r^½ cos ½[theta] = a^½, or r + x = 2a, (3)
the conditions are satisfied by
[psi]´ = Ur sin [theta] - 2Ua^½ r^½ sin ½[theta]
= 2Ur^½ sin ½[theta](r^½ cos ½[theta] - a^½), (4)
[psi] = 2Ua^½ r^½ sin ½[theta] = -U[root][2a(r-x)], (5)
w = -2Ua^½ z^½, (6)
and the resistance of the liquid is 2[pi][rho]aV²/2g.