Properties of Fluids

Fluid mechanics is the study of fluids at rest and in motion. A fluid is a substance that deforms continuously under the application of a shear stress, no matter how small the stress may be.

Viscosity

Viscosity is the property of a fluid that determines its resistance to shearing stresses. It is a measure of the internal fluid friction which causes resistance to flow.

Newton's Law of Viscosity

Shear stress ($\tau$) is proportional to the velocity gradient ($du/dy$).

$\tau = \mu \frac{du}{dy}$

• $\mu$ = Dynamic (Absolute) Viscosity ($Pa\cdot s$)
• $\nu$ = Kinematic Viscosity ($\nu = \mu / \rho$) ($m^2/s$)

Surface Tension

Surface tension ($\sigma$) is the tensile force acting on the surface of a liquid in contact with a gas or another immiscible liquid.

$\Delta P = \frac{2\sigma}{R} \quad (\text{Droplet})$ $\Delta P = \frac{4\sigma}{R} \quad (\text{Bubble})$ $h = \frac{4\sigma \cos\theta}{\gamma d} \quad (\text{Capillary Rise})$

Solved Problems