Question

An incompressible fluid flows steadily past a circular cylinder as shown in Fig. P3.8. The fluid velocity along the dividing streamline $(-\infty \leq x \leq-a)$ is found to be $V=V_{0}\left(1-a^{2} / x^{2}\right),$ where $a$ is the radius of the cylinder and $V_{0}$ is the upstream velocity. (a) Determine the pressure gradient along this streamline. (b) If the upstream pressure is $p_{0},$ integrate the pressure gradient to obtain the pressure $p(x)$ for $-\infty \leq x \leq-a,$ (c) Show from the result of part (b) that the pressure at the stagnation point $(x=-a)$ is $p_{0}+\rho V_{0}^{2} / 2,$ as expected from the Bernoulli equation.

          An incompressible fluid flows steadily past a circular cylinder as shown in Fig. P3.8. The fluid velocity along the dividing streamline $(-\infty \leq x \leq-a)$ is found to be $V=V_{0}\left(1-a^{2} / x^{2}\right),$ where
$a$ is the radius of the cylinder and $V_{0}$ is the upstream velocity.
(a) Determine the pressure gradient along this streamline.
(b) If the upstream pressure is $p_{0},$ integrate the pressure gradient to obtain the pressure $p(x)$ for $-\infty \leq x \leq-a,$ (c) Show from the result of part (b) that the pressure at the stagnation point $(x=-a)$ is $p_{0}+\rho V_{0}^{2} / 2,$ as expected from the Bernoulli equation.

Added by Milagros B.

Question

Please give Ace some feedback