Home >> Science & Nature >> Science

How to Test for the Terminal Velocity of Particulates in Water

The terminal velocity of a particle, or particulate, is the point at which the velocity of a falling particle in a fluid no longer changes. When a particle is placed in a fluid and it begins to fall and settle, the acceleration due to gravity provides the applied force and the drag from the fluid causes the resistance force. When those two forces equal, that rate of settling is the terminal velocity.

Things You'll Need

Clear cylinder, with one end open and one end sealed, 6-inch diameter, 2 feet high
Small particle such as a small marble with a diameter of 1/8 inch, which is 0.125 inches in decimal form
Stopwatch

Instructions

- 1
  Fill a cylinder with water at room temperature. The density of water is 62.4 pounds per cubic foot and has a viscosity of 0.5 centipoise.
- 2
  Determine the density of the marble or whatever particle you are using. For most solid materials, the density is the bulk density. For a small marble, assume the density is 80 pounds per cubic foot.
- 3
  Calculate the theoretical terminal velocity using the equation V = D^2 x a x (denp - denf) / 18 x u, where D is the particle diameter, a is the acceleration due to gravity (32.2 ft/sec^2), denp is the density of the particle, denf is the density of the fluid (water) and u is the fluid viscosity. The theoretical terminal velocity is 0.125^2 x 32.2 x (80-62.4) / 18 x 0.5 or 0.98 feet per second.
- 4
  Time the fall of the marble or particle, and compare that to the theoretical terminal velocity. Do this by dropping the marble into the cylinder and timing how long it takes to reach the bottom. Hold the marble at the surface of the water, release the marble and start the stopwatch. Stop the time once the marble hits the bottom. A drop through 2 feet of water should have only taken 2.04 seconds, calculated based on 2 feet at 0.98 feet per second.

Science