Pressure and area relationship in fluids

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SUMMARY

The relationship between pressure and area in fluids is significantly influenced by the fluid's state of motion. In moving fluids, decreasing the area results in lower pressure due to uniform translational motion, which reduces molecular collisions. Conversely, in static fluids, reducing the area increases pressure because of increased random translational motion and more frequent molecular collisions. This phenomenon aligns with Bernoulli's equation, where total pressure remains constant in flowing fluids, while static fluids experience a change in total pressure when volume is reduced.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with Bernoulli's equation
  • Knowledge of pressure-area relationships (P=F/A)
  • Concept of static vs. dynamic pressure
NEXT STEPS
  • Study the implications of Bernoulli's equation in various fluid flow scenarios
  • Explore the concept of dynamic pressure in moving fluids
  • Investigate the effects of area changes on pressure in static fluids
  • Learn about the principles of fluid mechanics and their applications in engineering
USEFUL FOR

Students and professionals in fluid mechanics, engineers designing fluid systems, and anyone interested in the principles governing pressure and flow in fluids.

David513
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Hoping to clarify something about this...

Is it fair to say that you should consider the relationship between pressure and area as a function of whether a fluid is moving or standing still?

In other words, when a fluid is moving and you decrease the area, the pressure goes down because there is more uniform translational motion in a moving fluid, therefore fewer molecules of the fluid collide with each other.

Meanwhile, when a fluid is standing still and you decrease the area, the pressure goes up because there is more random translation motion in a resting fluid, therefore more molecules of the fluid collide with each other.

This seems to defy P=F/A and Bernoulli's equation but makes sense intuitively... help!
 
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In a flowing fluid the total pressure = static pressure + dynamic pressure; so, the total pressure does not change nor does the mass flow change from one cross section to the other smaller one. For a static fluid when the mass does not change but the volume is reduced then there is an a change of total pressure.
 

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