OSH/Example/1

Example problem statement

The drag force on a sphere is given by the product of the sphere's velocity and its drag coefficient. The drag coefficient is proportional to the sphere's cross-sectional area. The gravitational force on a sphere is proportional to its volume. The velocity at which these two forces are equal is called the terminal velocity. How does the terminal velocity of a sphere depend on its radius?

Solution 1

$F_1= - \mu V$

$\mu=\pi r^2 k_1$

$F_1=\pi r^2 k_1 V$

$F_2= 4/3 \pi r^3 k_2 d g$

$\pi r^2 k_1 v= 4/3 \pi r^3 k_2 d g$

$V=4 r k_2 d g / (3k_1) $