Velocity, area averaged

Here, V is the area average velocity, K is the number of velocity heads of pressure drop provided hy the uniform resistance, Ap = FCpV/2, and a is the velocity profile factor used in the mechanical energy bal-... 

Here, V is the area average velocity, K is the number of velocity heads of pressure drop provided by the uniform resistance, Ap = KpV2/2, and a is the velocity profile factor used in the mechanical energy balance, Eq. (6-13). It is the ratio of the area average of the cube of the velocity, to the cube of the area average velocity V. The shape of the exit velocity profile appears twice in Eq. (6-154), in V%mIV and a2. Typically, K is on the order of 10, and the desired exit velocity profile... 

Because Ay and Az are small compared to the size of the system, u may be regarded as the area-averaged velocity component at a point in the flow. The area-averaged velocity components in the other coordinate directions at a point in the flow are defined in the same way, i.e., by ... 

The analyses of convection in porous media presented in this chapter will all be based on the use of these area-averaged velocity components. Their use is, of course, similar to the use of time-averaged velocity components in turbulent flows. ... 

By definition, with the area-averaged velocity defined as above, the continuity equation for flow in a porous medium w ill have the same form as that for the flow of a pure fluid, i.e., the continuity equation for flow through a porous medium is, if density variations are negligible ... 

Here, V is the area average velocity, K is the number of velocity heads... 

Provided that the interfacial area averaged velocities are parameterized in a consistent manner (i.e., Pyfc((vfc) j — ( V() y ) = 0), this condition shows that the introduction of the surface tension force is in accordance with Newton s 3. law. 

In practice, however, it is difficult to parameterize the interfacial area averaged velocity so in the momentum equation it s often set equal to the bulk velocity and in the momentum jump condition the mass transfer terms are simply neglected enabling a closure relation for the interfacial drag terms which are in agreement with Newton s 3. law. Hence,... 

The area-averaged velocity at the outlet of the channel with a probe is strongly dependent on the probe position and decreased from D to A. The area-averaged velocity at the outlet of a reference channel slightly changes vice versa because the reduction of volume flux in the channel with the probe is distributed toward the neighboring empty channels. From configuration A over B and C to D, the probe is positioned closer and closer to the comer of the channel. As the velocity profiles in the channels develop fast, the channels are filled with boundary. Hence, the probe lies more and more in the area of influence of the channel walls where the velocity... 

A further point about Poiseuille flow concerns the area-average velocity, U. Clearly, U = Q/ cross-sectional area = (jtKa I8/j,)I7TO = ka /S/u,. But, as was pointed out, the maximum velocity in the tube is Wmax = Ka /4/x. Hence U = Mmax/2 = (l/2)M r=o = (1/2)mcl-... 

Consider a circular cylindrical pipe of diameter D = 2R in which water flows with an established velocity profile (r) whose area-average velocity is W. ... 

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