physics

Velocity triangle

Velocity triangle is a physics 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 Velocity triangle rather than just read about it. In short: In turbomachinery, a velocity triangle or a velocity diagram is a triangle representing the various components of velocities of the working fluid in a turbomachine. Velocity triangles may be drawn for both the inlet and outlet sections of any turbomachine.

Key takeaways

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

Reference excerpt

In turbomachinery, a velocity triangle or a velocity diagram is a triangle representing the various components of velocities of the working fluid in a turbomachine. Velocity triangles may be drawn for both the inlet and outlet sections of any turbomachine. The vector nature of velocity is utilized in the triangles, and the most basic form of a velocity triangle consists of the tangential velocity, the absolute velocity and the relative velocity of the fluid making up three sides of the triangle.

Components

A general velocity triangle consists of the following vectors:

V = absolute velocity of the fluid. U = blade linear velocity. Vr = relative velocity of the fluid after contact with rotor. Vw = tangential component of V (absolute velocity), called Whirl velocity. Vf = flow velocity (axial component in case of axial machines, radial component in case of radial machines). The following angles are encountered during the analysis:

α = absolute angle is an angle made by V with the plane of the machine (usually the nozzle angle or the guide blade angle) i.e. angle made by absolute velocity V and the direction of blade rotation U. β = relative angle is an angle made by relative velocity and direction of blade rotation.

References

Worked examples

Example 1 — a first encounter with Velocity triangle

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

In research: Velocity triangle appears in physics 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 Velocity triangle 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: Velocity triangle is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fluid mechanics, Mechanical engineering, so understanding it makes those chapters shorter.
In everyday life: Look for Velocity triangle 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.

Affiliate

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

How to study Velocity triangle in 20 minutes

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

Frequently asked questions

What is Velocity triangle in simple terms?

Why does Velocity triangle matter?

Because it connects several physics 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 Velocity triangle?

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 Velocity triangle.