Question

A tank containing water upto a depth of 500 mm is moving vertically downward with a constant acceleration of $2.45m/s^2$. Find the total pressure (here its force) exerted by the water on the side of the tank given its width is 2m.

• A. 1839.37 N
• B. 4568 N
• C. 568 N
• D. 2365 N

Answer 1

Answer: (A)

1839.37 N

Here the concept used is:

Pressure at at given height when accelerated vertically downwards $=\rho \times g\times h(1-\frac{a}{g})$

This can be derived easily by taking a coloumn of water of height $h$ from top and width $dA$ and balancing all the forces.

Now to calculate the total force on the wall, take a section of width $2m$ and height $dh$.

Therefore, force on that section $=\rho \times g\times h(1-\frac{a}{g})[2\times dh]$

Now integrate it from $h=[0,0.5]$

This gives $F=1839.37N$