Fluid mechanics – isotropy of pressure at a point If, for a fluid in motion, the pressure measured at a point is the same in all directions (i.e., normal stresses are equal in every orientation), the fluid can be idealized as which of the following?

Introduction:
Pascal’s law states that at rest, pressure in a fluid is equal in all directions. In moving fluids, additional shear stresses arise if viscosity is present. Understanding when pressure remains isotropic helps distinguish idealized models used in analysis.

Given Data / Assumptions:

• Fluid at a point in motion exhibits equal normal stress in all directions.
• Question addresses constitutive idealization, not specific numerical values.
• Continuum mechanics framework.

Concept / Approach:

In a viscous (real) fluid in motion, the stress tensor generally includes both isotropic pressure and deviatoric components from viscosity. If the measured stress is isotropic at a point during motion, the deviatoric part is negligible—an assumption consistent with an inviscid (ideal) fluid model. Newtonian and non-Newtonian refer to viscosity behavior; both allow shear stresses during motion and thus do not guarantee isotropy of the stress field.

Step-by-Step Solution:

Verification / Alternative check:

Euler’s equations of motion for inviscid flow use only pressure forces without viscous terms, consistent with isotropic pressure.

Why Other Options Are Wrong:

Real/Newtonian/non-Newtonian fluids exhibit viscous shear under velocity gradients; compressible viscous fluids also have anisotropic stress due to viscosity.

Common Pitfalls:

Assuming Newtonian means inviscid; conflating static Pascal’s law with moving viscous fluids.

Final Answer:

an ideal fluid