Friction coefficient parallel flow

When the inlet length is expressed in terms of number of gap widths , the difference between the flow in a tube and the flow in an annulus of narrow gap differs only by 25% [(0.05 - 0.04)/0.05]. This situation is an indication that the growth of the laminar boundary layers from the wall to the center of the channel is similar in both cases. Because duct friction coefficients, a measure of momentum transfer, do not vary by more than a factor of 2 for ducts of regular cross sections when expressed in terms of hydraulic diameters, the use of the inlet length for tubes or parallel plates can be expected to be a reasonable approximation for the inlet lengths of other cross sections under laminar flow conditions. In the annular denuder, the dimensionless inlet length for laminar flow development, L, can be expressed as... 

For parallel flow over a flat plate, the pressure drag is zero, and thus the drag coefficient is equal to the friction coefficient and the drag force is equal to the friction force. 

For parallel flow over a flal plate, (he local friction and convection coefficients are... 

Such a friction coefficient accounts only for flow parallel to the Inner tubes and lead screw. To account for the resistance caused by cross-flow at the top and bottom of the cell, the friction coefficient was determined by assuming that the cross-flow velocity at the top and bottom of the enclosure Is the same as the recirculating velocity to yield... 

Equation [213] can be equivalently obtained using the Mori-Zwanzig formalism. " It is also seen that, in contrast to LRT developed for shear flow in bulk fluids, the one presented here has two coefficients, (which is similar to the shear viscosity q) and, which has no parallel in bulk fluids. should be interpreted as an average location at which hydrodynamics is found to be nominally invalid. Note that although the surface may have corrugations in the X as well as the y direction, the corrugation in the x direction alone matters to the frictional force in the planar Couette geometry. 

The resistance that a liquid offers to flow, caused by internal friction between adjacent moving layers, is known as its viscosity. For a pure liquid, Newton defined the coefficient of viscosity as follows. Consider two parallel, adjacent planes in a liquid, of area A, distant x m. apart, moving relative to one another with a velocity v m.sec.-L The frictional force per unit area, F/A, is then given by — F/A = rj dv/dx,... 

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