## Chapter 12

## Q. 12.1

Find the sedimentation velocities of (i) a pollen grain, diameter 10 µm, density 0.8 g cm^{−3}, and (ii) a hailstone, diameter 6 mm, density 0.5 g cm^{−3}. (Hint: You will have to estimate the Reynolds number and decide whether to use the trial-and error method described in the text).

## Step-by-Step

## Verified Solution

i. If the pollen grain obeys Stokes’ Law, then V_{s} = 2\rho gr^{2} / 9\rho_{a} v . Hence V_{s} = 2\times 0.8\times 10^{6} \times 9.81\times (5\times 10^{-6} )^{2} / 9\times 1.29\times 10^{3} \times 15\times 10^{-6} = 2.4 \; mm \; s^{-1} .

To determine whether using Stokes’ Law is appropriate, calculate the particle Reynolds number Re_{p}.

Re_{p} = 2.4\times 10^{-3} \times 10\times 10^{-6} /(15\times 10^{-6} ) = 1.6 \times 10^{-3} .

So Stokes’ Law is valid.

ii. In this case, Stokes’ Law predicts that V_{s} = 545 \; m \; s^{-1} , but then Re_{p} = 109 × 10³, so Stokes’ Law clearly is not adequate for calculating V_{s}. Using the iterative method described in the text, with a first guess for drag coefficient of 0.44 eventually yields V_{s} = 13 \; m \; s^{-1} . There is an interesting discussion of drag coefficients at