0.01 represents the spreading of a tracer in a reactor, indicating how much the tracer diffuses across a unit area in 1 second under the influence of a gradient of one unit. It is particularly relevant for small extents of dispersion where the dispersion number is less than 0.01.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_p = \frac{\sigma^2 \cdot u^3}{2 \cdot L} \]

Where:

\( D_p \) — Dispersion Coefficient at Dispersion Number < 0.01 (m²/s)
\( \sigma^2 \) — Variance of Spread for Dispersion Number <0.01 (m²)
\( u \) — Velocity of Pulse (m/s)
\( L \) — Length of Spread for Small Extents (m)

Explanation: This formula calculates the dispersion coefficient based on the variance of spread, velocity of the pulse, and the length of spread for small extents.

3. Importance of Dispersion Coefficient Calculation

Details: Accurate calculation of dispersion coefficient is crucial for understanding and predicting the behavior of tracers in various systems, including chemical reactors, environmental flows, and biological systems. It helps in designing efficient processes and systems.

4. Using the Calculator

Tips: Enter the variance of spread in m², velocity of pulse in m/s, and length of spread for small extents in m. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of dispersion number being less than 0.01?
A: When the dispersion number is less than 0.01, it indicates that the system has small extents of dispersion, meaning the spreading of the tracer is relatively limited and can be described by this specific formula.

Q2: How is variance of spread measured?
A: Variance of spread is typically determined experimentally by measuring the concentration profile of a tracer over time and calculating the statistical variance of the distribution.

Q3: What units should be used for input values?
A: Variance should be in square meters (m²), velocity in meters per second (m/s), and length in meters (m) to ensure the result is in square meters per second (m²/s).

Q4: Can this formula be used for large dispersion numbers?
A: No, this formula is specifically derived for dispersion numbers less than 0.01. For larger dispersion numbers, different formulas or models should be used.

Q5: What are typical applications of this calculation?
A: This calculation is commonly used in chemical engineering for reactor design, in environmental engineering for pollutant dispersion studies, and in various research fields involving tracer experiments.