What is the solution to the circular duct problem?

[Joon]

Homework Statement

Shown in the figure attached.
Circular duct with a diameter of 150 mm, strikes a cup and exits through a circumferential slot to the atmosphere.
Mean velocity in the duct = 100 ms^-1
Air density = 1.1 kg/m^3
Dynamic viscosity of air = 19.05 x 10^-6 kgm^-1s^-1

(a) Determine the mean outlet velocity, knowing the slot has an area of 6597 mm^2
(b) Determine the gauge pressure in the duct (point A), knowing that A and B are in the same horizontal plane
(c) Draw an appropriate control volume and hence determine the resultant force acting on the cup

Homework Equations

The Attempt at a Solution

I don't know where to start. How do you use air density and viscosity?

 

[Tom.G]

(a) Determine the mean outlet velocity, knowing the slot has an area of 6597 mm^2

Well, I can help with the first part. Someone else will have to jump in for the rest.

How much air is entering the duct each second?
How much air is leaving the slot each second?
Are they the same or different? Why?
How do the areas of the duct and the slot compare?

 

[haruspex]

Well, I can help with the first part. Someone else will have to jump in for the rest.

How much air is entering the duct each second?
How much air is leaving the slot each second?
Are they the same or different? Why?
How do the areas of the duct and the slot compare?

Air is compressible.

 

[Chestermiller]

Is it air flowing through the duct, or some other fluid?