Question

Pressure gradient in the horizontal direction in a static fluid is represented by $(z$- direction is vertically upwards, and $x$- axis is along horizontal, $d$ is density of fluid):

• A. $\frac{\partial p}{\partial z}=-dg$
• B. $\frac{\partial p}{\partial x}=dg$
  
• C. $\frac{\partial p}{\partial z}=0$
• D. $\frac{\partial p}{\partial x}=0$

Answer 1

The correct option is D $\frac{\partial p}{\partial x}=0$

In a static fluid pressure remains same at the same level, i.e., pressure does not vary with $x$ coordinate.
And if we comment on pressure variation along $z-\text{direction}$ then we can say pressure increases as we go deep in fluid , hence option $\left(a\right)$ is also correct, but question have asked along horizontal direction only .
Hence $\left(c\right)$ is the correctg option.

FINAL ANSWER: (c)