You are trying to find the velocity field in a rectangular channel driven by a pressure gradient and you are trying to find a steady solution to your problem. That means you need to compare your solution to the solution of the steady Poiseuille flow equation in a rectangular channel: d^2u/dx^2 = 1/mu*dp/dy. With no-slip boundary condition the solution is:
u(x) = 1/(2*mu)*dp/dy*x*(x-h)
you set p = 1 on inlet and p = 0 on outlet and use the unitsquare mesh, thus dp/dy = 1, and also h = 1. You use nu = 0.01 and rho = 1 (by omitting rho), therefore mu = nu*rho = 0.01. Inserting these numbers, the solution becomes.
u(x) = 50*x*(x-h)
Max_x | u(x) | = 50*0.5*0.5 = 12.5
Therefore you would expect the maximal velocity in the channel to be 12.5. In your example it has not even reached 8 so there is no problem with what you are describing or posting. If I run your code with dt = 1 and T = 200 I reach a steady-state maximum value of 13.5. At this point the velocity is constant. I guess the solution is a bit inaccurate due to the mesh, the coarse time step or similar. Let me know if this helps.