[Physics Class Notes] on Boundary Layer Pdf for Exam

In fluid mechanics, the term boundary layer refers to a thin layer of flowing liquid or gas in contact with a surface like a boundary layer in pipe flow or the surface of an aeroplane wing. The fluid present in the boundary is subjected to shearing forces, and there exists a range of velocities across the boundary from maximum to zero. This occurs only when the fluid comes in contact with the surface of an object.

 

Boundary layer concepts in an aircraft wing are thicker toward the trailing edge while thinner at the leading edge. The boundary layer flow is generally turbulent in the downstream or trailing portion and laminar at the top or upstream.

What is Boundary Layer Theory?

Boundary-Layer theory states that when a real fluid flows over a solid body, the boundary’s velocity remains zero only if the boundary is stationary. However, if the object moves away from the boundary in a perpendicular direction, the rate increases to the free stream velocity; this means a velocity gradient- (du/day). Velocity gradient  (du/day) does not exist outside the boundary as the outside boundary layer velocity is equal and constant to the free stream velocity. The development of the boundary layer is of three regions- laminar, turbulent, and transition. 

Boundary Layer Theory in Fluid Mechanics

The boundary layer theory in fluid mechanics states that when a fluid has a relative motion to the surface, the liquid particles next to it adheres. This adhering mechanism is known as the ‘no-slip condition. Through viscosity, this layer then creates a barrier or resists the next layer, thus slowing it down, which, in turn, affects the layer above it, and this mechanism goes on. 

Therefore, when an object moves away from the surface, it experiences fluid layers of increasing velocity till the object reaches the layer where the fluid holds no velocity reduction or moves toward free stream velocity. Theoretically, this occurs at infinity. For brevity’s sake, boundary layer definition is the thickness starting from the surface to the point that comprises 99 per cent fluid velocity of the free stream velocity. 

Therefore, the real fluid phenomena are restricted within the boundary layer, and this is why an object experiences friction drag or vice-versa. The layer will also keep growing along the surface’s length. 

For instance, the ripples around the boat or a canoe in calm water are limited to only a certain distance from the canoe or boat’s body. This is a simple visualisation of the boundary layer around the boat or canoe.

Boundary Layer in Aerodynamics

The boundary layer in aerodynamics is significant because the shape of the aerofoil changes effectively in its presence. The boundary layer flow can be attached to the aerofoil’s surface at lower angles of attack, resulting in Laminar flow, or it can be separated from the aerofoil surface at high angles of attack, resulting in a separated flow. 

The nature of the boundary’s characterisation regards Reynold’s number, which determines the ratio between inertial and viscous forces. If the viscous forces dominate the inertia forces, the boundary remains attached to the aerofoil resulting in a laminar flow. If the inertia forces dominate the viscous forces, then the boundary is no longer attached to the aerofoil resulting in a separated flow. The viscous flow acts parallel to the surface of the aerofoil resulting in shear forces. 

In aerodynamics, the boundary layer definition will be in terms of viscosity. Thus, the boundary layer is a region in the vicinity of the viscous forces’ aerofoil surface.