Pressure Loads on Cone - Conservation of Momentum

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SUMMARY

This discussion centers on the analysis of pressure loads on a flanged cone and the application of conservation of momentum principles. The user raises a question about whether static pressure inside the cone contributes to the axial force on the walls, emphasizing the importance of not double-counting forces in the summation. The conversation references the need to consider momentum changes, specifically the term (\dot{m} v), and highlights a relevant example from the textbook "Fluid Mechanics" by Munson, Young, and Okiishi. The conclusion stresses the significance of selecting the appropriate control volume for accurate analysis.

PREREQUISITES
  • Understanding of fluid mechanics principles, particularly conservation of momentum.
  • Familiarity with pressure forces in fluid systems.
  • Knowledge of control volume analysis in fluid dynamics.
  • Experience with the textbook "Fluid Mechanics" by Munson, Young, and Okiishi.
NEXT STEPS
  • Study the concept of control volume selection in fluid mechanics.
  • Learn about the implications of static pressure on axial forces in fluid systems.
  • Review examples of momentum conservation in fluid flow from "Fluid Mechanics" by Munson, Young, and Okiishi.
  • Explore the relationship between mass flow rate and velocity changes in fluid dynamics.
USEFUL FOR

Engineers, fluid mechanics students, and professionals involved in the design and analysis of fluid systems, particularly those working with pressure loads and momentum conservation in conical structures.

minger
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Wow, I should really know this but I can't think of it. Let's assume (totally assume, haha) that I have a flanged cone with a flow through it. The flange is of course going to have a reaction force on it based on the flow. I know that summing forces, I have forces at the inlet and outlet
(pA)_1 = (pA)_2 + R

Now, will the static pressure inside the cone also generate a force normal to the walls? I know that any radial component of that force will cancel. However, I'm concerned about the axial component. Is this static pressure force taken into account in the summation of forces?

I just don't want to count the force twice is all (but definitely don't want to leave it out).

edit: shoot, I also need to sum momentum and consider the change in (\dot{m} v)

edit Part Deux - I guess it doesn't matter since the flow is at ambient pressure. I suppose it there was a dP across the cone, then there would be a component.
 
Last edited:
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There is a good example in Munson, Young and Okiishi for this very problem. It all comes down to how you select the control volume. I'll scan it in and post it.

Edit: Enjoy
 

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Last edited:
Thanks Fred, I appreciate the annotations.
 

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