When fluid is flowing between two flat plates and there is a hole or slit in the bottom plate, there

When fluid is flowing between two flat
plates and there is a hole or slit in the bottom plate, there is also a
difference between the pressure at the bottom of the hole/slit and the top
plate. This is called the hole pressure and the effect can be used to measure
the first normal stress coefficient of polymers (a measure of elasticity). Here
consider a Newtonian fluid and solve the hole pressure problem in two
dimensions (i.e., for a slit) when W = H = L for Re = 1 (see Figure 10.34).
Plot the pressure on the bottom of the hole and the top just across it.^{1}

^{1}This
problem was the first problem solved by the Galerkin finite element method by
the author and his students (Jackson and Finlayson, 1982a,b). At the time, we
wrote our own finite element code, computers were much slower and very much
smaller, so only 12, 29, and 110 elements were used for a 2D problem. Despite
that limitation, comparison with experiment was quite reasonable for Newtonian
fluids.