Euler’s equation for inviscid flow — key assumptions: Which of the following is a core assumption used in deriving Euler’s equation of motion for liquids in continuum mechanics?

Introduction / Context:
Euler’s equation provides the inviscid form of the linear momentum balance along a streamline (or in vector form in the field). It underpins Bernoulli’s equation and many first-approximation models in hydraulics and aerodynamics when viscous effects are negligible.

Given Data / Assumptions:

• Continuum fluid with negligible viscosity (inviscid).
• Often treated as homogeneous and incompressible for liquids.
• Body forces (usually gravity) may act.
• No requirement that the flow be steady; Euler’s equation has both steady and unsteady forms.

Concept / Approach:

Euler’s equation is derived from Newton’s second law applied to a fluid element, neglecting viscous stresses (no shear stress terms). For many liquid-flow problems, additional simplification assumes a homogeneous, incompressible fluid. These assumptions lead to the familiar relationships that integrate to Bernoulli’s equation under steady flow.

Step-by-Step Solution:

Verification / Alternative check:

Bernoulli’s equation follows from steady, incompressible, inviscid Euler along a streamline, confirming the appropriateness of the assumption.

Why Other Options Are Wrong:

(a) contradicts the inviscid premise; (c) non-uniformity is permitted but not an assumption; (d) Euler allows steady or unsteady; (e) surface tension is generally negligible in bulk momentum balances.

Common Pitfalls:

Equating Euler’s equation with only steady flow; assuming viscosity can be small yet included—by definition Euler neglects it.

Final Answer:

The fluid is homogeneous and incompressible