Why should an ideal fluid be incompressible?

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SUMMARY

An ideal fluid is defined as being both frictionless and incompressible, which simplifies mathematical treatment in fluid dynamics. The high bulk modulus of most materials indicates that they are largely incompressible under typical pressures, making this assumption valid for analysis. Ignoring compressibility significantly reduces the complexity of fluid dynamics equations, allowing for more straightforward solutions. The discussion emphasizes that the term "ideal" serves as a useful simplification rather than a reflection of real-world fluid behavior.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the concept of bulk modulus
  • Knowledge of mathematical modeling in physics
  • Basic grasp of compressibility effects in materials
NEXT STEPS
  • Research the implications of bulk modulus in material science
  • Explore mathematical models for compressible versus incompressible fluids
  • Learn about the Navier-Stokes equations in fluid dynamics
  • Investigate real-world applications of ideal fluid assumptions in engineering
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Students and professionals in physics, engineering, and applied mathematics who are studying fluid dynamics and seeking to understand the foundational concepts of ideal fluids.

KingDaniel
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Hi,

I read that an ideal fluid needs to be frictionless and incompressible.
Please explain why, especially the incompressible part?

Thanks
 
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It makes their mathematical treatment substantially easier.
 
KingDaniel said:
Hi,

I read that an ideal fluid needs to be frictionless and incompressible.
Please explain why, especially the incompressible part?Thanks
The bulk modulus of most materials is very high compared to usual pressures, resulting in insignificant compression of most materials. Solids usually are even more incompressible than liquids. Wiki the bulk modulus to get a feel for the forces involved.
 
As boneh3ad said, "ideal", in the context of a lot of math and science isn't saying that we wish real fluids behaved like that, it's about making assumptions/simplifications that make analysis easier (or in some cases, that make analysis possible at all). Compressibility dramatically increases the difficulty of fluid dynamics, so if you can ignore it, it makes a lot of sense to do so.
 
As my PhD advisor often said, an ideal fluid is an 18-year-old, single malt Scotch whisky.
 
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I think that's a definition I can get behind.
 
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Likes boneh3ad

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