Question

A tall glass cylinder is filled with a layer of water 17.0 cm deep, and floating on top of the water, a layer of oil 34.0 cm thick. The oil has a specific gravity of 0.900. What is the absolute pressure (in Pa) at the bottom of the cylinder? (Assume the atmospheric pressure is 1.013 ✕ 105 Pa. Round your answer to at least three significant figures.)

Answer 1

To develop this problem it is necessary to apply the law of Pascal. The pressure exerted on an incompressible and equilibrium fluid within a container of non-deformable walls is transmitted with equal intensity in all directions and at all points of the fluid. For which the pressure is defined as,

$P = P_{atm}+P_{oil}+P_{water}$

The pressure of an object can be expressed by means of density, gravity and height

$P = \rho*g*h$

Our values are given as,

$g=9.8m/s^2\\h_w = 0.17m\\h_o = 0.34\\\gamma_g = 0.9\rightarrow \rho=0.9*10^{-3}$

Replacing we have to,

$P = P_{atm}+P_{oil}+P_{water}$

$P = P_{atm}+\rho_{oil}gh_{oil}+\rho_{water}gh_{water}$

$P = 1.013*10^5+(0.9*10^3)(9.8)(0.34)+(10^3)(9.8)(0.17)$

$P = 105964.8Pa$