B2.1 Physical Properties and Dimensionless Numbers

Flows are characterized by the following material constants:

• Density ρ of the fluid: The density of air depends on pressure (or geodetic height), temperature, and humidity content and is often assumed to be 1.25 kg/m³
• Kinematic viscosity ν : This depends on the fluid and for air is 15×10^-6 m²/s at 20^o C and 1000 hPa
• Dynamic viscosity μ : This is the product of ν and ρ

To compare flows and, in particular, to distinguish the effects to be considered, various dimensionless numbers are defined:

• Reynolds number:

It describes the ratio of inertial forces to viscous shear forces, where u is the velocity of the fluid and D_ref is a characteristic dimension. For blunt bodies, for example, it is the "hydraulic" diameter, and for streamlined bodies, it is usually the dimension in the flow direction.

• Froude number:

It describes the ratio of inertial forces to gravitational forces, where u is the velocity of the fluid and L is also a characteristic dimension.

• Mach number:

It describes the ratio of flow velocity u to the speed of compression waves c in the medium, where K is the bulk modulus and ρ is the is the fluid density.