Fluid Mechanics Theoretical Pipe Diameter

In summary: So would I be right in thinking that the diameter I have calculated is correct for laminar flow?In summary, the conversation discusses finding the pipe diameter or mean velocity given the flow rate, density, viscosity, and maximum velocity. The equation for mean velocity is mentioned, but it is noted that there are two unknowns and a correction is made to show the correct equation. The topic of laminar and turbulent flow is also brought up, with a suggestion to check the Reynolds number to determine the type of flow. The conversation concludes with a question about the accuracy of the calculated diameter for laminar flow.
  • #1
eastend111
3
0

Homework Statement


I need to find the pipe diameter or mean velocity.
Q= 0.01m^3s
Density= 960kg m^3
Viscosity = 0.081 Pa s
Max Velocity = 1.8 m s

Homework Equations


Mean velocity= 4Q/pi.D^2

The Attempt at a Solution


I have two unknowns in this equation so I'm unable to find D or Mean Velocity. Am I right in thinking the mean velocity is max velocity/2? And does this work for laminar/Turbulent/transitional flow? Any help appreciated. Thanks
 
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  • #2
eastend111 said:
Q= 0.01m^3s
Density= 960kg m^3
Viscosity = 0.081 Pa s
Max Velocity = 1.8 m s
Even I know that velocity does not have units of m s :eek:

Your first priority should be to show units correctly. Not only will it help discipline your thinking, but units correctly incorporated into equations allow an independent check of formulae.

Please fix all the units, and show them correctly in a follow-up post.
eastend111 said:

Homework Equations


Mean velocity= 4Q/pi.D^2
Another example of sloppiness. :mad: This desperately needs some parentheses to make it correct.
 
  • #3
eastend111 said:

Homework Statement


I need to find the pipe diameter or mean velocity.
Q= 0.01m^3s
Density= 960kg m^3
Viscosity = 0.081 Pa s
Max Velocity = 1.8 m s

Homework Equations


Mean velocity= 4Q/pi.D^2

The Attempt at a Solution


I have two unknowns in this equation so I'm unable to find D or Mean Velocity. Am I right in thinking the mean velocity is max velocity/2? And does this work for laminar/Turbulent/transitional flow? Any help appreciated. Thanks
They must be referring to laminar flow, where the maximum velocity is twice the average velocity. In turbulent flow, the ratio is much closer to 1. As a check on this, once you find the diameter for laminar flow, you should calculate the Reynolds number to make sure that the laminar-turbulent transition hasn't been exceeded. If it has, then you need to start looking at the case of turbulent flow.
 
  • #4
Thanks for your reply, much appreciated. I have divided by 2 to get the mean velocity. I've then plugged it into the Reynolds Number formula to get 1280. Which means it is laminar flow.
 

FAQ: Fluid Mechanics Theoretical Pipe Diameter

1. What is fluid mechanics and why is it important?

Fluid mechanics is the study of how fluids (liquids and gases) behave under various conditions. It is important because it helps us understand and predict the behavior of fluids, which is crucial in many engineering and scientific applications such as designing pipes, pumps, and airplanes.

2. What is the theoretical pipe diameter and how is it calculated?

The theoretical pipe diameter is the ideal size of a pipe that would result in the most efficient flow of fluid. It is calculated using the Darcy-Weisbach equation, which takes into account factors such as fluid velocity, viscosity, and pipe roughness.

3. How does the theoretical pipe diameter affect the flow rate?

Theoretical pipe diameter directly affects the flow rate of fluid. A larger diameter results in a higher flow rate, while a smaller diameter leads to a lower flow rate. This is because a larger diameter allows for a greater volume of fluid to pass through the pipe at a given time.

4. Can the theoretical pipe diameter be different from the actual pipe diameter?

Yes, the theoretical pipe diameter is often different from the actual pipe diameter. This is because the actual diameter can be affected by factors such as manufacturing tolerances, corrosion, and buildup of deposits inside the pipe. However, the theoretical diameter is still a useful guideline for determining the optimal size of a pipe.

5. How can the theoretical pipe diameter be optimized for a specific application?

The theoretical pipe diameter can be optimized by considering the specific requirements of the fluid flow in a given application. Factors such as desired flow rate, pressure drop, and cost can be taken into account to determine the most efficient and practical pipe diameter for the application.

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