Fluid Mechanics: Laminar Boundary Layer on a Flat Plate (31 of 34) 

A man of culture as well

We're glad it was helpful!

Thanks

You're welcome.

Reading the book adds a lot of additional information and context... Dr. Biddle certainly read many fluid mechanics textbooks over the years. :)

The book is Fluid Mechanics (8th) by Frank M. White.

Sorry, Dr. Biddle's lecture notes are not available.

go back to navier-stokes equation, it is just an algebraic manipulation of the equation nothing else

More fluid is in contact with wall.....so there is more effect of wall stress

As you move along the wall, the influence of the wall (no slip boundary condition) has more time to impact the flow near the wall.

Due to Viscosity

What assumption are involved in the derivation of momentum eq and energy eq for laminar boundary layer?

Kinematic viscosity... it is (absolute viscosity / density)

@@CPPMechEngTutorials Thank you very much.

Me.

the analysis of order of magnitude in that video is totally valid. as the whole point of that analysis is to non-dimensioalize the navier-stokes equation to actually obtain the order of magnitude of the pertaining values. and if you are still confused about what is the order of magnitude is all about, the reasoning goes something like this: first we analyze the navier-stokes for the x component which is the most prominent id we are dealing with a uniform fluid velocity (Uo) then we can obtain through non-dimensionlaization that the partial second order derivative of the velocity (u in respect to x is 1:1) which means that suppose that the velocity is 2m/s then the change of x is in the same order of magnitude (ie something like 5m or something) however, when we analyze the partial second order derivative of velocity u in respect to the horizontal height of the boundary layer, then through the nondimeonalized equation, we can observe that the previously assumed velocity in x (Uo) is 5m/s but the change in boundary layer is something like 0.000001 for example which gives us a way larger value than the (delsquared(u)/del(x)squared) and thus we can ignore it accordingly. the same thing goes with the navier-stokes in the y direction, you can see from the nondimenosionalized equation that (dp over the change in y) is by sandwiching the order by the previous analysis that have been done in the video is going to be something like 0.00001 and thus we can ignore the change in the pressure over the vertical displacement overall as it shows no significant change overall. and if the change in pressure over the vertical is almost insignificant then we can assume that navier-stokes is only viable for the horizontal direction only

@@NostalgiaGames_Gamer Many many thanks for exaplining that. Two questions: 1. Do you need a pressure change to make NS equation viable? 2. Now that we have the boundary layer equation, how do I go about solving it? I'm relatively basic level and the PDE looks very complex.

@@marquez2390 no worries, 1) a pressure change is negligible in the x direction because of the constant uniform flow velocity U, an thus can be ignored in the xmomentum equation of NS, thus we will have the equation that the professor wrote down, and also the pressure change in the y direction is similarly neglected when we talk about the y-momentum in general, and thus pressure change in the BL theorem equations are mostly neglected in laminar flow, however, in general (not related to BLT) we of course have to take the NS equation with all it's glory, however solving it requires computational power and it is beyond our ability without numerical approximations 2) Don't worry about the partial differentials for now in the BLT, blasius has already done the job by using a similarity solution (i advise you to watch (Mod-01 Lec-12 Laminar External flow past flat plate (Blasius Similarity Solution) ) video, very informative, and yielded a beautiful simple approximate solution for laminar BLs , but as a general note please review the partial differential equation solving methods as they will be helpful later on. Greetings .

@@NostalgiaGames_Gamer Thank you a lot.

Can you provide a timestamp?

@@CPPMechEngTutorials 53:08

@@CPPMechEngTutorials Fr=v/(Lg)^0.5

@@tuanle4958 You are correct. We will place a correction in the video comments. Thanks for catching this!