A class 10(10 particles/ft^3 > 5 mu m diameter) cleanroom is designed with 9 - foot high ceilings. To maintain this level of cleanliness, 50 air exchanges per hour are required (the total volume of air in the room is replaced with new air 50 times/hour). What is the total number of particles that would hit a surface one square foot in an area perpendicular to the airflow in 1 minute? 1 hour? 24 hours?

a)  1 particle, b) 55.56 particles , c) 1332 particles

Explanation:

The number of particles per unit volume is 10, the volume of a quarter is its area by height

           V = A h

Where the height h = 9 ft, whereby the particle number per foot of height is

          # _Particle = 10 / V = 10 / A 9 = 1,111 / A

The number of air exchanges per unit of time is

          #_change = 50/60 = 0.8333

1 change every 1.2 min

           .t_change = 1.2 min

a) in one minute there has been no air exchange, so the number of particles that collides with the surface must be random and the particles directed by the air current of sir

          # _particle = 1,111 particles

1 particle per square meter

b) in a time or 1 hour = 60 minutes

During this time, 50 air exchanges have taken place, so the particle number must be the number of exchanges for the number of particles carried in each exchange

               Particle = 50 * #_par = 50 1.11

               Particles = 55.56 particles

c) in a time of 24 h = 1440 min

In this time they have happened

             #_change = 1440 / exchange

            #_exchanges = 1440 / 1.2 = 1200 exchanges

At each exchange the number of particles collide

             Particle = #_change # _particle

             Particle = 1200 1.11

             Particle = 1332 particles

i will answer your question if you answer mine

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west