Flow vector field in bucket of water with hole I'm looking to calculate the vector field that governs the flow of water out of an orifice with a view to comparing it to the movement of a crowd out of a building through a single exit point.
What equations should i be looking at?
Thanks for any help.
 A: This really depends on the details that you wish to get out. In the most ideal scenario, you could use a potential flow solution and just focus on one quadrant of a sink solution. This would give you the streamlines and vector field of the solution in a closed form analytical answer. Although, in this case the velocity becomes a singularity at the sink, so perhaps maybe not your best model, but would be a start. If you wished to have a more reduced order model, (i.e. forget the slogging of people along the walls as they try to squeeze through a door), then you could go with the Euler equation. This equation neglects the effects of vicious forces and dissipation and is commonly used to model the ideal motion of fluids. You might be able to obtain a closed form analytical answer, however, you could always seek a numerical route. Finally, as nrabbit mentioned, the full fledged equations of motion for a fluid are the Navier-Stokes equation. This equation will allow you to account for the viscous forces and dissipation within your solution. However, an analytical answer for this equation is few and far between. Only a select few exact answers exist for very reduced problems. If you go a numerical route, I would seek a laminar solution to avoid complications with the closure problem, as I doubt people will be fluctuating around in a room or through a door. 
A: For most fluid mechanics problems the governing equations are the Navier-stokes equations. Here specifically you'd want the momentum equations.
