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Boundary layer Theory:

Introduction:

Flow abt a solid body can be divided into 2 regions, one thin layer in the neighbourhood of the body

called as boundary later, where friction plays a imp part. The second region is outside the layer,

where friction is least neglected.

Designed to calculate the asymptotic expansions of the soln to the complete equation of motion.

This problem is further reduced to a single perturbation.

BL is used for the calculation of skin friction drag which acts on the body as it moved thr a fluid.

Flow is the immediate vicinity of the solid wall becomes reversed causing th BL to separate from it.

This helps in the formation of eddies in the wake of the body. Hence the pressure distribution is

changed. This diff in pressure will create the drag and its calculation is possible with the help of

boundary layer.

This separation can also occur in internal flow thr channels and its not confined to external flows.

The phenomena which occur at the point of maximum lift of an aerofoil and stalling can be

understood with the help of boundary layer.

Also the problem of heat transfer between a solid body and the fluid can be explained with the help

of the boundary layer.

At first, the BL was developed for Laminar flow and lots of research papers were published on this

topic and this topic was solved.

So the topic was focussed into turbulent BLs, with the introduction on Turbulent stresses.

Later with the prandtls mixed length theory (1925) together with the systematic experiment paved

the way for the analysis of turbulent flows using BLs.

In addition to a velocity BL, there exists a thermal BLs and its existence plays an important part in

the process of heat transfer between and fluid and a solid body.

At very high mach nos, the surfaces of the solid wall become heated to a high temperature with the

production of frictional heat.

The phenomenon of transition from laminar to Turbulent is the fundamental for fluid dynamics

which was observed by O.Renolds.

Tollimien.W computed theoretically the critical Reynolds no for transition on a flat plate at zero

incidences.

Later many expt were carried out and among them is the design of aerofoils of very low drag.

Later started carrying out a small no:of fundamental expts backed by theoretical consideration.

END OF INTRODUCTION

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Real and perfect fluids:

With perfect fluids: Two contacting layers experience no tangential forces( shear stress) but act on

each other with normal forces(Pressure) only.

Perfect fluid with a drag? This is only the possible way...!!

In the perfect fluids, the inner layers of the fluid will transmit tangential and normal stresses

connected by a property called viscocity.

The existence of tangential stresses and the condition of no slip near solid wall tell the diff between

a perfect and a real fluid.

Water and air having low coefficient of viscosity.

Small viscosity=small shearing stress

Even with less viscosity, the condition of no slip prevails.

Partly convergent and divergent behaviour of perfect and real fluids can be explained wrt viscosity.

VISCOSITY: