Convert the density of the liquid to SI units.

10. The figure below shows a water U-tube manometer used to measure the gas pressure of a gas cylinder.

Step 1: Convert the density of the liquid to SI units.

$$\rho = 0.8 \text{ g/cm}^3 = 0.8 \times \frac{1 \text{ kg}}{1000 \text{ g}} \times \left(\frac{100 \text{ cm}}{1 \text{ m}}\right)^3 = 0.8 \times 1000 \text{ kg/m}^3 = 800 \text{ kg/m}^3$$

Step 2: Determine the height difference of the liquid columns and convert to meters.
The liquid level at X is 9 cm below the tap. The liquid level at Y is 9 cm above the level Z (which is at the same horizontal level as X).
The total height difference $h$ is the sum of these two displacements.

$$h = 9 \text{ cm} + 9 \text{ cm} = 18 \text{ cm}$$ $$h = 0.18 \text{ m}$$

Step 3: Calculate the pressure due to the liquid column difference.
Assume the acceleration due to gravity $g = 10 \text{ m/s}^2$.

$$P_{liquid} = \rho g h$$ $$P_{liquid} = 800 \text{ kg/m}^3 \times 10 \text{ m/s}^2 \times 0.18 \text{ m}$$ $$P_{liquid} = 1440 \text{ Pa}$$

Step 4: Calculate the gas pressure in N/m$^2$ (Pascals).
Since the liquid level in the arm connected to the gas supply (X) is lower than the level in the arm open to the atmosphere (Y), the gas pressure is greater than the atmospheric pressure.

$$P_{gas} = P_{atm} + P_{liquid}$$ $$P_{gas} = 101400 \text{ Pa} + 1440 \text{ Pa}$$ $$P_{gas} = \boxed{\text{102840 Pa}}$$

Step 5: Convert the gas pressure to cmHg.
To convert pressure to the height of a mercury column, use the formula $P = \rho_{Hg} g h_{Hg}$. The density of mercury ($\rho_{Hg}$) is $13600 \text{ kg/m}^3$.

$$h_{Hg} = \frac{P_{gas}}{\rho_{Hg} g}$$ $$$$