In fluid mechanics, the Euler number (Eu) is defined as the ratio of pressure force to ______ force. Select the correct type of force from the options.

Difficulty: Easy

Correct Answer: inertial

Explanation:


Introduction:
Euler number (Eu) is a key dimensionless parameter in fluid mechanics used to compare pressure effects with inertia effects in a flow. It helps engineers judge when pressure differences dominate compared to the kinetic (inertial) behavior of a moving fluid.


Given Data / Assumptions:

  • Euler number is defined for a flowing fluid.
  • Pressure force and inertial force are the compared effects.
  • No special fluid properties are required beyond density and velocity for interpretation.


Concept / Approach:
By definition, Eu = pressure force / inertial force. In practice this is written as Eu = Δp / (rho * V^2), where Δp is a representative pressure difference, rho is fluid density, and V is a characteristic velocity. Therefore the denominator represents inertial effects. The missing word in the stem must be 'inertial'.


Step-by-Step Solution:
1) Write the definition: Eu = pressure force / inertial force.2) Express in common engineering form: Eu = Δp / (rho * V^2).3) Identify the compared forces: numerator is pressure effect; denominator represents inertia (mass * velocity^2 scaling).4) Hence the blank corresponds to 'inertial' force.


Verification / Alternative check:
Other common dimensionless groups confirm the pattern: e.g., Reynolds number compares inertial to viscous, Froude compares inertial to gravity, and Weber compares inertial to surface tension. Euler uniquely involves pressure in the numerator over inertia in the denominator.


Why Other Options Are Wrong:

  • Gravitational: Gravity-based comparisons define the Froude number, not Euler.
  • Viscous: Viscous comparisons define the Reynolds number, not Euler.
  • Surface tension: Surface-tension comparisons define the Weber number.


Common Pitfalls:

  • Reversing the ratio (inertial over pressure) is incorrect for Euler.
  • Confusing Eu with Re or Fr due to similar symbols and frequent use.


Final Answer:
inertial

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