Circular jets directed at one another have been used to study gas-phase combustion. Typically, one jet contains a fuel such as methane and the other contains oxygen. Upon ignition, a stationary flame front is created where the jets meet. This arrangement is advantageous because opposed jets are straightforward to set up and the velocity field, which is needed to analyze the mass and heat transfer, is relatively simple. Suppose that jets coming from the +z and –z directions have identical flow rates and properties and that the resulting symmetry plane is at z = 0.

Show that the irrotational velocity field in Eq. (P9.3-1) applies throughout each jet. In particular, explain why there is no boundary layer at z = 0, even though the velocities might be large.

(r, z) = Cr, v(r; 2) = -2Cz (P9.3-1)