---
title: "Streamline, pathline and streakline differentiated"
subject: "Applied Computational Fluid Dynamics"
chapter: 1
key: "semester_7/applied_computational_fluid_dynamics:streamline-pathline-streakline"
source: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/streamline-pathline-streakline
site: BCT Engineering
---

# Streamline, pathline and streakline differentiated

Applied Computational Fluid Dynamics · Chapter 1: Introduction to CFD and Fluid Mechanics Review

- Asked in: year not given, 5 marks
- Video: [Streamlines, Pathlines, and Streaklines - Eulerian vs. Lagrangian in 10 Minutes!](https://www.youtube.com/watch?v=AGve4RZ4zjw) — Less Boring Lectures
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/streamline-pathline-streakline
- Whole chapter: https://www.bctengineer.com/md/semester_7/applied_computational_fluid_dynamics/chapter-1

## Question

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

## 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.

## Answer

#### 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A streamline is a curve that is:
   A. The trajectory of one particle over time
   B. The line joining present positions of particles released from a point
   C. Tangent to the velocity vector at every point at one instant
   D. Always perpendicular to the velocity
   Answer: C. A streamline is tangent to the velocity vectors at an instant; dx/u = dy/v = dz/w with time held constant. (Key point: Streamline definition)

2. Smoke leaving a chimney from a fixed point shows which line?
   A. Streakline
   B. Streamline
   C. Pathline
   D. Equipotential line
   Answer: A. A streakline joins, at one instant, all particles that have passed through a fixed point earlier. (Key point: Streakline definition)

3. When do streamlines, pathlines and streaklines coincide?
   A. In any turbulent flow
   B. In unsteady flow
   C. Only at stagnation points
   D. In steady flow
   Answer: D. In steady flow velocity at a point does not change with time, so every particle from a point follows the same path as the streamline. (Key point: When lines coincide)

4. Which statement about crossing is correct?
   A. Streamlines cannot cross (except at stagnation), but pathlines and streaklines can
   B. Pathlines can never cross
   C. All three can never cross
   D. Streamlines cross freely at any point
   Answer: A. A point has only one velocity direction at an instant, so streamlines cannot cross; pathlines and streaklines may. (Key point: Crossing of lines)

## Related in Applied Computational Fluid Dynamics

- [Euler equation, Bernoulli and Pitot tube](https://www.bctengineer.com/question.md?key=semester_7%2Fapplied_computational_fluid_dynamics%3Aeuler-equation-pitot-numerical) — Applied Computational Fluid Dynamics, chapter 2
- [Explicit, implicit and Crank-Nicolson schemes](https://www.bctengineer.com/question.md?key=semester_7%2Fapplied_computational_fluid_dynamics%3Aexplicit-implicit-crank-nicolson) — Applied Computational Fluid Dynamics, chapter 3

## Related in other subjects

- [Types of flow, streamline, pathline, streakline](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Aflow-types-streamline-pathline-streakline) — Fluid Mechanics, chapter 3
- [Draw streakline and pathline of dye](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Astreakline-pathline-dye-two-stage) — Fluid Mechanics, chapter 4