Page 90 - Aerodynamics for Engineering Students

Governing equations of fluid mechanics 73

Fig. 2.13 Rectangular element at P (r, 0) in a system of polar coordinates

and accumulation per second tangentially is:

Total accumulation per second

(2.50)
and this by the previous argument equals the rate of change of mass within the region
of space

(2.51)
Equating (2.50) and (2.51) gives:

(2.52)

Hence for steady flow

(2.53)
and the incompressible equation in this form becomes:

(2.54)

2.5 The stream function and streamline

2.5.1 The stream function y/
Imagine being on the banks of a shallow river of a constant depth of 1 m at a pos-
ition 0 (Fig. 2.14) with a friend directly opposite at A, 40m away. Mathematically