Frictional drag losses

When fluid flows around the outside of an object, an additional loss occurs separately from the frictional energy loss. This loss, called form drag, arises from Bernoulli s effect pressure changes across the finite body and would occur even in the absence of viscosity. In the simple case of very slow or creeping flow around a sphere, it is possible to compute this form drag force theoretically. In all other cases of practical interest, however, this is essentially impossible because of the difficulty of the differential equations involved. 

Friction drag is a strong function of viscosity, and an idealized" fluid with zero viscosity would produce z.ero friction drag since the wall shear stress would be zero. The pressure drag would also be zero in this case during steady flow regardless of the shape of the body since there are no pressure losses. For flow in the horizontal direction, for example, the pressure along a horizontal line is constant (just like stationary fluids) since the upstream velocity is... 

Drag reduction (DR), which was discovered more than 50 yr ago, is a turbulent flow phenomenon in which frictional energy losses can be significantly reduced by the addition of a small amount of a DR additive (DRA) to a turbulent flow system) Drag reduction in internal flows is calculated using the following equation ... 

Anyhow, (1.255) is not properly closed yet as the pressure drop variable is still undetermined. Therefore, before we can apply (1.255) we need to parameterize the losses in terms of known flow parameters in pipes, valves, fittings, and other internal flow devices. Assuming that the viscous stress tensor reduces to a single shear stress component per unit wall surface (e.g., [102] ]185]), Apf per unit cross sectional area can be related directly to the friction drag force on the tube wall surface —Cwt DL. That is, since the friction drag force in a horizontal tube with a constant rate of flow is given by Z p/(- )D, the wall shear stress 3uelds ... 

The situation is complicated, however, because some of the drag on a skidding tire is due to the elastic hysteresis effect discussed in Section XII-2E. That is, asperities in the road surface produce a traveling depression in the tire with energy loss due to imperfect elasticity of the tire material. In fact, tires made of high-elastic hysteresis material will tend to show superior skid resistance and coefficient of friction. 

Friction factor, dimensionless Flow rate of one phase, GPM Aqueous phase flow rate, GPM Cy clone friction loss, expressed as number of cy clone inlet velocity heads, based on Drag or resistance to motion of body in fluid, poundals... 

Example 6-1 Friction Loss in Drag-Reducing Solutions. Determine the percentage reduction in the power required to pump water through a 3 in. ID smooth pipe at 300 gpm by adding lOOwppm of degraded Separan AP-30. 

The presence of small amounts of certain polymers can produce spectacular reduction in the frictional losses of fluids in turbulent flow through conduits. Drag reduction has an immense field of applications, both currently and potentially. The list of exploitable situations as described in Sect. 2 could be extended, but a big snag exists drag reduction decreases with flow time. This is believed to be due to mechanical degradation of added polymer (Brostow 1983). In Fig. 32 and Fig. 33 the influence of Mw on drag reduction is displayed. 

The particle model This model attributes pressure drop to friction losses due to drag of a particle. The preeence of liquid reduces the void fraction of the bed and also increases the particle dimensions. Ergun (94) applied this model for single-phase flow (e.g., fixed and fluidized beds). Stichlmair et al. (95) successfully extended this model to correlate pressure drop and flood for both random and structured packings. Their correlation is complex and requires some additional validation, but is the most fundamental correlation available. 

---