Question

What fact about liquid pressure does the diagram in figure illustrate?

Answer 1

Hint: In the diagram, we can see that both the glass test tubes are identical. But the water level in one is greater than the water level in another. Also, one of them has a less bulged balloon while the other has a more bulged balloon. This means that these balloons are somehow being affected by the different water levels in the glass tubes. We shall find this relation to come to our concluding statement.

Complete step-by-step solution:
Let the atmospheric pressure at the surface of water in both the glass tubes be given by ${{P}_{0}}$. And the density of water in these columns is denoted by $\rho $.
Also, let the heights of the water column in two glass tubes be ${{h}_{1}}$ and ${{h}_{2}}$. Where,
$\Rightarrow {{h}_{1}}< {{h}_{2}}$
Then, the pressure at the bottoms of the two tubes could be written as follows:
Let the pressure at the bottom of the first glass tube be ${{P}_{1}}$. Then it is equal to:
$\Rightarrow {{P}_{1}}={{P}_{0}}+\rho g{{h}_{1}}$ [Let this expression be equation number (1)]
Also, let the pressure at the bottom of the second glass tube be ${{P}_{2}}$. Then it is equal to:
$\Rightarrow {{P}_{2}}={{P}_{0}}+\rho g{{h}_{2}}$ [Let this expression be equation number (2)]
On comparing equation number (1) and (2), we see that:
$\Rightarrow {{P}_{2}} > {{P}_{1}}$ [$\because {{h}_{2}} > {{h}_{1}}$]
Hence, we can conclude that the liquid pressure increases with the increase in height of the liquid column above it. This is the reason why the balloon in the second column is more bulged.

Note: This difference in height to generate pressure is used in Hydraulics. For example, in the arms of a construction bulldozer, the arms move front and back at the point of their joint. This is done by using some specialized hydraulic liquids. When one end of the machine compresses the fluid, the other end moves ahead due to the increase in liquid column inside the arm.