What is the solution to the circular duct problem?

In summary, the conversation discusses a circular duct with a diameter of 150 mm that strikes a cup and exits through a circumferential slot to the atmosphere. The mean velocity in the duct is 100 ms^-1 and the air density is 1.1 kg/m^3 with a dynamic viscosity of 19.05 x 10^-6 kgm^-1s^-1. The participants of the conversation ask for help in determining the mean outlet velocity, gauge pressure, and resultant force on the cup. They also discuss the use of air density and viscosity in the problem. One participant mentions the need to consider the amount of air entering and leaving the duct and how the areas of the duct and slot compare. The conversation ends with
  • #1
Joon
85
2

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?
 

Attachments

  • 38391396_2100219723575365_4675978393198526464_n.jpg
    38391396_2100219723575365_4675978393198526464_n.jpg
    25.8 KB · Views: 378
Physics news on Phys.org
  • #2
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?
 
  • #3
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.
 
  • #4
Is it air flowing through the duct, or some other fluid?
 

FAQ: What is the solution to the circular duct problem?

1. What is a circular duct problem?

A circular duct problem is a common engineering challenge where a circular duct or pipe is used to transport fluids, gases, or other substances. It involves calculating the pressure drop, flow rate, and other parameters within the duct to ensure efficient and safe operation.

2. What causes circular duct problems?

Circular duct problems can be caused by various factors such as blockages, leaks, improper sizing, and friction losses. These issues can lead to decreased efficiency, increased energy consumption, and potential safety hazards.

3. How do you solve a circular duct problem?

To solve a circular duct problem, you need to use fundamental equations and principles of fluid mechanics, such as Bernoulli's equation, the continuity equation, and the Darcy-Weisbach equation. These equations help to calculate the pressure drop, flow rate, and other parameters within the duct.

4. What are the common techniques for optimizing circular duct problems?

Some common techniques for optimizing circular duct problems include changing the duct diameter, using different materials with lower friction coefficients, and implementing flow control devices such as dampers and valves. Additionally, incorporating computational fluid dynamics (CFD) simulations can help to fine-tune the design and improve efficiency.

5. How can circular duct problems be prevented?

Prevention of circular duct problems involves proper design and maintenance. Ensuring correct duct sizing, regular cleaning and inspection, and using high-quality materials can help prevent issues like blockages and leaks. Regular performance testing can also detect potential problems early on and allow for timely repairs or adjustments.

Similar threads

Back
Top