Blasius flat plate boundary layer solution

Blasius steady-flow, laminar, flat-plate, boundary-layer solution is a numerical solution of his simplification of Prandtl s boundary-layer equations, which are a simplified, one-dimensional momentum balance and a mass balance. This type of solution is known in the boundary-layer literature as an exact solution. Exact solutions can be found for only a very limited number of cases. Therefore, approximate methods are available for making reasonable estimates of the behavior of laminar boundary layers (Prob. 11.8). 

In this case, the diffusion boundary layer is embedded in the viscous boundary layer and the velocity it sees is that close to the wall. The Blasius solution for flat plate boundary layer in the series form is... 

Of much greater interest is the case where Sc= v D>, since our principal concern is with dilute solutions. For this situation the diffusion boundary layer is imbedded in the viscous boundary layer, and the velocity it sees is that close to the wall. Solution to the steady, Blasius, flat plate, viscous boundary layer equation shows the velocity components close to the wall (y[Pg.108]

The transition to a turbulent boundary layer for a flat plate has been experimentally determined to occur at an Rcx value of between 3 x 10 and 6 x 10. For this example, the transition would occur between 15 and 30 cm after the start of the plate. Thus, the computations for a laminar boundary layer at 0.6 and 1 m are not realistic. However, the Blasius solution helps in the analysis of experimental data for a turbulent boundary layer, because it can tell us which parameters are likely to be important for this analysis, although the equations may take a different form. 

Blasius solution for the laminar boundary layer on a flat plate, shown in Fig. 11.3, rests on a considerable string of assumptions and simplifications. However, it has been tested by numerous investigators and found to represent the experimental data very well (note that Fig. 11.3 shows the comparison between Blasius solution and Nikuradse s experimental data). Thus, these assumptions and simplifications seem to be justified. 

Blasius solution for the laminar boundary layer on a flat plate and Nikuradse s experimental tests of same. [From J. Nikuradse, Laminar Reibungsschichten an der laengsangestroemten Platte (Laminar friction layers on plates with parallel flow), Monograph Zentralefuer Wiss. Berichtwesen, Berlin (1942). 

For boundary layers on curved surfaces, the pressure will change with distance. This greatly complicates the solution of the boundary-layer equations compared with that on a flat plate (in which dPIdx was zero), and so very few exact solutions are known for such boundary layers. Some estimate of the behavior of such boundary layers is given by several methods. To illustrate, we apply them to the laminar boundary layer on a flat plate, where we can compare the results with Blasius exact solution. These methods begin by assuming a velocity profile of the form V tV where S is the boundary-layer thickness. 

Introduction and derivation of integral expression. In the solution for the laminar boundary layer on a fiat plate, the Blasius solution is quite restrictive, since it is for laminar flow over a flat plate. Other more complex systems cannot be solved by this method. An approximate method developed by von Karman can be used when the configuration is more complicated or the flow is turbulent. This is an approximate momentum integral analysis of the boundary layer using an empirical or assumed velocity distribution. 

Integral momentum balance for laminar boundary layer. Before we use Eq. (3.10-48) for the turbulent boundary layer,.this equation will be applied to the laminar boundary layer over a flat plate so that the results can be compared with the exact Blasius solution in Eqs. (3.10-6)-(3.10-12). 

In section 3.IOC an exact solution was obtained for the velocity profile for isothermal laminar flow past a flat plate. The solution of Blasius can be extended to include the convective heat-transfer problem for the same geometry and laminar flow. In Fig. 5.7-1 the thermal boundary layer is shown. The temperature of the fluid approaching the plate is Tjj and that of the plate is Tg at the surface. 

Here, we concentrate on general similarity criteria and behavior that can be deduced from the well-known Blasius solution, for flow past a nonreacting flat plate. For high Reynolds number boundary layer flow past a flat plate with no gravitational force in the streamwise direction, for constant viscosity, the boundary layer equation is given by... 

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