A 2 cm plastic ball with a specific gravity of 1.2 is released from rest in water at 20°C. Find the time and distance needed to achieve 99% of the terminal velocity. Write out the equation of motion by equating the mass times acceleration to the buoyant force, weight, and drag force and solve by developing a computer program or using available soft ware. Use Eq. (11.9) for the drag coefficient. 

The equation of motion can be expressed in the form where ρ_b is the density of the ball and ρw is the density of the water. This form avoids the problem of the drag coefficient approaching infinity when the velocity approaches zero because C_D Re/24 approaches unity as the Reynolds number approaches zero. An “if statement” is needed to avoid a singularity in Eq. (11.9) when the Reynolds number is zero.

Transcribed Image Text:

dv CpRe 18µ Pb - Pw dt 24 Pod? Po