A steady incompressible laminar flow passes through 90° tube bend placed on a horizontal surface. In horizontal diametric plane, two pressure taps P_i and P_o are provided across the cross section at inner and outer walls of the bend, respectively. Which of the following statements is correct?

The correct answer is (P_o > P_i).

Explanation:
When a fluid flows through a curved tube or a 90° bend, the fluid particles follow curved streamlines. For any fluid particle to travel along a curved path, a centripetal force must act on it directed toward the center of curvature. This force is supplied by a pressure gradient that develops across the tube cross-section in the radial direction.

For a fluid of density $\rho$ flowing at velocity $v$ through a bend with a local radius of curvature $r$, Euler's equation of motion in the radial direction relates the change in pressure to the centrifugal action:

$$\frac{dP}{dr}=\frac{\rho v^2}{r}$$

In this equation:
- $dP/dr$ represents the rate of change of pressure with respect to the radius.
- Fluid density $\rho$, velocity squared $v^2$, and radial distance $r$ are all strictly positive quantities.

Since the right-hand side of the radial momentum equation is positive, the radial pressure gradient must also be positive:

$$\frac{dP}{dr}>0$$

A positive gradient means that pressure increases as we move radially outward from the inner wall to the outer wall of the bend. Let $P_i$ be the pressure measured at the inner wall tap (at radius $r_i$) and $P_o$ be the pressure measured at the outer wall tap (at radius $r_o$, where $r_o>r_i$).

Because pressure increases continuously along the radial direction, the pressure at the outer wall must be greater than the pressure at the inner wall:

$$P_o>P_i$$

Therefore, the statement (P_o > P_i) is correct.