Question

Which of the following statements is true about the variation of pressure in function of the depth? O Pressure decreases exponentially with the depth O Pressure increases exponentially with the depth O Pressure decreases linearly with the depth o Pressure increases linearly with the depth O None of the above

Answer 1

Answer:

The answer is: Pressure increases linearly with the depth

Explanation:

In this case, the definition of pressure is:

$P = \frac{F}{A}$

where F = mg is the weight of the fluid over the body, and A is the area of the surface to which the force is exerted. If we consider $\rho = m/V$, then

$P = \frac{mg}{A} = \frac{\rho Vg}{A}$.

Volume can be expressed as V = A*h, where A is the cross section of the column of the fluid over the body and h is the height of the column, in other words, the depth.

So

$P = \frac{A\rho gh}{A}= \rho g h$,

which means that pressure increases linearly with the depth in a factor of $\rho g$.