Terminal Falling Velocity of a Sand Grain

Application ID: 983

The first stop for polluted water entering a water work is normally a large tank, where large particles are left to settle. Generally, gravity settling is an economical method of separating particles. If the fluid in the tank is moving at a controlled low velocity, the particles can be sorted in separate containers according to the time it takes for them reach the bottom.

This model simulates a spherical sand grain falling in water. The grain accelerates from standstill and rapidly reaches its terminal velocity. The results agree very well with experimental studies. The model is an axially symmetric fluid-flow simulation in a moving coordinate system, coupled to an ordinary differential equation (ODE) describing the grain’s motion.