Force Analysis in Circular Pipe: How to Approach Vertical Force Balance?

In summary: I forgot about the viscous force acting on the fluid element I think. Would I represent this using Stoke's Law or some other way? If using Stoke's law would the radius be the pipe radius or the fluid element's radius?Stokes Law would not be appropriate for this problem.I am not currently taking a course in Fluid Mechanics, sorry.I have not heard of the book Transport Phenomena, sorry.I am not familiar with the following concepts: stress tensor, Newton's law of viscosity.
  • #1
cruckshank
17
0
"Consider a fully developed laminar flow in a circular pipe, perform force analysis on an element of the real fluid."

I've just started this type of question, and I'm a bit confused about where to go from here:

I've managed to do a force balance horizontally to show that the partial derivative of pressure with respect to x should be zero (which is obvious anyway?), but I have no idea what to do with the vertical force balance and what the question is really asking me to do.

Thanks in advance!
 
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  • #2
Are you assuming that the pipe is horizontal or vertical?
 
  • #3
The pipe is horizontal in the diagram, sorry should have mentioned that.
 
  • #4
cruckshank said:
The pipe is horizontal in the diagram, sorry should have mentioned that.
Is x the direction along the pipe axis?
 
  • #5
Yes, along the pipe axis.
 
  • #6
cruckshank said:
Yes, along the pipe axis.
What was your rationale for saying that the partial derivative of the pressure with respect to x is zero?
 
  • #7
I did a force balance on the horizontal and it came out with that, which I believe is correct?

I have no idea about the vertical force balance though.
 
  • #8
cruckshank said:
I did a force balance on the horizontal and it came out with that, which I believe is correct?
It is not correct. How are you supposed to be doing this: (a) using shell momentum balances or (b) using the Navier Stokes equations?

What forces are acting horizontally on the fluid, besides the pressures.
 
  • #9
I haven't heard of either of these methods, and upon looking them up they don't look familiar to me either.

I forgot about the viscous force acting on the fluid element I think. Would I represent this using Stoke's Law or some other way? If using Stoke's law would the radius be the pipe radius or the fluid element's radius?

Thanks
 
  • #10
Are you currently taking a course in Fluid Mechanics? What textbook are you using? Have you ever heard of the book Transport Phenomena by Bird, Stewart, and Lightfoot? Are you familiar with the following concepts: stress tensor, Newton's law of viscosity?

Stokes Law would not be appropriate for this problem.
 

1. What is force analysis in relation to circular pipes?

Force analysis is the process of determining the internal and external forces acting on a circular pipe. This includes calculating the forces due to pressure, gravity, and any other external loads.

2. How is force analysis used in designing circular pipe systems?

Force analysis is an important step in designing circular pipe systems, as it allows engineers to determine the strength and stability of the pipes under various loading conditions. This information is crucial in selecting appropriate pipe materials and dimensions to ensure the system can withstand the expected forces.

3. What are some common methods used for force analysis of circular pipes?

There are several methods for force analysis of circular pipes, including the simplified method, the Hooke's Law method, and the elastic theory method. These methods use different assumptions and equations to calculate the internal and external forces acting on the pipe.

4. Can force analysis be used for both pressurized and non-pressurized pipes?

Yes, force analysis can be used for both pressurized and non-pressurized pipes. For pressurized pipes, the analysis includes the forces due to pressure, while for non-pressurized pipes, the analysis focuses on the forces due to gravity and other external loads.

5. How does the curvature of a circular pipe affect force analysis?

The curvature of a circular pipe affects force analysis by changing the distribution of forces along the pipe. As the curvature increases, the stresses and forces at the inner and outer edges of the pipe become more unequal. This must be taken into consideration when designing and analyzing circular pipe systems.

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