Question

The return-air ventilation duct in a home has a cross-sectional area of 900 cm^2. The air in a room that has dimensions 5.0 m x 11.0 m ×x 2.4 m is to be completely circulated in a 50-min cycle.

1) What is the speed of the air in the duct? (Express your answer to two significant figures.)

Answer 1

To solve the problem it is necessary to apply the concepts related to the flow rate of a fluid.

The flow rate is defined as

`Q = Av`

Where,

`Q = Discharge (m^3/s)`

`A = Area (m^2)`

v = Average speed (m / s)

And also as

`Q = (V)/(t)`

Where,

V = Volume

t = time

Let's start by finding the total volume according to the given dimensions, that is to say

`V = 5*11*2.4`

`V = 132m^3`

The entire cycle must be completed in 50 min = 3000s

In this way we know that the
`132m ^ 3` must be filled in 3000s, that is to say that there should be a flow of

`Q = (V)/(t)`

`Q = (132)/(3000)`

`Q = 0.044m^3/s`

Using the relationship to find the speed we have to

`Q = Av`

`v = (Q)/(A)`

Replacing with our values,

`v = (0.044)/(900*10^(-4)m^2)`

`v = 0.488m/s`

Therefore the air speed in the duct must be 4.88m/s