Moment-of-Momentum Equation

The moment-of-momentum equation analyzes the torque produced by the rotating blades of a wind turbine.

The moment-of-momentum equation is found by applying Newton's second law to a small fluid particle. This law states that the rate of change of linear momentum equals the external force acting on it.

The moment of force is calculated by considering the position of the fluid particle to determine the torque.

The position vector is combined with the external force to find the torque acting on the particle.

The time derivative is then expanded into two parts. One part represents the rate of change of angular momentum due to the fluid's velocity, while the other accounts for how the fluid moves through space.

The change in position over time equals the particle's velocity, simplifying the expansion.

The moment-of-momentum equation is obtained by integrating these terms over the control volume.

This equation relates the torque on the system to the angular momentum entering and exiting the control volume and the external forces acting on it.