The pressure at a depth of $1.25 \mathrm{~m}$ in a tank of liquid is measured to be $125.5 \mathrm{kPa}$. The tank is open to the outside air, which is at a pressure of $102.0 \mathrm{kPa}$. What is the density of the fluid?
A) $10,200 \mathrm{~kg} / \mathrm{m}^{3}$
B) $18,800 \mathrm{~kg} / \mathrm{m}^{3}$
C) $2,400 \mathrm{~kg} / \mathrm{m}^{3}$
D) $1,920 \mathrm{~kg} / \mathrm{m}^{3}$

Question

Quizplus · Accepted Answer

The pressure difference between the pressure at depth and the atmospheric pressure is due to the liquid column. This difference is $125.5 \mathrm{kPa} - 102.0 \mathrm{kPa} = 23.5 \mathrm{kPa}$. Using the formula $\Delta P = \rho g h$, where $\Delta P = 23.5 \times 10^3 \, \text{Pa}$, $g = 9.81 \, \text{m/s}^2$, and $h = 1.25 \, \text{m}$, solving for $\rho$ gives $\rho = \frac{\Delta P}{gh} = \frac{23.5 \times 10^3}{9.81 \times 1.25} \approx 1920 \, \text{kg/m}^3$.

The Pressure at a Depth Of 1.25 m1.25 \mathrm{~m}1.25 m In a Tank of Liquid Is Measured to Be

The Pressure at a Depth Of $1.25 \mathrm{~m}$ In a Tank of Liquid Is Measured to Be