Boundary Layer Theory PDF

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Boundary Layer Theory Definition: A very thin layer of fluid, which is in the immediate in contact of the body, is called boundary layer. This layer of fluid behaves like a thin coating, as if it fixed or glued to the surface of the body. Therefore, velocity of fluid at the boundary layer is zero. The velocity of flow goes on increasing rapidly at extreme level of boundary and reaches to the level where velocity of liquid is 0.99V. The remaining portion of fluid, which is outside the layer, has high velocity and high Reynold’s number. Since, Reynold’s number (RNX): R NX 

Vx 

Where, V= velocity of liquid x = horizontal distance from plate from starting edge of plate to the point where thickness of boundary layer is required to be found out. υ = kinematic viscosity of liquid If the Reynolds number is less than 500 000, the flow is fully laminar and if it is between 500000 and 1000000, the flow in transition. But if it is more than 1000000 then flow is turbulent.

The thickness of boundary layer is different in laminar flow than turbulent flow.

Thickness of boundary layer in a Laminar Flow  lam 

5.835x R NX

5x Recently modified lam  R NX

Example.1: A smooth plate of 2 m side is kept immersed in water, which moves with a velocity of 300 mm/s. Find the thickness of boundary layer at a distance of 0.5 m from the leading edge. Take kinematic viscosity as 1.0× 10-6 m2/s. (Ans: 6.50 mm) Example.2: In an experiment, a smooth two-dimensional flat plate is exposed to wind of 90 km/hr velocity. If a laminar boundary layer exists up to a value of RNX = 2.0× 105, find

the maximum distance from the leading edge up to which laminar boundary layer exists and also find its maximum thickness with kinematic viscosity of air as 1.6× 10 -5 m2/s. (Ans: distance = 128 mm, and BL thickness = 1.4 mm)

Thickness of boundary layer in a Turbulent flow 0.377 x  R NX  1 / 5 Example.3: A smooth plate 1 m wide and 3 m long moves through stationary air with a velocity of 3 m/s. Determine the thickness of boundary layer at the trailing edge. Assume kinematic viscosity as 0.5 stoke.  turb ...