Assignment 1
Deadline: Week 13
Figure 1 shows the air exchange process in a room.
It can be governed by the following equation:
\[\frac{dV}{dt} =\dot{V}_{fresh\ air} -\dot{V}_{stale\ air} =\frac{0.04}{100} F-\frac{V}{R} F\ \ \ \text{(Note: } F\ \text{and} \ R\ \text{are constants)}\]where,
(i) \(V(t)\) is the volume of CO\(_{2}\) (in m\(^{3}\)) in the room at time \(t\) (in min), i.e. \(\frac{CO_{2} \ \text{in } \%}{100} \times \text{room size} ,\ R\).
(ii) \(\dot{V}_{fresh\ air}\) is the input rate of fresh air that is circulated into the room at a constant F (in m\(^{3}\)/min) with 0.04% CO\(_{2}\). Assume the stale air and fresh air mix immediately in the room.
(iii) \(\dot{V}_{stale\ air}\) is the output rate of stale air that leave the room at a constant \(F\) m\(^{3}\)/min with CO\(_{2}\) concentration of \(\left\{V(t) \div \text{room size}\right\}\).
(1) Initially, the room contains 0.30% by volume of CO\(_{2}\). Design the required flow rate of the fresh air, \(F\) (in m\(^{3}\)/min) if you wish to reduce the level of CO\(_{2}\) in the room to 0.05% in 5 minutes.
(2) Continue from (Q1), plot the table and graph for the change of level of CO\(_{2}\) (in m\(^{3}\)) over time for 1 hour duration with 5 minutes interval by using Excel or any other software.
(3) Continue from (Q2), estimate the steady state level of CO\(_{2}\) (in m\(^{3}\)) within 4 significant figures and the time taken to reach the steady state level.
(4) Assume the room has no ventilation system initially, calculate and comment on the CO\(_{2}\) level (in m\(^{3}\)) in the room over the time.
(5) After the installation of the ventilation system as you design in (Q1-Q3), calculate the reduction percentage (%) of the steady state CO\(_{2}\) level (in m\(^{3}\)). If the safety level of CO\(_{2}\) in an indoor space is less than 0.1% (or 1000 ppm) according to standard, comment if the proposed ventilation system is useful to achieve this requirement.