Question

Why does it happen? The wall of a dam is broad at its base.

Answer 1

The relationship between pressure, average density of the fluid and the depth from the surface is given as $P= \rho gh$. From this relationship, it can be understood that the pressure is proportional to the depth from the surface of the fluid. This relationship can be used to find why the wall of a dam is broad at its base where the depth is maximum.
Formula used:
$P= \rho gh$

Complete step-by-step solution:
We know, the relationship between pressure and depth is given by,
$P= \rho gh$ …(1)
Where P is the pressure due to the weight of a fluid
$\rho$ is the average density of the fluid
g is the gravity
h is the depth below the surface
From the equation. (1), it can be inferred that the pressure due to the weight of the fluid is directly proportional to the depth below the surface. This implies as the depth below the surface increases, the pressure of the fluid also increases. Thus, the pressure is maximum when the depth is maximum. In the given question, depth is maximum at the base of the dam, thus the pressure is also maximum at the base. To withstand this pressure of the fluid, the wall of the dam is made broad at its base.
Hence, the wall of a dam is broad at its base to withstand the pressure of the liquid.

Note: Students must know the basic formulas such as the relationship between pressure and height and pressure and depth to answer such types of questions. The pressure decreases as the altitude or height is increased from the surface. While the pressure increases with increasing depth. So, we can say that at the maximum height the pressure is least, and as the height decreases pressure increases. And as we go below the surface the pressure keeps increasing.