Because we have two-dimensional flow in both fluids, Taylor attempted a stream function solution to the equations of motion (Stokes Equation in this case). For a velocity field
The stream function is defined by
And must satisfy the biharmonic equation
Where 
and 
is given by
The required 
dependence of the viscous stress suggests that a
solution of the form 
is plausible.
Substituting this form into the biharmonic equation (16) provides
the following characteristic equation for n:
Therefore, possible values of n are 
. With the
assumed form of the stream function, the velocity and stress components are
given by
The pressure force is obtained by inserting the expressions for the velocity components in the equations of motion and integrating. Suffice it to say that it can be done, the resulting pressures at the interface, according to Taylor, are
