Variance Of Spread Of Tracer For Small Extents Of Dispersion Calculator

Formula Used:

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

Dispersion Coefficient at Dispersion Number < 0.01:

m²/s

Length of Spread for Dispersion Number <0.01:

Velocity of Pulse for Dispersion Number <0.01:

m/s

Variance of Spread for Dispersion Number <0.01:

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1. What is Variance of Spread for Dispersion Number <0.01?

Variance of Spread for Dispersion Number <0.01 relates to how much a distribution or concentration profile spreads out from a central point. It quantifies the dispersion characteristics of a tracer in a system with small extents of dispersion.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \sigma^2 \) — Variance of Spread for Dispersion Number <0.01 (s²)
\( D_p \) — Dispersion Coefficient at Dispersion Number < 0.01 (m²/s)
\( L' \) — Length of Spread for Dispersion Number <0.01 (m)
\( u' \) — Velocity of Pulse for Dispersion Number <0.01 (m/s)

Explanation: The formula calculates the variance of spread based on dispersion coefficient, length of spread, and pulse velocity, providing insight into how a tracer disperses in a system.

3. Importance of Variance Calculation

Details: Calculating variance of spread is crucial for understanding dispersion characteristics in chemical reactors, environmental systems, and various engineering applications where tracer studies are conducted.

4. Using the Calculator

Tips: Enter dispersion coefficient in m²/s, length of spread in meters, and velocity in m/s. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What does Dispersion Number <0.01 indicate?
A: A dispersion number less than 0.01 indicates small extents of dispersion, meaning the system exhibits minimal spreading of the tracer.

Q2: How is dispersion coefficient measured?
A: Dispersion coefficient is typically determined through tracer experiments where a pulse of tracer is introduced and its spreading is monitored over time.

Q3: What factors affect variance of spread?
A: Variance of spread is influenced by the dispersion coefficient, length of the system, and the velocity at which the pulse travels.

Q4: When is this formula applicable?
A: This formula is specifically applicable for systems with dispersion numbers less than 0.01, where dispersion effects are relatively small.

Q5: What are typical units for variance of spread?
A: Variance of spread is typically measured in square seconds (s²), representing the squared spread of the concentration profile over time.