Viscosities of Gases and Liquidsβ’ The viscosity of a Newtonian fluid depends primarily on temperature and to a lesser degree on pressure. π π = π0 273 π β’ π β 0.65 πππ πππ β’ π β 0.90 πππ πΆπ2 πππ ππ‘πππ π πππππ ππ¦ππππππππππ β’ π β 1.10 πππ ππ2 πππ π π‘πππ Flow in Boundary Layers . Boundary Layer β’ 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 β’ Flow in this part of the boundary layer is essentially laminar. β’ Turbulent boundary layer has three zones: β’ Viscous sublayer β’ Buffer layer β’ Turbulent zone . temporarily disrupting the velocity profile. β’ Between the zone of fully developed turbulence and the region of laminar flow is a transition. layer of intermediate character. or buffer. but occasionally eddies from the main portion of the flow or the outer region of the boundary layer move very close to the wall. β’ Actually it is laminar most of the time. Laminar and Turbulent Flow in Boundary Layers . Laminar and Turbulent Flow in Boundary Layers β’ The factors that determine the point at which turbulence appears in a laminar boundary layer are coordinated by the dimensionless Reynolds number defined by ππ π.π₯ β’ β’ β’ β’ π₯π’β π = π π₯ = πππ π‘ππππ ππππ πππππππ ππππ ππ ππππ‘π π’β = ππ’ππ πππ’ππ π£ππππππ‘π¦ π = ππππ ππ‘π¦ ππ πππ’ππ π = π£ππ πππ ππ‘π¦ ππ πππ’ππ . 05ππ π π· . π₯ = 0.Laminar and Turbulent Flow in Boundary Layers β’ Transition length for laminar and turbulent flow β’ 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. the boundary layer is thin.Laminar and Turbulent Flow in Boundary Layers Near the leading edge of a flat plate immersed in a fluid of uniform velocity. at distances farther from the leading edge. and the flow in the boundary layer is entirely laminar. . however. a point is reached when turbulence appears. As the layer thickens. Example β’ Estimate the transition length at the entrance to a 15-mm tube through which 100% glycerol at 60Β°C is flowing at a velocity of 0. The density of glycerol is 1240 kg/m3. .3 m/s. Boundary Layer Separation and Wake Formation β’ Boundary-layer separation occurs whenever the change in velocity of the fluid. a sharp bend. It is most frequently encountered when there is an abrupt change in the flow channel. either in magnitude or direction. is too large for the fluid to adhere to the solid surface. like a sudden expansion or contraction. or an obstruction around which the fluid must flow . by drawing part of the fluid into the solid surface at the area of potential separation. Because of the large energy losses resulting from the formation of a wake. Most often.Boundary Layer Separation and Wake Formation β’ Separation may also occur from velocity decrease in a smoothly diverging channel. however. it is often desirable to minimize or prevent boundary-layer separation. 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. i. In some cases this can be done by suction.. .e.