Drag force potential flow

In potential flow, = 0, and there is no wall drag. Also, the pressure drag in the direction of flow is balanced by an equal force in the opposite direction, and the integral of the form drag is zero, There is no net drag in potential flow. 

This result may be contrasted with potential flow past a sphere, where the streamlines again have fore-and-aft symmetry but p is an even function of 9 so that there is no net pressure force (see Chapter 1). Additional drag components arise from the deviatoric normal stress ... 

Problem 10-2. Inviscid, Potential Flow Past a Half Cylinder. Consider inviscid, potential flow past the half cylinder depicted in the figure. Calculate the force (life and drag) on the object, assuming that the flow does not separate. If the flow does separate at 90°, what happens to the lift and drag ... 

When a nondeformable object is implanted in the flow field and the streamlines and equipotentials are distorted, the nature of the interface does not affect the potential flow velocity profiles. However, the results should not be used with confidence near high-shear no-slip solid-liquid interfaces because the theory neglects viscous shear stress and predicts no hydrodynamic drag force. In the absence of accurate momentum boundary layer solutions adjacent to gas-liquid interfaces, potential flow results provide a reasonable estimate for liquid-phase velocity profiles in Ihe laminar flow regime. Hence, potential flow around gas bubbles has some validity, even though an exact treatment of gas-Uquid interfaces reveals that normal viscous stress is important (i.e., see equation 8-190). Unfortunately, there are no naturally occurring zero-shear perfect-slip interfaces with cylindrical symmetry. 

Sampling whole cells for CE involves either siphoning the cell by either applying a pressure differential or applying a potential across the capillary to electrokinetically inject the cell. In each case, a drag force is produced by the fluid flow, driving the cell into the capillary for lysis and the separation of its contents. Though these schemes are the most simplistic forms of injection, there have been several recently developed complementary techniques for introduction of cells and their contents into capillaries. 

At infinite Reynolds number, potential flow theory may be used to investigate bubble motion. As a consequence of D Alembert s paradox (see, e.g., Ref. 10), potential flow theory predicts no drag on a steadily rising bubble. However, it provides a result for the force on an accelerating sphere ... 

At high flowrates the potential exists for an adsorption bed to expand, lift or fluidize. At the point of expansion, the net weight of the bed is fully supported by the drag forces due to the flow of fluid ... 

The second parameter influencing the movement of all solutes in free-zone electrophoresis is the electroosmotic flow. It can be described as a bulk hydraulic flow of liquid in the capillary driven by the applied electric field. It is a consequence of the surface charge of the inner capillary wall. In buffer-filled capillaries, an electrical double layer is established on the inner wall due to electrostatic forces. The double layer can be quantitatively described by the zeta-potential f, and it consists of a rigid Stern layer and a movable diffuse layer. The EOF results from the movement of the diffuse layer of electrolyte ions in the vicinity of the capillary wall under the force of the electric field applied. Because of the solvated state of the layer forming ions, their movement drags the whole bulk of solution. 

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