Fluid Mechanics seventh edition by Frank M. White · Problem P3.44

Integral Relations for a Control Volume — Frank M. White

Physics — Fluid Mechanics · linear-momentum-equation

Problem

When a uniform stream flows past an immersed thick cylinder, a broad low-velocity wake is created downstream, idealized as a V shape in Fig. P3.44. Pressures p1p_1 and p2p_2 are approximately equal. The upstream velocity is UU; at section 2 the wake profile varies from U/2U/2 at the centerline to UU at z=±Lz = \pm L. If the flow is two-dimensional and incompressible, with width bb into the paper, derive a formula for the drag force FF on the cylinder. Rewrite your result in the form of a dimensionless drag coefficient based on body length CD=F/(ρU2bL)C_D = F/(\rho U^2 bL).

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