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

For a static fluid, pressure variation is defined by the equation:
\[\frac{dp}{dy} = -Y,\]
where:
$p$ represents pressure,
   $y$ denotes the vertical direction,
   $Y$ is the specific weight of the fluid ($= \rho g$),
   The negative sign indicates that pressure decreases with upward movement.