Thermodynamics - Bernoulli Equation question

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SUMMARY

The Bernoulli Equation applies exclusively to frictionless, incompressible fluids, while the Steady Flow Energy Equation (S.F.E.E) does not share these limitations. The Bernoulli Equation can be derived through two methods: integrating the Euler equations, which assume incompressible flow, or applying conservation of energy along a streamline while neglecting heat transfer, compressibility, and viscosity. Both derivations inherently disregard viscosity and compressibility, making the Bernoulli Equation valid only under specific conditions. In contrast, the S.F.E.E accommodates a broader range of fluid behaviors.

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  • Knowledge of the principles of conservation of energy in fluid flow
  • Basic concepts of viscosity and compressibility in thermodynamics
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Thermodynamics -- Bernoulli Equation question

"The Bernoulli Equation is restricted to frictionless incompressible fluids, the S.F.E.E is not".?
Explain the fact ?
 
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There are two ways to derive the Bernoulli equation. The first involves integration of the Euler equation, during which you assume the flow to be incompressible. The Euler equations themselves are only valid for inviscid flow by definition since they are simply the Navier-Stokes equations with the viscous terms and heat conduction terms removed. The other method is to apply conservation of energy along a streamline while ignoring the effects of heat transfer, compressibility and viscosity. Either way, you have ignored viscosity ("friction") and compressibility, so the equation itself is not valid except in incompressible, "frictionless" flows.

The steady flow energy equation makes no such assumptions.
 

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