Chapter 2

Question #15: Negative Pressure Room

Negative pressure room is a technique used in hospitals and medical centers to isolate a specific space and prevent cross-contamination. A pressure guage installed in the negative pressure room reads a pressure of \(P_g=10\:Pa,Negative\).

a) calculate the pressure inside this room

b) assuming a door with dimesnions \(1.7\:m\times 0.9\:m\) isolates a negative pressure room from a hallway in atmospheric pressure, calculate how much force is imposed on this door as a result of this negative pressure.

Solution Approach for a)

from gauge pressure

\(P_{room}=P_{atm}+P_g\)

#define variables

P_atm = 101325   #atmospheric pressure in Pa
P_g = -10   #gauge pressure inside the room

P_room = P_atm + P_g   #pressure inside the negative pressure room

print('The pressure inside the room is', f"{P_room:.1f}", 'Pa')

The pressure inside the room is 101315.0 Pa

Solution Approach for b)

from pressure

\(P=F/A\)

so

\(F=P\times A\)

and the net force on the door is associated with the difference between the forced imposed by atmospheric air from one side and the room pressure from the other side

\(F=F_{atm}-F_{room}\)

#define variables
A = 1.7 * 0.9   #door surface area

F_room = P_room * A   #force imposed by room pressure
F_atm = P_atm * A   #force imposed by atmospheric pressure

F = F_atm - F_room

print('The net force on the door is', f"{F:.1f}", 'N')

The net force on the door is 15.3 N