Question

A room has a volume of 160 m3. An air-conditioning system is to replace the air in this room every 21.3 minutes, using ducts that have a square cross section. Assuming that air can be treated as an incompressible fluid, find the length of a side of the square if the air speed within the ducts is (a) 3.00 m/s and (b) 6.00 m/s.

Answer 1

A. 0.204203928 m

b. 0.1443939822

Step-by-step explanation:

Givens:

Volume (V) = 160 m^3

velocity 1 (v1) = 3.00 m/s

velocity 2 (v2) = 6.00 m/s

Time (t) = 21.3 minutes = 1278 seconds

Side length = ?

V = A*v*t

A = s^2

V = s^2*v*t

s=
`\sqrt{(V)/(v*t) }`

A.

s =
`\sqrt{(V)/(v*t) }` =
`\sqrt{(160)/(3.00*1278) }` = 0.204203928 m

B.

s =
`\sqrt{(V)/(v*t) }` =
`\sqrt{(160)/(6.00*1278) }` = 0.1443939822 m

I hope this helped!! Have a good day.