Boundary Layer Theory - Introduction

now let's talk about the boundary layer theory this is a very very important topic and you should be very good in understanding of this topic so let's introduce the concept to you so let us say you have a solid body of this shape so this is the solid body okay and a real fluid is flowing across or you can say a stream of real fluid is flowing over this solid body okay so when this real fluid so the entire velocity let us say is capital u and this capital u is called the free stream velocity free stream velocity now when this new fluid passes over the surface of the body the fluid particles they will cling on to the surface okay this means that the velocity of the fluid particles at this you know boundary of this surface or boundary of this body will be equal to the velocity of the body this means that the body is not moving the movement is always of the fluid so when I say that the velocity of these fluid particles which are on the boundary of this body will have the same velocity as that of the surface of the body this means that the velocity of the fluid reduces to zero and the layer or at the boundary of this body so we can make the make a generalization out of this that as a real fluid flows over a solid body fluid particles fluid particles they cling on they cling on to the surface of the body to the surface of the body okay this means that the velocity of these fluid particles will be same as the velocity of this surface of the body this means velocity of the fluid particles okay on the surface should be equal to the velocity of the surface this means the velocity of the surface is zero the velocity of the fluid also at the surface is zero okay now and you start going up or away from the surface the velocity starts to rise means there is a variation in the velocity which is witnessed as we go you know away from the boundary of the surface or the boundary of the body the surface of the body okay so this means that there is an existence of a velocity gradient means velocity will change with respect to distance from the surface okay and after a certain time or at a certain height you will have a velocity which will no longer vary with respect to distance means this velocity would be equal to capital u which is the free stream velocity so this again gives us a generalization that the velocity gradient the velocity gradient this exists only for a small portion above the or you can say this velocity gradient is occurring in a small layer above the surface of the body this is occurring in a small layer okay above the surface and below this beyond this beyond this D velocity great into advantage so this you can say a region in which the velocity gradient is occurring that is the velocity is varying with respect to the distance from the surface of the body this small layer is called the boundary layer because it is very close to the boundary okay so because there is some velocity variation with respect to distance in this boundary layer this means there will be some production of shear stress so the value of the shear stress in the boundary layer would be given by mu D u by dy mu u by dy okay so this means that if you go beyond this boundary layer there will be no velocity gradient that means there will be no production of shear stress so there is no tau over here tau becomes zero once you go beyond the boundary layer okay so to summarize I would say the fluid particles which are on the surface of the body have zero velocity means they are at rest this condition is called no slip condition because there is no relative motion in between the fluid particles and the body surface right they're doing they are at rest the velocity becomes zero as you start going away from the body surface the velocity will start to change this means that a velocity gradient welcome to make sure alright and as you keep on moving further away and ultimately this velocity would vanish and the entire flow would have a same velocity off d you can say the free free velocity okay so the height above which or up to which this gradient is occurring or this velocity variation is occurring is called the boundary layer within the boundary layer because there is some D u by dy occurring so you will have some value of tau okay and as you go above this you know boundary layer there is no D u by D where this means the value of tau becomes zero and the entire flow moves with a single velocity which is the free stream velocity so I hope you got this basic introduction of the boundary layer theory now let's move on to the next topic and talk about the kind of flows which occur in a boundary layer flow

Channel: Tutorials Point (India) Ltd.

Views: 91,599

Keywords: Engineering class, mechanical Engineering, GATE Exam, Boundary Layer Theory - Introduction, Boundary Layer Theory

Id: 54zf68IoPWU

Length: 6min 58sec (418 seconds)

Published: Mon Jan 22 2018