Kick’s energy equation

Kick’s energy equation

Kick's energy equation is one of the empirical laws for estimating energy requirements in comminution processes, particularly for coarse particle size reduction. It is expressed as:

$$E = k \cdot \ln \left(\frac{D_1}{D_2}\right)$$

Variables:

• $E$: Energy required per unit mass of material (J/kg or other energy units).
• $k$: Kick's constant, which depends on the material properties and machine characteristics.
• $D_1$: Initial particle size (before size reduction).
• $D_2$: Final particle size (after size reduction).

Key Assumptions:

• Kick's equation assumes that the energy required for size reduction is proportional to the size reduction ratio ($D_1/D_2$).
• It is most accurate for coarse crushing where the reduction in particle size is relatively small.

Usage:

This equation is often used in engineering applications to estimate power requirements for crushing operations in mineral processing systems.

You can find a detailed discussion of Kick's law in R.P. King's book under comminution operations, starting from Chapter 5 (Comminution Operations), especially under energy requirements for comminution (page 150–152).