mathematics

Krogh model

Krogh model is a mathematics 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 Krogh model rather than just read about it. In short: Krogh model is a scientific model of mass transfer explaining the concentration of molecular oxygen through a cylindrical capillary tube as a function of a changing position over the capillary tube's length. It was first conceptualized by August Krogh in 1919 with the help of Agner Krarup Erlang to describe oxygen supply in living tissues from human blood vessels.

Key takeaways

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

Reference excerpt

Krogh model is a scientific model of mass transfer explaining the concentration of molecular oxygen through a cylindrical capillary tube as a function of a changing position over the capillary tube's length. It was first conceptualized by August Krogh in 1919 with the help of Agner Krarup Erlang to describe oxygen supply in living tissues from human blood vessels. Its applicability has been extended to various academic fields, and has been successful explaining drug diffusion, water transport, and ice formation in tissues.

Mathematical modeling Krogh model is derived by applying Fick's laws of diffusion and the law of conservation of mass over a radial interval R c ≤ r ≤ R t {\displaystyle Rc\leq r\leq Rt}

Limitations Although Krogh model is a good approximation, it underestimates oxygen consumption because the cylinder model does not include all the tissue surrounding the capillary.

Notes

References Truskey, George; Fan, Yuan; Katz, David (2009), Transport phenomena in biological systems, Prentice Hall, ISBN 978-0-13-156988-1 Wei, James; Anderson, John (1995), Advances in chemical engineering, Volume 19, Academic Press, ISBN 978-0-12-008519-4

Worked examples

Example 1 — a first encounter with Krogh model

Start with the simplest possible case. Write down what Krogh model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Krogh model 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 Krogh model 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 Krogh model

In research: Krogh model appears in mathematics 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 Krogh model 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: Krogh model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Diffusion, Mathematics in medicine, Scientific models, so understanding it makes those chapters shorter.
In everyday life: Look for Krogh model 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.

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How to study Krogh model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Krogh model 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 Krogh model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Krogh model in simple terms?

Why does Krogh model matter?

Because it connects several mathematics 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 Krogh model?

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 Krogh model.