Dimensionless numbers – is the reciprocal of Euler number called the Newton number? The statement “The reciprocal of the Euler number is called the Newton number” is:

Introduction:
Dimensionless numbers help compare the relative importance of physical effects in fluid systems. Euler number (Eu) and Newton number (often used to mean power number, Np) describe different ratios. The question challenges a common confusion about their relationship.

Given Data / Assumptions:

• Euler number Eu typically defined as Eu = Δp / (rho * V^2) (pressure forces to inertial forces).
• So-called Newton number in mixing literature is the power number Np = P / (rho * N^3 * D^5).
• Other contexts may use “Newton number” loosely, but it is not standardly the reciprocal of Eu.

Concept / Approach:

The reciprocal of Eu would be (rho * V^2) / Δp, which is not generally named the Newton number in standard fluid mechanics. Newton (power) number relates agitator power to inertial scaling and is independent of pressure-coefficient definitions like Eu. Therefore, the statement is incorrect.

Step-by-Step Solution:

Verification / Alternative check:

Textbook tables of dimensionless groups list Eu separately from Np and do not present a reciprocal relation naming convention. Some fields use a “pressure coefficient” Cp similar to Eu; again, no standard Newton-number reciprocity exists.

Why Other Options Are Wrong:

Any “Yes/True” variants propagate a nonstandard and misleading equivalence.

Common Pitfalls:

Interchanging names of dimensionless groups across subdomains (e.g., mixing vs external aerodynamics) and assuming simple reciprocal relationships where none are defined.

Final Answer:

No