External flow pressure drag

B Develop an intuitive understanding of friction drag and pressure drag, and evaluate the average drag and convection coefficients in external flow, a Evaluate the drag and heat transfer associated with flow over a flat plate for both laminar and turbulent flow,... 

An externally imposed pressure gradient may also be present along with the drag flow, as in devolatilizing screw extruders for polymers. 

Removal of the melt, also discussed in Section 5.1, is made possible, in principle, by two mechanisms drag-induced flow and pressure-induced flow (Fig. 5.4). In both cases, the molten layer must be sheared, leading to viscous dissipation. The latter provides an additional, important source of thermal energy for melting, the rate of which can be controlled externally either by the velocity of the moving boundary in drag-induced melt removal or the external force applied to squeeze the solid onto the hot surface, in pressure-induced melt removal. 

Flow in a capillary can be maintained by a steady pressure difference Ap applied between inlet and outlet ends. We assume gravitational (and other external) forces to be negligible (true for a horizontal tube or for any tube with a large Ap). With the application of Ap, the fluid in the tube accelerates to a flowrate at which the viscous drag forces balance the applied pressure forces. For thin tubes the Newtonian acceleration forces are significant for only a brief moment before steady flow is achieved. 

Extensional flow takes place when the liquid is squeezed into a small opening (see Figure 15.6b). It occurs when the liquid enters (or exits) a chaimel or is pushed through a small hole (e.g., with high-pressure homogenization). In most praetieal cases, the flow pattern is a mixture of simple shear flow and extensional flow. A droplet in extensional flow will also experience a drag force exerted by the flow only now the external force exerted on the droplet is not equal to r ddvldz) but equal to t c dvldy), where y is the coordinate in the direction of the extension. We ean use the same relations as with simple shear flow, only in this ease the value of We, is different. So, also here. 

As with drag flow rtieometers, there are two basic design types one features controlled drive pressure and measurement of flow rate, and the other uses controlled flow rate and measures pressure drop. Pressure is controlled by a hydrostatic head, external gas or hydraulic pressure, or even a weight. Flow rate can be controlled by motion of a driving piston. Whoriow (1992) has an extensive review of pressure driven iheometer design. 

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