An ideal fluid in theoretical fluid mechanics is defined by which combination of properties?

Introduction / Context:
Many fundamental flow theorems (e.g., Bernoulli’s equation in its simplest form) are derived for an “ideal fluid.” Knowing the precise definition prevents misuse of inviscid formulas in situations where viscosity or compressibility matters.

Given Data / Assumptions:

• Idealization for analytical convenience, not a real substance.
• Used in potential flow theory and elementary Bernoulli applications.

Concept / Approach:
An ideal fluid is inviscid (μ = 0) and incompressible (density constant). With μ = 0, there is no viscous shear; with constant density, the continuity equation simplifies and pressure–velocity relationships are tractable.

Step-by-Step Solution:
State “non-viscous” (inviscid) → neglect shear stresses.State “incompressible” → ρ = constant, acoustic effects ignored.Thus, the correct pair is: incompressible and non-viscous.

Verification / Alternative check:
Potential flow solutions assume irrotational, inviscid, incompressible flow. Low-speed water flows are often modelled as nearly incompressible, but never exactly inviscid in reality—hence the term “ideal”.

Why Other Options Are Wrong:
Incompressible and viscous: describes many real liquids, but not “ideal”.Compressible and non-viscous: used in some aerodynamics models, but not the textbook “ideal fluid” in basic hydraulics.Compressible and viscous: most general real fluid; far from “ideal”.“Inviscid only”: omits the incompressibility part of the classical definition.

Common Pitfalls:

• Applying ideal inviscid results near walls where boundary layers dominate.
• Neglecting compressibility at high Mach numbers in gases.

Final Answer:
Incompressible and non-viscous (inviscid)