There are two identical small holes on the opposite side of a tank containing full of a liquid. The tank is open at the top. The difference in height between the two holes is ' $h$ '. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to
Show Hint
For liquid jets from holes, use Torricelli’s theorem:
\[
v=\sqrt{2gh}
\]
and momentum flux arguments to relate force with depth.
Step 1: Understanding the Concept:
Exiting liquid exerts a reaction force (thrust) on the tank equal to $\rho A v^2$. Step 2: Key Formula or Approach:
Thrust force $F = 2 \rho Ag y$, where $y$ is depth from the top. Step 3: Detailed Explanation:
Force from hole 1: $F_1 = 2 \rho Ag y_1$. Force from hole 2: $F_2 = 2 \rho Ag y_2$.
Net force $= |F_1 - F_2| = 2 \rho Ag (y_1 - y_2) = 2 \rho Ag h$.
Therefore, force $\propto h$. Step 4: Final Answer:
The net horizontal force is proportional to $h$.
