In the far field, velocity becomes uniform and equal to In terms of stream function, this condition is expressed as:

for

(26.5)

usually, a large cylinder surface is considered for implementing the far field condition (Figure 26.1). Therefore, the far field boundary condition (Equation (26.5)) is approximate as:

(26.6)

For the vorticity, the far field boundary condition is given below

(26.7)

Since the velocity is uniform and velocity gradients are zero, the above-mentioned condition is justified. On the axis due to axisymmetry and for all

Thus, from Equation (26.1) and (26.3) it can be seen that