science

Taylor–Culick flow

Taylor–Culick flow is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Taylor–Culick flow rather than just read about it. In short: In fluid dynamics, Taylor–Culick flow, a type of a stagnation point flow, describes the axisymmetric flow inside a long slender cylinder with one end closed, supplied by a constant flow injection through the sidewall. The flow is named after Geoffrey Ingram Taylor and F.

Key takeaways

Taylor–Culick flow belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Taylor–Culick flow to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Taylor–Culick flow from memory before moving on to harder problems.

Reference excerpt

In fluid dynamics, Taylor–Culick flow, a type of a stagnation point flow, describes the axisymmetric flow inside a long slender cylinder with one end closed, supplied by a constant flow injection through the sidewall. The flow is named after Geoffrey Ingram Taylor and F. E. C. Culick. In 1956, Taylor showed that when a fluid forced into porous sheet of cone or wedge, a favorable longitudinal pressure gradient is set up in the direction of the flow inside the cone or wedge and the flow is rotational; this is in contrast in the vice versa case wherein the fluid is forced out of the cone or wedge sheet from inside in which case, the flow is uniform inside the cone or wedge and is obviously potential. Taylor also obtained solutions for the velocity in the limiting case where the cone or the wedge degenerates into a circular tube or parallel plates. Later in 1966, Culick found the solution corresponding to the tube problem, in problem applied to solid-propellant rocket combustion. Here the thermal expansion of the gas due to combustion occurring at the inner surface of the combustion chamber (long slender cylinder) generates a flow directed towards the axis.

Flow description Consider a slender porous tube of radius a {\displaystyle a} and length l {\displaystyle l} (such that ϵ = a / l ≪ 1 {\displaystyle \epsilon =a/l\ll 1} ) through which fluid is injected uniformly with a speed ⁠ V {\displaystyle V} ⁠. Far away from the open or closed ends, the radial velocity and axial velocity induced is of the order v r ∼ V {\displaystyle v_{r}\sim V} and v ∼ V / ϵ {\displaystyle v\sim V/\epsilon } and the flow can be described using self-similar solution, which was described for laminar, viscous flows by S. W. Yuan and A. Finkelstein, following the earlier work for planar flows (or Berman flow). When the Reynolds number R e = V a / ν {\displaystyle Re=Va/\nu } becomes large, the solution approaches the Taylor–Culick flow, which is described by

v r V = − a r sin ⁡ ( π r 2 2 a 2 ) , v θ = 0 , v z V / ϵ = π z l cos ⁡ ( π r 2 2 a 2 ) . {\displaystyle {\frac {v_{r}}{V}}=-{\frac {a}{r}}\sin \left({\frac {\pi r^{2}}{2a^{2}}}\right),\quad v_{\theta }=0,\quad {\frac {v_{z}}{V/\epsilon }}={\frac {\pi z}{l}}\cos \left({\frac {\pi r^{2}}{2a^{2}}}\right).}

The pressure field and Stokes stream function are given by

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Taylor–Culick flow

Start with the simplest possible case. Write down what Taylor–Culick flow claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Taylor–Culick flow before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Taylor–Culick flow ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Taylor–Culick flow

In research: Taylor–Culick flow appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Taylor–Culick flow in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Taylor–Culick flow is common in secondary-school and first-year university syllabi. It links to neighbouring topics Flow regimes, Fluid dynamics, so understanding it makes those chapters shorter.
In everyday life: Look for Taylor–Culick flow outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Taylor–Culick flow” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Taylor–Culick flow in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Taylor–Culick flow means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Taylor–Culick flow out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Taylor–Culick flow in simple terms?

Why does Taylor–Culick flow matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Taylor–Culick flow?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Taylor–Culick flow.