Note:

This calculator estimates the Plume Rise Height (ΔH) for non-buoyant plumes, typically from stacks with gas temperatures close to ambient or less than 50°C above ambient and exit velocities of 10 m/s or more.

It is used in air pollution studies, emission dispersion analysis, and industrial stack design to evaluate the vertical displacement of plumes where buoyancy is negligible, and momentum is the primary driver.

Explanation of Parameters:

• D_s (Stack Diameter): Diameter of the emission stack in meters.
• V_s (Exit Velocity): Velocity of the gas plume as it exits the stack (m/s). For this formula, it should be ≥ 10 m/s.
• T (Stack Gas Temperature): Absolute temperature of the emitted gas in Kelvin.
• ΔH (Plume Rise Height): The estimated additional height (in meters) gained by the plume due to exit momentum.

Why is Plume Rise Height Important?

It helps in:

• Assessing Air Pollution Spread: Determines how far emissions will rise before dispersing.
• Designing Industrial Stacks: Ensures emissions are released at sufficient height to minimize ground-level impact.
• Meeting Environmental Guidelines: Helps industries comply with dispersion and health safety regulations.
• Improving Air Quality: Reduces potential for pollutant accumulation near population zones.

Validations:

• Positive Inputs: D_s, V_s, and T must be greater than zero.
• Minimum Exit Velocity: V_s must be at least 10 m/s for the formula to be applicable.
• Units: Use SI units: D_s in meters, V_s in m/s, T in Kelvin, ΔH in meters.
• Applicable Conditions: Best suited for plumes with little or no thermal buoyancy, such as cool or mechanically forced emissions.

Real-life Applications:

• Low-Temperature Emission Analysis: Evaluates plume rise when temperature differential is minimal.
• Urban Emission Control: Helps in managing stack design in densely populated areas.
• Ventilation System Design: Used in modeling discharge from industrial fans or ducts.
• Environmental Impact Assessment: Ensures safe dispersion of emissions under mechanical force.

Conclusion:

The Plume Rise Height (ΔH) for non-buoyant plumes is essential in scenarios where thermal effects are minimal. Accurate modeling ensures better environmental protection, efficient stack design, and compliance with emission standards.