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
[tex]Q = Av[/tex]
Where,
[tex]Q = Discharge (m^3/s)[/tex]
[tex]A = Area (m^2)[/tex]
v = Average speed (m / s)
And also as
[tex]Q = \frac{V}{t}[/tex]
Where,
V = Volume
t = time
Let's start by finding the total volume according to the given dimensions, that is to say
[tex]V = 5*11*2.4[/tex]
[tex]V = 132m^3[/tex]
The entire cycle must be completed in 50 min = 3000s
In this way we know that the [tex]132m ^ 3[/tex] must be filled in 3000s, that is to say that there should be a flow of
[tex]Q = \frac{V}{t}[/tex]
[tex]Q = \frac{132}{3000}[/tex]
[tex]Q = 0.044m^3/s[/tex]
Using the relationship to find the speed we have to
[tex]Q = Av[/tex]
[tex]v = \frac{Q}{A}[/tex]
Replacing with our values,
[tex]v = \frac{0.044}{900*10^{-4}m^2}[/tex]
[tex]v = 0.488m/s[/tex]
Therefore the air speed in the duct must be 4.88m/s
