Viscosity and drag

MDCAT Physics · Physics · Fluid dynamics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Viscosity is the friction between the layers of a fluid as they slide over one another. A body moving through a fluid feels a resistive force called drag, which grows as the speed grows. For a small sphere moving slowly, Stokes' law gives the drag.

A body falling through a fluid speeds up at first. The drag rises until it balances the weight. The net force is then zero and the body falls at a constant speed, the terminal velocity.

In laminar (streamline) flow every particle passing a point follows the same smooth path, and streamlines never cross. Above a certain speed the flow becomes turbulent: irregular, with eddies, and with much more drag.

Rules to remember

Common mistake

Students say no forces act at terminal velocity, or that the body stops. The forces are balanced, so the body keeps moving at its greatest, constant speed.

Worked example

A tiny water droplet of radius r falls through air with a terminal velocity of 1.2 cm s−1. Eight such droplets join to form one drop. Find the terminal velocity of the large drop.

  1. Volume ∝ r3. The volume is 8 times larger, so the radius is 2 times larger, because 23 = 8.
  2. From Stokes' law, vt ∝ r2, so the terminal velocity is 22 = 4 times larger.
  3. vt = 4 × 1.2 = 4.8 cm s−1.

Answer: 4.8 cm s−1.

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