Typical inviscid flow solutions for flow around bodies indicate that the fluid flows smo...

Typical inviscid flow solutions for flow around bodies indicate that the fluid flows smoothly around the body, even for blunt bodies as shown in Video V6.6. However, experience reveals that due to the presence of viscosity, the main flow may actually separate from the body, creating a wake behind the body. As discussed in a later section (Section 9.2.6), whether separation takes place depends on the pressure gradient along the surface of the body, as calculated by inviscid flow theory. If the pressure decreases in the direction of flow (a favorable pressure gradient), no separation will occur. However, if the pressure increases in the direction of flow (an adverse pressure gradient), separation may occur. For the circular cylinder of Fig. P6.54 placed in a uniform stream with velocity, U, determine an expression for the pressure gradient in the direction of flow on the surface of the cylinder. For what range of values for the angle θ will an adverse pressure gradient occur?