Question

Constant-volume vessels that contain flammable mixtures of hydrocarbon vapors and air at low pressures are frequently used. Although the ignition of such mixtures is very unlikely as there is no source of ignition in the tank, the Safety and Design Codes require that the tank withstand four times the pressure that may occur should an explosion take place in the tank. For operating gauge pressures under \(25 \mathrm{kPa}\), determine the pressure for which these vessels must be designed in order to meet the requirements of the codes for \((a)\) acetylene \(\mathrm{C}_{2} \mathrm{H}_{2}(g),(b)\) propane \(\mathrm{C}_{3} \mathrm{H}_{8}(g),\) and \((c) n\) -octane \(\mathrm{C}_{8} \mathrm{H}_{18}(g) .\) Justify any assumptions that you make.

Short answer

The required pressure for the constant-volume vessels for acetylene, propane, and n-octane is 505.2 kPa, assuming the worst-case possible operating conditions.

Step-by-step solution

Calculate the maximum possible operating pressure

Given the operating gauge pressure is below \(25\,\text{kPa}\), let's assume the maximum possible operating pressure is \(25\,\text{kPa}\), which represents the pressure that is being read by the pressure gauge, not considering the atmospheric pressure. Keep in mind that at sea level, the atmospheric pressure is about \(101.3\,\text{kPa}\). To find the absolute pressure, we need to add the atmospheric pressure to the gauge pressure: $$ P_\text{abs} = P_\text{gauge} + P_\text{atm} $$

Calculate the absolute pressure for the given operating gauge pressure

Since we are using the maximum possible operating pressure in this scenario, the gauge pressure is \(25\,\text{kPa}\), and we know the atmospheric pressure is approximately \(101.3\,\text{kPa}\). We can now calculate the absolute pressure: $$ P_\text{abs} = 25\,\text{kPa} + 101.3\,\text{kPa} = 126.3\,\text{kPa} $$

Determine the required pressure based on the Safety and Design Codes

The Safety and Design Codes require that the tank withstand four times the pressure that may occur should an explosion take place. To find the required pressure for designing the vessels, we multiply the absolute pressure by a safety factor of 4: $$ P_\text{required} = 4 \times P_\text{abs} $$

Calculate the required pressure for each case

Since the pressure requirement is the same for all given hydrocarbons, the required pressure can be calculated as: $$ P_\text{required} = 4 \times 126.3\,\text{kPa} = 505.2\,\text{kPa} $$ So, the required pressure for the constant-volume vessels is \(505.2\,\text{kPa}\) in each case: \((a)\) For acetylene \((C_{2}H_{2}(g))\), the required pressure is \(505.2\,\text{kPa}\). \((b)\) For propane \((C_{3}H_{8}(g))\), the required pressure is \(505.2\,\text{kPa}\). \((c)\) For n-octane \((C_{8}H_{18}(g))\), the required pressure is \(505.2\,\text{kPa}\). We have made the assumption that the explosion scenario is the same for all three hydrocarbons, and we have used the same safety factor (4) to maintain consistency with the given information. The same required pressure calculated is based on the worst-case possible operating conditions.