Momentum equation, laminar boundary derivation

If the turbulent momentum equation is expressed in nondimensional form in the same way as was done in deriving the laminar boundary layer equations then the additional term becomes ... 

The boundary layer integral equations have been derived above without recourse to the partial differential equations for boundary layer flow. They can, however, be determined directly from these equations. Consider, for example, the laminar momentum equation (2.140). Integrating this equation across the boundary layer to some distance from the wall, i being greater than the boundary layer thickness, gives because du/dy is zero outside the boundary layer and because dp/dx is independent of y ... 

First consider the finite difference form of the momentum equation, i.e., Eq. (6.128). As with laminar boundary layer flow, the four nodal points shown in Fig. 6.9 are used in deriving the finite difference form of this equation. 

What is the momentum equation for the laminar boundary layer on a flat plate What assumptions are involved in the derivation of this equation ... 

In this section we derive the equation of motion that governs the natural convection flow in laminar boundary layer. The conservation of mass and energy equations derived in Chapter 6 for forced convection are also applicable for natural convection, but tlie momentum equation needs to be modified to incorporate buoyancy. 

With terms III-V in Eq. 4.7 deleted, Eqs. 4.5-4.7, together with the x and y momentum equations, constitute the simplified equations of motion appropriate to natural convection problems. For constant T . and 7U, the boundary conditions on these equations are 0 = 1 and u = v = w = 0 on the body and 0 = 0 far from the body. Steady-state laminar solutions to these equations are those that are obtained after setting the time partials (i.e., terms containing partial derivatives with respect to t ) in the equations equal to zero. Steady-state turbulent... 

In order to derive the basic equation for a laminar or turbulent boundary layer, a small control volume in the boundary layer on a flat plate is used as shown in Fig. 3.10-5. The depth in the z direction is b. Flow is only through the surfacesand dj and also from the top curved surface at 8. An overall integral momentum balance using Eq. (2.8-8) and overall integral mass balance using Eq. (2.6-6) are applied to the control volume inside the boundary layer at steady state and the final integral expression by von Karman is (B2, S3)... 

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