Viscous flow: laminar and turbulent is a core Mechanical Engineering (ME) concept in Engineering. This guide explains what it is, walks through a fully worked example, and lists the key equations you need — with a short quiz to test yourself.

Key equations and worked example

Water flows at 2 m/s through a 10 cm pipe that narrows to 5 cm. By continuity (A₁v₁ = A₂v₂), halving the diameter quarters the area, so the throat speed is 2×4 = 8 m/s. Bernoulli then says pressure drops at the throat — the manometer column there stands shorter. Try it with the throat slider.

• <code>Continuity: A₁·v₁ = A₂·v₂</code>
• <code>Bernoulli: P + ½ρv² + ρgh = constant</code>
• <code>Volume flow rate: Q = A·v</code>
• <code>Reynolds number: Re = ρ·v·D / μ</code>

Viscous flow: laminar and turbulent in detail

Viscous flow: laminar and turbulent is one of the central ideas in Mechanical Engineering (ME), and it appears in Engineering curricula under Fluid Mechanics. It is worth learning deeply because it connects to so many other topics in this section.

Continuity: incompressible flow speeds up where the pipe narrows (A·v constant). Bernoulli&#39;s equation trades pressure for speed: where velocity rises, pressure falls (P + ½ρv² + ρgh = constant). Viscosity adds friction — laminar flow is smooth layers, turbulent flow is chaotic above a critical Reynolds number.

For exams, the pattern is predictable: first a definition or statement of the result, then a direct numerical application of one of the equations above, then a "why" question — why the formula takes that form, or what changes when a variable is doubled or halved. The worked example and quiz below cover exactly that progression.

Quick self-check:

• Q: A pipe&#39;s diameter halves. By what factor does the flow speed change?<br />A: It quadruples — area falls by 4×, so v rises 4× to keep A·v constant.
• Q: Why does pressure drop in the narrow throat of a venturi?<br />A: Bernoulli&#39;s principle: higher speed means lower pressure when height is unchanged.
• Q: What does the Reynolds number tell you?<br />A: Whether flow is laminar (low Re) or turbulent (high Re) — it compares inertial to viscous forces.