Velocity of air moving past a duct.

[Jbreezy]

Homework Statement

A hospital room has dimensions 8m by 9m by 3.25m tall. A round duct of diameter 12cm is used to supply air to the room. If the air in the room is to be exchanged 6 times every hour, how fast must the air move through the duct?

The Attempt at a Solution

OK, I want to use this equation
I'm using
A = area of duct
V = velocity of duct.
The lower case letters represent the room.
AV = av
We want V.
So we get V = (av)/(V)
Now looking that the equation I don't have given information for the velocity of the air in the room (v). So , v = L/T where L = length and T = time.
So putting this back in we get

V = aL / VT
aL is just volume so
V = Volume of room / VT
Now from the problem they give us the period is 6 cycles per hour.
So T = 1/f
Then , (1hr/6cycles) (360 seconds) = 60 seconds ( I question this conversion because my answer seems high.)

Plugging all the values in we get.
V = ( 8m x 9m x 3.25m) / (Pi(0.06)^2 )(60 seconds))
So I got V = 334.8 m/s this seems totally wrong. Because of how fast it is.
What did I do wrong? Maybe 3.34 m/s seems more reasonable.

Please help me find my error.
Thanks,

 

[Andrew Mason]

Homework Statement

A hospital room has dimensions 8m by 9m by 3.25m tall. A round duct of diameter 12cm is used to supply air to the room. If the air in the room is to be exchanged 6 times every hour, how fast must the air move through the duct?

The Attempt at a Solution

OK, I want to use this equation
I'm using
A = area of duct
V = velocity of duct.
The lower case letters represent the room.
AV = av
We want V.
So we get V = (av)/(V)
Now looking that the equation I don't have given information for the velocity of the air in the room (v). So , v = L/T where L = length and T = time.
So putting this back in we get

V = aL / VT
aL is just volume so
V = Volume of room / VT
Now from the problem they give us the period is 6 cycles per hour.
So T = 1/f
Then , (1hr/6cycles) (360 seconds) = 60 seconds ( I question this conversion because my answer seems high.)

Plugging all the values in we get.
V = ( 8m x 9m x 3.25m) / (Pi(0.06)^2 )(60 seconds))
So I got V = 334.8 m/s this seems totally wrong. Because of how fast it is.
What did I do wrong? Maybe 3.34 m/s seems more reasonable.

Please help me find my error.

There are 3600 seconds in an hour. So each cycle would be 600 seconds, not 60.

AM