Bernoulli’s equation holds only for _____________

Question

BlackTom AI · Accepted Answer

Starting with the concept itself, Bernoulli’s equation is derived under a set of ideal conditions and assumptions about a fluid flow scenario.
Option 1: 'low viscosity and incompressible fluids in streamline flow' This aligns with the standard derivation: negligible viscous losses, incompressible fluid (constant density), and steady, streamline (laminar) flow along a streamline. Under these conditions, Bernoulli’s principle relates pressure and velocity along a streamline, making this option correct.
Option 2: 'low viscosity and incompressible fluids in turbulent flow' Turbulent flow introduces chaotic fluctuations and energy dissipation due to viscosity and eddies, which violate the streamlined, steady-flow assumption; Bernoulli’s equation does not hold in general for turbulent flow, so this option is incorrect.
Option 3: 'high viscosity and compressible fluids in streamline flow' High viscosity implies significant viscous losses, and compressibility means density changes with pressure, both of which violate the ideal assumptions used to derive Bernoulli’s equation; therefore this choice is incorrect.
Option 4: 'low viscosity and compressible fluids in turbulent flow' Although viscosity might be low, the fluid is compressible and the flow is turbulent; this combination breaks both the incompressibility and streamline flow requirements, so Bernoulli’s equation in its basic form does not apply here; this makes the option incorrect.
In summary, only the first option satisfies the classical, derivation-friendly conditions of Bernoulli’s equation: low viscosity, incompressible fluid, and streamline (laminar) flow, ensuring the relation between pressure and velocity along a streamline holds as described.

Bernoulli’s equation holds only for _____________ 单项选择题

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