Fluid Mechanics Lesson 11B: Boundary Conditions for the Navier-Stokes Equation

Fluid Mechanics Lesson Series - Lesson 11B: Boundary Conditions for the Navier-Stokes Equation.

In this 13.5-minute video, Professor Cimbala shows how to calculate the required number of boundary conditions for a given set of partial differential equations, showing three examples. He then discusses several boundary conditions that are commonly used in solving the continuity and Navier-Stokes equations: no-slip, interface, free-surface, inlet, outlet, and symmetry boundary conditions, along with initial conditions.

This video incorporates material from Section 9-6 of the Fluid Mechanics textbook by Cengel and Cimbala, edition 4.

An Excel file listing of all the videos in this series, along with the annotated notes generated during filming of the videos, can be found at


You can also watch all related short videos with one click by going to one of Dr. Cimbala's playlists:

[Eltaurus]

0:30 This is a very nice and clear formulation, but is there any associated theorem that prooves existence/uniquness of a solution for the required number of BCs? What are the other conditions on the (or anything else) for the functions involved?

Also, what counts as a single boundary condition in a general case, when we have curved boundaries?

[SashaPrival]

Nice vid, professor. How about IC and BCs for channel flows in general. I.e. 1) for open channel flow (as I understand, in this case there will be free surface on top of the fluid, and air pressure); 2) for closed channel flow or pipe flow (as I understand, in this case there will be no free surface, the fluid will "fill" the whole space between the plates and flow). In each of these cases, what would be the pressure grad terms and force terms in NS eqs? Sorry for my English. Not a native speaker. Again, thank you for the great video.