Question

In a static fluid with $y$ as the vertical direction, the pressure variation is given by:

• A. $\frac{dp}{dy} = \rho$
• B. $\frac{dp}{dy} = -\rho$
• C. $\frac{dp}{dy} = -\gamma$
• D. $\frac{dp}{dy} = -Y$

Hint:

The pressure variation in a static fluid is given by:
\[\frac{dp}{dy} = -Y,\]
where $Y$ is the specific weight. Remember, pressure decreases with height.

Answer 1

The Correct Option is D

In a static fluid, the pressure variation is governed by the equation:
\[\frac{dp}{dy} = -Y,\]
where:
 $p$ is the pressure,
   $y$ is the vertical direction,
   $Y$ is the specific weight of the fluid $= \rho g$,
   $-$ sign indicates that pressure decreases as we move upward.
The specific weight $Y$ is the product of the fluid density $\rho$ and gravitational acceleration $g$, so the pressure variation depends on both.