Question

An open container as shown in figure is filled with water $(\rho ={10}^3{\text{kg/m}}^3)$ upto height $8\text{m}$. If it starts moving with acceleration $9.81{\text{m/s}}^2$, determine the pressure difference between points $A$ and $B$.
[Take $g=9.81{\text{m/s}}^2$]

• A. $20\text{kPa}$
• B. $15\text{kPa}$
• C. $10\text{kPa}$
• D. $25\text{kPa}$

Answer 1

The correct option is A $20\text{kPa}$


As the container is moving rightward, the water in the container will experience a pseudo force toward the left which results in the rise in water level as shown in the image.
So, $\tan \theta =\frac{a}{g}$
$\Rightarrow \tan \theta =1[a=g=9.81{\text{m/s}}^2]$
$\Rightarrow \theta ={45}^{\circ }$
Now at center point $C$,
$\text{tan}\theta =\frac{x}{1}$
$\Rightarrow x=1\text{m}$
So, at point B
$P_B=\rho g(h-x)=1000\times 9.81\times (8-1)$
and at point A, $P_A=\rho g(h+x)$
$=1000\times 9.81\times (8+1)$
So, $P_A-P_B=1000\times 9.81\times 2$
$=19.62\text{kPa}\approx 20\text{kPa}$