Question

4.9 a barometer (see figure p4.9) is used to measure atmospheric pressure and is filled with a high - density fluid. in the past, mercury was used, but because of its toxic properties it has been replaced with a variety of other fluids. the pressure p measured by a barometer is the height of the fluid column, h, times the density of the liquid, ρ, times the acceleration due to gravity, g, or p = hρg. this equation could be solved for the height: h = \frac{p}{ρg}. find the height to which the liquid column will rise for pressures from 0 to 100 kpa for two different barometers. assume that the first uses mercury, with a density of 13.56 g/cm³ (13,560 kg/m³) and the second uses water, with a density of 1.0 g/cm³ (1000 kg/m³). the acceleration due to gravity is 9.81 m/s². before you start calculating, be sure to check the units in this calculation. the metric measurement of pressure is a pascal (pa), equal to 1 kg/ms². a kpa is 1000 times as big as a pa. your answer should be a two - dimensional array.

Explanation:

Step1: Convert pressure range to Pa

The pressure range is from 0 to 100 kPa. Since 1 kPa = 1000 Pa, the range in Pa is from 0 to 100000 Pa.

Step2: Calculate height for mercury - based barometer

Using the formula $h=\frac{P}{
ho g}$, with $
ho_{mercury}=13560\ kg/m^{3}$ and $g = 9.81\ m/s^{2}$.
For $P = 0\ Pa$, $h_1=\frac{0}{13560\times9.81}=0\ m$.
For $P = 100000\ Pa$, $h_2=\frac{100000}{13560\times9.81}\approx0.76\ m$.

Step3: Calculate height for water - based barometer

Using the formula $h=\frac{P}{
ho g}$, with $
ho_{water}=1000\ kg/m^{3}$ and $g = 9.81\ m/s^{2}$.
For $P = 0\ Pa$, $h_3=\frac{0}{1000\times9.81}=0\ m$.
For $P = 100000\ Pa$, $h_4=\frac{100000}{1000\times9.81}\approx10.2\ m$.
The two - dimensional array representing the heights (in meters) is

$$\begin{bmatrix}0&0.76\\0&10.2\end{bmatrix}$$

, where the first row corresponds to mercury and the second row corresponds to water, and the first column is for $P = 0\ Pa$ and the second column is for $P=100000\ Pa$.

Answer:

$$\begin{bmatrix}0&0.76\\0&10.2\end{bmatrix}$$