Conservation of mass (a.k.a., continuity) [Fluid Mechanics #2]

In this video, we start exploring the conservation laws of fluid mechanics---a set of equations that define how fluids move and respond to force.
Our first step is to build the Conservation of Mass, a.k.a. Continuity. In observing a fluid through an observation window, if mass flows in it either must flow out or our window's mass changes. We build the balance of mass equation and consider the incompressible assumption, meaning we can't change the fluid density. By the end of the video, you should have a better physical intuition of what mass conservation means for a fluid.
Free downloadable notes (PDF with white background) can be found at my website: sites.udel.edu/vanburen/educa...

[@gloxe1282]

Sir, you are amazing

[@prof.vanburen]

Aw thanks!

[@eveleenkaur4349]

Excellent Explanation👌

[@prof.vanburen]

Thanks!

[@user-es3tk3oz9p]

I did not get why the mass flow rate (mdot on the rigth side of the equation) = the change on the cube mass at 06:10

[@prof.vanburen]

dot indicates "change in time", so it is just the symbolic definition of mass change of the cube.

[@evangelinblessyhknzrypjimp4972]

Sir, can you also explain the integral form of continuity equation? Can you also please define the difference between steady and incompressible flow in an understandable way??

[@prof.vanburen]

Hi! I will certainly consider a video on the integral form of the equations. It's common to see these in derivations, but I have always defaulted to the differential form of the equations which, to me, are more useful and understandable. Regarding the steady vs. incompressible flow, see the "common assumptions in fluid mechanics video". Steady flow - means not changing in time. If you stare at a point in a steady flow, you will not see any changes in the flow characteristics no matter how long you look at it. You could sit there a minute, an hour, a week, it would be the same flow. Flow can still accelerate, but it has to happen through convective acceleration. This is as if you were to start changing where you look, you could see changes in the flow. Incompressible flow - means the flow itself cannot change the fluid density, and generally means the density is constant throughout the fluid. This means, you can't make the molecules get closer together or further apart. It's common for liquids and slow moving gases. For fast gases, we can't assume incompressible because the pressure differences in the flow are large enough to start to compress the fluid. Hope this helps!

[@evangelinblessyhknzrypjimp4972]

@@prof.vanburen thank you so much sir.....this explanation is amazing

[@mikeshan417]

Sir, I think you missed a minus sign on the RHS of the 1D mass conservation equation? Shouldn't it be [ - (delta rho/delta t) delta x delta y delta z ] ?

[@prof.vanburen]

You mean around 7:25? I think you're right, I was lazy and lost a minus sign in there.

[@mikeshan417]

@@prof.vanburen Yes got it thank you

[@xavii297]

Really, you are big

[@prof.vanburen]

Thanks I think!