Mach Number

The Mach number is a very important similarity parameter, which comes out of the fluid dynamic equations of motion and captures the compressibility effect. It is defined by the following relation:

TAS _ TAS

a pgRT

An expression for Mach number can also be obtained in terms of PT and Ps, by integrating Bernoulli’s equation [2].

Equation A.19 can be used to compute Mach at subsonic speeds, i. e., for M < 1. The aircraft is said to be flying at supersonic speeds when M > 1.

Reynold’s Number

Reynold’s number is the ratio of inertia force to the viscous force and is defined as

mass x acceration

The ratio of inertia force to viscous force =—————————-

mVd

density x d3 x velocity/time density x d2 x V2

=——————————————- =————————– and hence, we have

mVd mVd

Re = pVd (A. 20)

m

where d is the characteristic length (usually the mean aerodynamic chord), V is the TAS, and m is the coefficient of viscosity. If during a wind-tunnel (WT) test on an aircraft model, the Reynolds and Mach numbers are the same as the full-scale flight vehicle, then the flow about the model and the full-scale vehicle will be identical.

Viscosity

The frictional force in a flowing fluid is termed as viscosity of the fluid. Higher the friction, higher is the viscosity. In that sense, liquids are more viscous than gases. Mathematically, if t represents the frictional force per unit area (also called shear stress) and du/dy represents the velocity gradient, then the coefficient of viscosity can be obtained from the relation:

The viscosity of gases increases with an increase in temperature as per the relation (Rayleigh’s formula):

m / t3/4

The ratio of absolute viscosity m to density p is called the kinematic viscosity v, i. e.,

P