Flow across cylinders separated

Flows across cylinders and spheres, in general, involve flow separation, which is difficult to handle analytically. Therefore, such flows must be studied experimentally or numerically. Indeed, flow across cylinders and spheres has been studied experimentally by numerous investigators, and several empirical correlations have been developed for (he heat transfer coefficient. 

A third common technique for separating mixtures of proteins, as well as other molecules, is based on the principle that molecules dissolved in a solution will interact (bind and dissociate) with a solid surface. If the solution is allowed to flow across the surface, then molecules that interact frequently with the surface will spend more time bound to the surface and thus move more slowly than molecules that interact infrequently with the surface. In this technique, called liquid chromatography, the sample Is placed on top of a tightly packed column of spherical beads held within a glass cylinder. The nature of these beads determines whether the separation of proteins depends on differences in mass, charge, or binding affinity. 

Flow across a tube produces a series of vortices in the downstream wake formed as the flow separates alternately from the opposite sides of the tube. This alternate shedding of vortices produces alternating forces which occur more frequently as the velocity of flow increases. For a single cylinder the tube diameter, the flow velocity, and the frequency of vortex shedding can be described by the dimensionless Strouhal number ... 

Consider a system enclosed in a piston-cylinder assembly, which constrains pressure at the value F. The assembly is immersed in a heat bath, which constrains temperature at the value T. Experience shows that spontaneous processes under these conditions consist of spontaneous flow of molecules across a boundary completely internal to the system, separating different regions (called phases) of the system (Fig. 13.9). 

Many standard sizes of hydrocyclone are available with cylinder diameters of 1-30 cm and cone angles of 25°-50°. The particle cut size, which is the size equally likely to find its way into the underflow or overflow, is limited to about 5 pm and dependent on several factors including the size and geometry of the hydrocyclone, the inlet flow rate and the pressure drop across the unit. Separation is often more effective (in terms of a lower cut size) with a series of smaller diameter hydrocyclones as higher tangential velocities can be achieved. 

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