What is the solution to the circular duct problem?

AI Thread Summary
The discussion focuses on solving a problem related to a circular duct with a specific diameter, air velocity, density, and viscosity. Participants are tasked with calculating the mean outlet velocity through a circumferential slot, determining the gauge pressure in the duct, and analyzing the resultant force on a cup. Key considerations include the comparison of airflow entering and exiting the duct, as well as the implications of air's compressibility. The conversation highlights the need for clarity on how to apply fluid dynamics principles and relevant equations to find the solutions. Understanding these factors is crucial for accurately addressing the circular duct problem.
Joon
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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?
 

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Joon said:
(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?
 
Tom.G said:
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.
 
Is it air flowing through the duct, or some other fluid?
 

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