ENGR217 2023 Q A2 (ENGR5003)

ENGR217 2023 Q A2Past paperOld spec ENGR2172:125 marks30 min

ENGR217 Summer 2023 Q A2[VALID] official answers

Answer ALL parts (a) - (d).

A carbon dioxide fire extinguisher consists of a 5 litre rigid tank, pressurised to 55 bar at a temperature of $20^\circ\mathrm{C}$ , which is the same as the ambient temperature. The fire extinguisher is discharged for 5 seconds and afterwards the pressure of the vessel is 10 bar. The external pressure may be assumed to be 101 kPa, and you may assume $R_g = 0.189\ \mathrm{kJ/kg/K}$ and $\gamma = 1.29$ , where $\gamma$ is the adiabatic index.

Formulas you may need

Unsteady flow energy equation (with $\Delta m_{in} = 0$ , $\Delta Q = \Delta W = 0$ ) (on the formula sheet)
Adiabatic discharge: $\dfrac{T_2}{T_1} = \left(\dfrac{p_2}{p_1}\right)^{(\gamma-1)/\gamma}$ (on the formula sheet)
Mass left in the tank: $\dfrac{m_2}{m_1} = \left(\dfrac{p_2}{p_1}\right)^{1/\gamma}$ (learn this; derived in Lecture 6)
Ideal gas $pV = mR_gT$ ; $c_v = \dfrac{R_g}{\gamma - 1}$ ; isochoric $\Delta Q = mc_v\Delta T$ (on the formula sheet)
Continuity: $\dot m = \rho AC = \dfrac{pAC}{R_gT}$ (learn this)
SFEE: $h_1 + \tfrac{C_1^2}{2} = h_2 + \tfrac{C_2^2}{2}$ (on the formula sheet)

(a)
Treating this as an unsteady flow problem, determine the change in mass of the tank as well as the final temperature of the gas discharged from the tank, as well as the final temperature of the gas inside the tank. Please state all assumptions made.
Delta m =kg
T discharged (final) =K
T_2 tank =K
[10]
(b)
The tank is allowed to warm back up to ambient temperature. Determine the pressure of the tank and the amount of heat added to the tank from the surroundings to increase the temperature.
p_3 =kPa
Q =kJ
[6]2:2
(c)
The output of the tank has a cross-sectional area of $1\ \mathrm{cm^2}$ , which is connected to a nozzle, which acts as a diffuser, the output of which has a cross-sectional area of $10\ \mathrm{cm^2}$ . Assuming the mass flow rate during the discharge is approximately constant, determine the flow velocity at the entrance and exit of the nozzle, as well as the temperature and pressure of the carbon dioxide at the exit of the nozzle. State all assumptions made. You may assume the flow velocity is much lower than the acoustic velocity.
C_in =m/s
C_out =m/s
T_exit =K
p_exit =kPa
[7]
(d)
For the temperature of discharged gas calculated from part (a), discuss whether it is appropriate to consider carbon dioxide as an ideal gas in this case and state whether we would expect the real temperature to be higher, lower or the same.
[2]2:2