Recap: Viscous Incompressible Flow | Fluid Mechanics for Mechanical Engineering PDF Download

 Recap

In this course you have learnt the following

• The boundary layer is the thin layer of fluid adjacent to the solid surface. Phenomenologically, the effect of viscosity is very prominent within this layer.
• The main-stream velocity undergoes a change from zero at the solid surface to the full magnitude through the boundary layer.Effectively, the boundary layer theory is a complement to the inviscid flow theory.
• The governing equation for the boundary layer can be obtained through correct reduction of the Navier-Stokes equations within the thin layer referred above. There is no variation in pressure in y direction within the boundary layer.
• The pressure is impressed on the boundary layer by the outer inviscid flow which can be calculated using Bernoulli's equation.
• The boundary layer equation is a second order non-linear partial differential equation. The exact solution of this equation is known as similarity solution. For the flow over a flat plate, the similarity solution is often referred to as Blasius solution. Complete analytical treatment of this solution is beyond the scope of this text. However, the momentum integral equation can be derived from the boundary layer equation which is amenable to analytical treatment.
• The solutions of the momentum integral equation are called approximate solutions of the boundary layer equation.
• The boundary layer equations are valid up to the point of separation. At the point of separation, the flow gets detached from the solid surface due to excessive adverse pressure gradient.
• Beyond the point of separation, the flow reversal produces eddies. During flow past bluff-bodies, the desired pressure recovery does not take place in a separated flow and the situation gives rise to pressure drag or form drag.