Journal of the Society of Motion Picture and Television Engineers (1950-1954)

portional to the thickness of the stagnant layer and, therefore, any methods by which the thickness of the stagnant layer can be reduced will proportionally reduce the resistance of the stagnant layer. This proportionality may not hold true when the stagnant layer becomes extremely thin, i.e., of molecular size, but as a first order approximation it will hold true. Reduction of Stagnant Layer From the foregoing explanation it can be seen that the stagnant layer in liquids and gases is an extremely important factor which determines the rate of diffusion. The problem which now exists is how to reduce this stagnant layer so that the mass transfer can be increased. One method of reduction of the stagnant layer which has met with success is the application of supersonic vibrations which so agitate the surroundings as to reduce the thickness. A simpler way which has met with greater success, however, has been found in the application of turbulence. Early investigations by experimenters interested in the problems of fluid flow indicated that if liquid flowed through a tube the velocity distribution across the tube would be approximately parabolic. The steep sides of the parabola represent the stagnant fluid on the sides of the wall in which the velocity was so low that it could effectively be considered as standing still. However, it was soon discovered that if conditions in the tube were changed and the velocities of the liquids increased, a point was reached where suddenly the nature of flow changed completely. Whereas previously the flow was relatively smooth and streamlined, the new condition was one of extreme turbulence in which a considerable agitation of the fluid inside the tubes took place, and the velocity distribution could no longer be represented by a parabola but was more rectangular. The first condition of flow was arbi trarily called laminar and the second condition was called turbulent flow. It was later discovered that the Reynolds number (Re = DVp/fj.) was the main governing factor in the determination of whether the flow was turbulent or laminar, and it was specifically found that a critical Reynolds number exists at a value of approximately 2300 above which all flow is turbulent and below which all flow is laminar. It should be noted, however, that conditions can be artificially made such that turbulent flow can exist at Reynolds numbers below 2300, and laminar flow can exist at Reynolds numbers above 2300. In general, however, the critical Reynolds number of 2300 is a reasonable point for the determination of the separation between the two kinds of flow. It is especially important to note that the critical Reynolds number (the number at which laminar flow is no longer possible and turbulent flow exists) is 2300 only in circular ducts, with fluids flowing axially. For rectangular ducts correction factors must be applied and for circular flow in the plane perpendicular to the axis of the tube turbulent flow sometimes occurs only at extremely high Reynolds numbers (approximately 500,000). Care should be taken not to confuse turbulent flow with "vigorous agitation." It is possible to have vigorous agitation in laminar flow, but turbulent flow is a specific condition in which the fluid provides its own agitation by breaking up into a series of vortices. It is only under these conditions that the stagnant layer is reduced as has been previously discussed. As a result of a large number of measurements in the field of heat transfer it was found that the heat transfer coefficients will be governed by the following correlation: * X 0.023 Katz and Esthimcr: Turbulent Fluid Processing (3) 109