Fluid Dynamics: Kinematics and Streamlines

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Questions and Answers

What defines a streamline in a flow field?

  • It can cross other streamlines without restriction.
  • It represents velocity at all particles in the flow.
  • It shows the pressure distribution in the fluid.
  • The tangent at any point indicates the direction of the velocity vector. (correct)

What is true about the relationship between path lines and streamlines in unsteady non-uniform flow?

  • Path lines and streamlines coincide for all particles.
  • Particles don't move along streamlines.
  • Path lines and streamlines are identical in appearance.
  • Path lines can deviate from streamlines. (correct)

How is velocity described along a streamline?

  • Every point along the streamline has the same velocity magnitude.
  • Velocity is defined as the average speed of the fluid over time.
  • Velocity at any point can be determined from the pressure distribution.
  • Velocity components can vary with respect to the coordinate axes. (correct)

What describes a streak line in fluid dynamics?

<p>It connects all particles passing through a single fixed point over time. (C)</p> Signup and view all the answers

Which of the following statements about instantaneous streamlines is correct?

<p>Instantaneous streamlines exhibit varying shapes in time-dependent flow. (C)</p> Signup and view all the answers

What does the differential equation of the streamline illustrate?

<p>The relationship between displacements in different directions. (A)</p> Signup and view all the answers

What is a key characteristic of path lines?

<p>They represent the trajectory of a fluid particle over time. (A)</p> Signup and view all the answers

What is typically true for a fluid particle moving along a streamline?

<p>It follows the streamline for only a short interval in time-dependent flow. (A)</p> Signup and view all the answers

What characterizes a stream tube?

<p>It is bounded by stream lines through a closed curve. (B)</p> Signup and view all the answers

How is steady flow defined?

<p>Velocity, pressure, and density remain constant at a point over time. (D)</p> Signup and view all the answers

What distinguishes laminar flow from turbulent flow?

<p>Laminar flow is typically associated with well-defined paths and parallel streamlines. (B)</p> Signup and view all the answers

What is meant by compressible flow?

<p>The density varies from point to point in the fluid. (A)</p> Signup and view all the answers

Which flow type is characterized as irrotational?

<p>Fluid particles do not rotate about their axes during flow. (B)</p> Signup and view all the answers

In the context of fluid dynamics, what does a one-dimensional flow imply?

<p>The flow parameter, such as velocity, is a function of one spatial coordinate. (A)</p> Signup and view all the answers

Which statement accurately defines uniform flow?

<p>The flow characteristics are identical at all cross-sections. (C)</p> Signup and view all the answers

What is the consequence of a fluid in a turbulent flow regime?

<p>Eddy formation leads to high energy loss. (D)</p> Signup and view all the answers

What happens in an incompressible flow concerning fluid density?

<p>Density changes are ignored, assuming it is constant. (B)</p> Signup and view all the answers

What does the Reynolds number indicate in fluid flow investigations?

<p>The ratio of inertial forces to viscous forces within the fluid. (A)</p> Signup and view all the answers

Flashcards

Streamline

An imaginary line in a flow field where the tangent at any point indicates the velocity vector direction. No flow occurs across a streamline.

Pathline

The actual path followed by a specific fluid particle over time.

Streakline

The line connecting all fluid particles that have passed through a fixed point.

Kinematics

Study of motion without considering the forces causing it. Focuses on velocity in a flow field.

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Steady Flow

Flow where streamlines don't change their position over time.

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Unsteady Flow

Flow where streamlines do change position over time.

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Velocity vector

Shows the speed and direction of a fluid particle at a given point in a flow field.

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Differential equation of streamline

dx/u = dy/v = ds/w; formula for calculating streamlines

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Uniform Flow

Fluid flow where velocity at any point in time remains the same regardless of location along the flow.

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Non-Uniform Flow

Fluid flow where velocity at any given time changes with location along the flow.

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Laminar Flow

Organized flow where fluid particles move in smooth layers.

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Turbulent Flow

Disorganized flow where fluid particles move erratically in a zigzag manner.

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Compressible Flow

Fluid flow where density changes from point to point.

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Incompressible Flow

Fluid flow where density remains constant throughout the flow.

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Stream Tube

Imaginary tube formed by streamlines, no fluid can cross its boundaries.

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Discharge (Q)

Volume of fluid flowing per unit time through a section.

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Study Notes

Kinematics

  • Kinematics studies motion without considering forces.
  • Velocity is crucial in fluid flow analysis to determine pressure and forces.

Streamlines

  • Streamlines are imaginary lines tangent to velocity vectors.
  • No flow crosses streamlines.
  • A differential equation describes streamlines: dx/u = dy/v = ds/w.

Path Lines

  • A path line shows the trajectory of a particular fluid particle.
  • It tracks the particle's movement over time.

Streak Lines

  • Streak lines trace the path of particles passing a fixed point.
  • Dye or smoke are typical tracers.
  • In steady flow, streamlines, path lines, and streak lines coincide.

Instantaneous Streamlines

  • In unsteady flow, streamlines change with time.
  • Instantaneous streamlines depict the streamline position at a specific time.

Stream Tubes

  • Streamlines forming a closed curve create a stream tube.
  • Fluid cannot cross a stream tube's boundary.
  • Fluid entering a stream tube equals fluid leaving.

Flow Classifications

  • Steady/Unsteady: Steady flow has constant properties over time, while unsteady flow changes with time.

  • Uniform/Non-uniform: Uniform flow has constant velocity throughout, while non-uniform flow changes with position.

  • Laminar/Turbulent: Laminar flow is smooth and in layers, while turbulent flow is erratic with eddies.

  • Compressible/Incompressible: Incompressible fluids have constant density, while compressible fluids do not.

  • Rotational/Irrotational: Rotational flow involves particle rotation, while irrotational flow does not.

  • One, Two, and Three-Dimensional Flows: One-dimensional flow varies in one direction, two-dimensional in two, and three-dimensional in three.

Discharge (Rate of Flow)

  • Discharge measures fluid quantity per second.
  • Liquid discharge is volume per second (e.g., m³/s).
  • Gas discharge is often weight or force per second (e.g., kgf/s, N/s).

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