Fluid Mechanics - Engineering

Q1:

An equipotential line is __________ to the velocity vector at every point.

A normal

B abnormal

C tangential

D none of these

ANS:A - normal

An equipotential line in fluid dynamics is normal to the velocity vector at every point.

Explanation:

  1. Equipotential Line:
    • An equipotential line in fluid flow represents a line where the potential (such as pressure or velocity potential) remains constant.
    • In the context of fluid dynamics, it is often associated with the pressure potential, where the pressure is constant along the equipotential line.
  2. Relationship with Velocity Vector:
    • The velocity vector in fluid flow is tangent to the streamlines. Streamlines are imaginary lines that are everywhere tangent to the velocity vector at a given instant.
  3. Normality to Velocity Vector:
    • An equipotential line is perpendicular (normal) to the velocity vector at every point where they intersect.
    • This relationship arises because in fluid flow, pressure (and thus potential) gradients drive fluid motion along streamlines, which are tangent to the velocity vector.
  4. Options Analysis:
    • Normal: Correct term in fluid dynamics indicating perpendicularity.
    • Abnormal: Not a standard term in this context.
    • Tangential: Describes the direction of streamlines in relation to the velocity vector, not equipotential lines.

Conclusion:

Therefore, an equipotential line is normal to the velocity vector at every point in fluid dynamics. This relationship helps to define the flow patterns and pressure distribution within a fluid system.