EXAMPLE 3.2A: CALCULATING DRAG FORCE WITH STOKES’ LAW (ELEMENTARY)

Imagine a sphere with fluid flowing around it. Can you calculate its drag force, using Stokes’ Law? And, what has Reynolds Number got to do with it?

EXAMPLE 3.2B: SINKING TIME OF PLANKTON (MEDIUM)

Consider a small micro-organism living in the ocean.

At some point, it dies and will slowly fall at its terminal velocity to the ocean floor. We assume that the micro-organism is a sphere with a diameter of 10 μ m.

It has a density that is slightly higher than that of sea water. The ocean has a depth of H = 1 km.

1. What is its terminal velocity?
2. How long does it take for the organism to reach the ocean floor?

EXAMPLE 3.2C: SETTLING TANK FOR OIL/WATER SEPARATION (ADVANCED)

During the production of crude oil, water is often produced along with natural gas. The result is a homogeneous water-in-oil emulsion, with water droplets settling at the bottom of the tank. One of the simplest methods to separate this emulsion is to design a huge settling tank and wait until the water and oil are separated by gravity.

Generally, an important question is: How long does it take to separate the emulsion? All water droplets can be represented by spheres with an average diameter of dwater = 50 µm. Furthermore, we know that:

– The viscosity of water is µwater = 10-3 Pa·s and the density of water is equal to ρwater = 1000 kg/m3

– The viscosity of crude oil is µoil = 5.10-3 Pa·s and the density is ρoil = 800 kg/m3

– The gravity constant is g = 9.81 m/s2

– The height of the tank is 4 meter.