# Pressure in a Fluid

## Problems from IIT JEE

**Problem (IIT JEE 1999):**
A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then, the pressure in the compartment is,

- same everywhere
- lower in front side
- lower in rear side
- lower in upper side

**Solution:**
Let $A$ be the cross-section area and $\rho$ be the gas density. Consider a small element of width $\mathrm{d}x$ at a distance $x$ (see figure). Let pressure at the distance $x$ be $p$ and that at distance $x+\mathrm{d}x$ be $p+\mathrm{d}p$. The net force on the element due to pressure difference is,
\begin{align}
\mathrm{d}F=[pA-(p+\mathrm{d}p)A]=-A\mathrm{d}p,\qquad \text{(towards right)}.
\end{align}
This force provides acceleration $a$ to the element. Apply Newton's second law on the element,
\begin{align}
-A\mathrm{d}p=ma=(\rho A \mathrm{d}x) a,
\end{align}
to get,
\begin{align}
{\mathrm{d}p}/{\mathrm{d}x}=-\rho a.
\end{align}
Negative sign indicates that the pressure decreases with $x$ i.e., as we go from the left to the right.