An ideal fluid flows steadily along a flat tube of constant cross-section, located in a horizontal p

Question

An ideal fluid flows steadily along a flat tube of constant cross-section, located in a horizontal plane and bent as shown. Point 1 is near the outer wall of the bend and point 2 is near the inner wall. Let $p_1$, $v_1$ and $p_2$, $v_2$ be the pressures and velocities of the fluid at points 1 and 2 respectively. Which of the following is/are correct?

Professor PC Thomas Classes · Answer

Fluid particles in the bend undergo centripetal acceleration, requiring a radially inward force, hence $p_1 > p_2$. For an ideal irrotational fluid, Bernoulli's sum $p + 0.5\rho v^2$ is constant across streamlines. Since $p_1 > p_2$, it follows that $v_1 < v_2$.