ENGR217 2024 Q B2 (ENGR5003)

ENGR217 2024 Q B2Past paperOld spec ENGR217First25 marks30 min

ENGR217 Summer 2024 Q B2[VALID]

Answer ALL parts (a) - (d).

A 20 litre scuba tank initially contains air at 1 bar and a temperature of 300 K. The tank is charged from a high pressure air supply, which is at an initial temperature of 315 K, until the scuba tank has a final pressure of 200 bar. You may assume that air is an ideal gas and that $R_g = 0.287\ \mathrm{kJ/kg/K}$ and $\gamma = 1.4$ , where $\gamma$ is the adiabatic index.

Formulas you may need

Unsteady flow energy equation: $\Delta U = \left(h + \tfrac{C^2}{2} + gZ\right)_{in}\Delta m_{in} - \left(h + \tfrac{C^2}{2} + gZ\right)_{out}\Delta m_{out} + \Delta Q - \Delta W$ (on the formula sheet)
Ideal gas $pV = mR_gT$ , $u = c_vT$ , $h = c_pT$ , $c_v = \dfrac{R_g}{\gamma-1}$ , $c_p = \dfrac{\gamma R_g}{\gamma-1}$ (on the formula sheet)
Isochoric cooling: $\Delta Q = mc_v\Delta T$ , $p/T = \text{constant}$ (on the formula sheet)
Adiabatic discharge: $\dfrac{T_2}{T_1} = \left(\dfrac{p_2}{p_1}\right)^{(\gamma-1)/\gamma}$ , $\dfrac{m_2}{m_1} = \left(\dfrac{p_2}{p_1}\right)^{1/\gamma}$ (first on the formula sheet; mass ratio learn this, Lecture 6)
Flow work: $W_{flow} = pV$ (per unit mass $pv = R_gT$ ) (on the formula sheet)
Isentropic efficiency $\eta_s = \Delta h_s/\Delta h_{actual}$ (given in the question)

(a)
Treating this as an unsteady flow problem, determine the change in mass of the tank as well as the final temperature, given that this can be assumed to be an adiabatic process. State all assumptions made.
Delta m =kg
T_2 =K
[8]2:2
(b)
The charging process has an isentropic efficiency ( $\eta_s = \Delta h_s / \Delta h_{actual}$ ) of 70%, what would be the final temperature of the tank after charging? Use this with the unsteady flow energy equation to estimate the heat lost during this process?
T_2 actual =K
Q (UFEE) =kJ
[6]
(c)
The tank is allowed to cool back to 300 K from your answer to part (b) and then discharged adiabatically through a valve to provide air to a diver. We can neglect kinetic and potential energy in this case and assume that the pressure is 2 bar during a dive. Determine the heat lost during cooling and the flow work done during the discharging process, assuming that the final pressure in the tank is 2 bar. What is the final temperature of the discharged gas?
Q lost in cooling =kJ
W_flow =kJ
T final discharged =K
[8]
(d)
From the final temperature of the tank from part (a), discuss whether this would increase or decrease if the gas constant, $R_g$ , or the adiabatic index, $\gamma$ , increased. What happens if $p_2$ is much larger $p_2$ ? What about when the temperature of the high pressure air line is much higher than the ambient temperature?
[3]2:1