A streamline is a curve that is:

Tangent to the velocity vector at every point at one instant

The trajectory of one particle over time

The line joining present positions of particles released from a point

Always perpendicular to the velocity

Which statement about crossing is correct?

Streamlines cannot cross (except at stagnation), but pathlines and streaklines can

Streamlines cross freely at any point

Practice · 5 marks

Streamline, pathline and streakline differentiated

Short answer

A streamline is tangent to velocity at an instant; a pathline is one particle's trajectory over time; a streakline joins particles that passed through a fixed point. They coincide in steady flow, and streamlines cannot cross except at stagnation.

Define streamline, pathline and streakline. Differentiate between them in tabular form and state when they coincide.

Definitions

Streamline: a curve that is tangent to the velocity vector of every fluid particle on it at one instant. Its equation is $\dfrac{dx}{u}=\dfrac{dy}{v}=\dfrac{dz}{w}$ (time held constant).
Pathline: the actual trajectory of one fluid particle over a period of time. It is found from $\dfrac{dx}{dt}=u,\ \dfrac{dy}{dt}=v,\ \dfrac{dz}{dt}=w$ .
Streakline: the curve joining the positions, at one instant, of all particles that have passed through a fixed point earlier (e.g. smoke from a chimney or dye injected at a point).

Comparison

Point	Streamline	Pathline	Streakline
Shows	Velocity direction at an instant	History of one particle	Present positions of many particles from one point
Time	Snapshot	Time-integrated	Snapshot of past injection
Number of particles	Many (field)	One	Many
Equation	$dx/u=dy/v$	$dx/dt=u$ , $dy/dt=v$	Pathlines of particles released at same point, joined at time $t$
Can two cross?	No (except at stagnation)	Yes	Yes
Experimental	Short-exposure photo of tracers	Long-exposure photo of one tracer	Dye or smoke injection

When they coincide

In steady flow the velocity at every point is independent of time, so a particle follows the same path as the streamline and all particles from one point follow it too. Hence streamlines, pathlines and streaklines are identical. In unsteady flow they are different.

Streamlines cannot cross because the velocity at a point has only one direction; there is no flow across a streamline, so a bundle of streamlines forms a streamtube.

✓ Answer checked by Claude Opus 5.5 (high effort)

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All Applied Computational Fluid Dynamics chapter 1 questions →

Streamline, pathline and streakline differentiated

Definitions

Comparison

When they coincide

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