Consider the two cases of a ping pong ball and a marble as shown in the figure below.
D
Part abc
y
Part d
a) Determine the non-dimensional equation relating the drag coefficient of a rising ping pong
ball to the drag force. Include all relevant parameters. Show your work.
b) (extra credit 0.5pts) What if anything would change is the water density was a function of
temperature and depth
c) Assuming a constant water density, write down the governing equation for the terminal
velocity of the ping pong ball as it rises in the ocean.
d) For a marble of Aluminum, with D=0.01[m], determine the distance into the water from the
surface at which the marble reaches its terminal velocity. Assume a starting velocity is
0.001[m/s], and it starts from y=0. Use the drag coefficient diagram provided to obtain an
iterative solution. Attach your numerical solution sheet with a plot of the velocity as a function
of depth. Assume constant density for this problem, thus $\rho$=1000[kg/m³], as well as the
\"smooth sphere assumption\"
g
