Boundary layer thickness laminar flow, flat plate

The properly (equation [1.31]) of bormdary layers regarding the pressure gradient is of the same nature as the property of pressure uniformity in planes perpendicular to the flow direction, which was observed for the Poiseuille and Couette solutions. Figure 1.6(a) shows that the bormdary layer thickness on a flat plate grows with increasing values of x. At a sufficient distance from the inlet of a pipe, the boundary layer thickness eventually exceeds the diameter of the pipe. The flow reverts to the Poiseuille type solutiou presented previously, if the Reynolds number is sufficiently low to allow the flow to remain laminar. Such flows are termed established laminar flows or developed flows , as the velocity field does not change any more when traveling downstream in the pipe, because the boundary... 

Laminar boundary layer theory assumes that a uniform flow (V = constant) approaches a flat plate. A laminar flow region develops near the plate where the thickness of the laminar boundary layer increases with thickness along the plate, as developed in Example 4.2. If we assign 5 to be the boundary layer thickness, or the distance from the plate where the velocity is equal to 0.99 times the velocity that approached the plate, and 5c to be the concentration boundary layer thickness, then we can see that both 5 and 5c are functions of distance, x, from the leading edge, as shown in Figure 8.11. 

Consider transition in the boundary layer flow over a flat plate. Using the expression for the thickness of a laminar boundary layer on a flat plate given in Chapter 3, find the value of the Reynolds number based on the boundary layer thickness at which transition begins. 

A vertical flat plate is maintained at a uniform surface temperature and is exposed to air at standard ambient pressure. At a distance of 10 cm from the leading edge of the plate the boundary layer thickness is 2 cm. Estimate the thickness of the boundary layer at a distance of 25 cm from the leading edge. Assume a laminar boundary layer flow. 

Note that /i, is proportional to Re and thus to. v- - for laminar flow. Therefore, is infinite at the leading edge (jc = 0) and decreases by a factor of.r in the flow direction. The variation of the boundary layer thickness 5 and the friction and heat transfer coefficients along an isothermal flat plate are shown in Fig. 7-9. The local friction and heat transfer coefficients are higher in... 

The thickness of the velocity boundary layer is normally defined as the distance from the solid body to the fluid layer at which the flow velocity reaches 99% of the free stream velocity, as illustrated in Figure 2.17. For a flat-plate body emerging in an incompressible and laminar fluid, the boundary layer thickness is given by... 

By assuming that the velocity was a function of y yj xv)X Blasius was able to solve Prandtl s equations for the steady-flow laminar boundary layer on a flat plate. He found that the laminar boundary-layer thickness is proportional to the square root of the length down the plate. 

A polymer solution (density 1022 kg/m ) flows over the surface of a flat plate at a free stream velocity of 2.25 m/s. Estimate the laminar boundary layer thickness and surface shear stress at a point 300 mm downstream from tlie leading edge of the plate. Determine the total drag force on the plate from the leading edge to this point. What is the effect of doubling the free stream velocity ... 

With such a flat plate, the boundaiy layer will increase in thickness in-dcfinitely if slowly (Fig. 1.10(c))l On the other hand if the flow is in a restricted channel (e.g. a circular-tube or a paraltel-plate cell) the boundary layers at the two walls must merge at some point and beyond, a steady-state situation or fully developed laminar flow will result (Fig. Ltl). Fundamental mass transport studies in electrolytic cells are usually carried out in cells with an entry length without electrodes so that the boundary-layer thickness is uniform over the current-carrying surface. 

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

Structure of the flow. Velocity profile. The flow in the boundary layer on a flat plate is laminar until Rex = U[X/v 3 x 105. On a longer plate, the boundary layer becomes turbulent, that is, its thickness increases sharply and the longitudinal velocity profile alters. 

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 where turbulence appears. The onset of turbulence is characterized by a sudden rapid increase in the thickness of the boundary layer, as shown in Fig. 3.7. 

The thickness of the laminar boundary layer on a flat plate Z, is approximately given by the equation = 5.5Qtx/u py. Show that at the transition to the turbulent flow the Reynolds number based on this thickness, instead of on x as in Eq. (3.21), is close to the transition Reynolds number for flow in a pipe,... 

Assuming that the transition from a laminar to a turbulent boundary layer takes place at a Reynolds number of 10 what is the maximum thickness for the laminar boundary layer on a flat plate for ( ) air flowing at 10 ft/s, (b) water flowing at jlOft/s, and (c) glycerin flowing at 10 ft/s = 8.07 x 10 ft /s) ... 

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