An incompressible fluid flows steadily past a circular cylinder as shown in Fig. P3.3 (s...

An incompressible fluid flows steadily past a circular cylinder as shown in Fig. P3.3 (see Video V3.7 also). The fluid velocity along the dividing streamline is found to be where a is the radius of the cylinder and is the upstream velocity. (a) Determine the pressure gradient along this streamline. (b) If the upstream pressure is integrate the pressure gradient to obtain the pressure p(x) for (c) Show from the result of part (b) that the pressure at the stagnation point is as expected from the Bernoulli equation.