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

The answer is: Pressure increases linearly with the depth

Step-by-step explanation:

In this case, the definition of pressure is:

`P = (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 = (mg)/(A) = (\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 = (A\rho gh)/(A)= \rho g h`,

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