Viscosities of Gases and Liquids• The viscosity of a Newtonian fluid depends primarily on

temperature and to a lesser degree on pressure.

Flow in Boundary Layers

Boundary Layer• The part of a moving fluid in which the fluid motion is

influenced by the presence of a solid boundary.

Boundary Layer

Laminar and Turbulent Flow in Boundary Layers• Flow in this part of the boundary layer is essentially laminar.• Actually it is laminar most of the time, but occasionally eddies

from the main portion of the flow or the outer region of the boundary layer move very close to the wall, temporarily disrupting the velocity profile.

• Between the zone of fully developed turbulence and the region of laminar flow is a transition, or buffer, layer of intermediate character.

• Turbulent boundary layer has three zones:• Viscous sublayer• Buffer layer• Turbulent zone

Laminar and Turbulent Flow in Boundary Layers

Laminar and Turbulent Flow in Boundary Layers• The factors that determine the point at which turbulence

appears in a laminar boundary layer are coordinated by the dimensionless Reynolds number defined by

Laminar and Turbulent Flow in Boundary Layers• Transition length for laminar and turbulent flow

• The length of the entrance region of the tube necessary for the boundary layer to reach the center of the tube and for fully developed flow to be established is called the transition length.

Laminar and Turbulent Flow in Boundary Layers

Near the leading edge of a flat plate immersed in a fluid of uniform velocity, the boundary layer is thin, and the flow in the boundary layer is entirely laminar. As the layer thickens, however, at distances farther from the leading edge, a point is reached when turbulence appears.

Example• Estimate the transition length at the entrance to a 15-mm

tube through which 100% glycerol at 60°C is flowing at a velocity of 0.3 m/s. The density of glycerol is 1240 kg/m3.

Boundary Layer Separation and Wake Formation

• Boundary-layer separation occurs whenever the change in velocity of the fluid, either in magnitude or direction, is too large for the fluid to adhere to the solid surface. It is most frequently encountered when there is an abrupt change in the flow channel, like a sudden expansion or contraction, a sharp bend, or an obstruction around which the fluid must flow

Boundary Layer Separation and Wake Formation

• Separation may also occur from velocity decrease in a smoothly diverging channel. Because of the large energy losses resulting from the formation of a wake, it is often desirable to minimize or prevent boundary-layer separation. In some cases this can be done by suction, i.e., by drawing part of the fluid into the solid surface at the area of potential separation. Most often, however, separation is minimized by avoiding sharp changes in the cross-sectional area of the flow channel and by streamlining any objects over which the fluid must flow.