Fluid Mechanics · Unit 1 · Lesson 1 of 13
What Exactly Is A Fluid?
Water, honey and air are all called fluids, but ice, steel and wood are not. What single test separates them?
1. Real-World Problem
A steel shaft spins inside a bearing with a thin film of oil around it. As long as the shaft turns, the oil keeps moving and keeps pulling back on the shaft. A rubber bushing on a car's suspension arm, pushed the same way, twists a little and then holds still. What is different about the oil?
2. Predict
Make your guess before you try the experiment. You will see the answer after the next step.
Predict
3. Experiment
Start in Visual mode: the top plate slides over a thin layer of water and the yellow dye line keeps tilting further for as long as the plate moves.
Switch to Engineering mode. Pick Water, set the plate speed U to 0.04 m/s and read the shear stress. Then choose Honey at the same speed and compare. Finally pick Solid block, choose Rubber and press Push: the block leans a little and stops.
Experiment mode asks you to predict the shear stress before you run it, then compares your answer with the simulation.
4. Understand
A shear stress is a force acting along a surface, divided by the area it acts on. A fluid is a substance that deforms continuously under an applied shear stress, however small that stress is.
This does not mean a fluid offers no resistance. At rest, an ordinary fluid cannot sustain any shear stress: if one acts, the fluid starts to move. Once it is moving, the fluid does resist the shearing, through viscous shear stress, which grows with how fast the layers slide past each other. That is why you must keep pushing the spoon through honey. So a fluid resists the rate of deformation, while a solid resists the amount of deformation: under a steady shear stress a solid deforms a fixed amount and then stays in equilibrium. Liquids and gases are both fluids.
A fluid at rest has no shear stress anywhere inside it. The only stress it carries at rest is pressure, which pushes straight onto surfaces.
5. Derive
Step 1. Shear stress is force along a surface per unit area:
\tau = \frac{F}{A}τ is shear stress (Pa), F the force along the surface (N), A the area (m²).
Step 2. A linear elastic solid deforms in proportion to the stress (Hooke's law in shear):
\tau = G\,\gammaG is the shear modulus (Pa), γ the shear strain (the lean angle in radians, for small angles).
Step 3. A fluid sticks to both plates (the no-slip condition), so the bottom layer has speed 0 and the top layer speed U. In steady flow between parallel plates, with no pressure difference pushing the fluid along, the speed changes in a straight line across the gap:
u(y) = U\,\frac{y}{h} \qquad \Rightarrow \qquad \frac{du}{dy} = \frac{U}{h}Step 4. For a Newtonian fluid, shear stress is proportional to the rate of shearing (Newton's law of viscosity, studied fully in Unit 2):
\tau = \mu \frac{du}{dy} = \mu \frac{U}{h} \qquad F = \tau A = \frac{\mu U A}{h}μ is dynamic viscosity (Pa·s), u the speed of a layer at height y (m/s), h the gap (m).
Step 5. The shear strain of the fluid grows at the rate du/dy, so after time t:
\gamma = \frac{U}{h}\,tIt never settles to a fixed value. That is continuous deformation, the definition of a fluid, written as an equation.
6. Calculate
Top plate speed U = 0.04 m/s, gap h = 1 mm, plate area A = 0.01 m².
- Shear rate: U/h = 0.04 ÷ 0.001 = 40 per second.
- Water: τ = 0.001 × 40 = 0.04 Pa; F = 0.04 × 0.01 = 0.0004 N.
- Honey: τ = 10 × 40 = 400 Pa; F = 400 × 0.01 = 4 N.
- Honey is 10,000 times more viscous, so it needs 10,000 times more force at the same speed.
- Solid for comparison: 200 N on the rubber block gives τ = 200 ÷ 0.01 = 20,000 Pa and γ = 20,000 ÷ 500,000 = 0.04 rad (about 2.3°), and it stays there.
7. Apply
- Engine oil in a journal bearing: the oil film keeps shearing as the shaft turns, and its viscous stress is the friction the engine must overcome.
- Air flowing over a moving car: a gas is a fluid too, and its viscous stress on the body is skin friction drag.
- Water from a tap taking the shape of whatever it lands in.
- The pitch drop experiment at the University of Queensland, running since 1927: pitch looks solid and shatters under a hammer, yet it flows, about one drop every decade.
8. Validate
In Engineering mode, set water at U = 0.04 m/s: the readouts must show τ = 0.04 Pa and F = 0.0004 N. Switch to honey: 400 Pa and 4 N. Check the model applies: Re = 998 × 0.04 × 0.001 ÷ 0.001 = 40, far below the range where this flow becomes unsteady, so the laminar straight-line profile is valid. Where τ = μU/h does not apply: at high speeds where the flow turns turbulent, in fluids that are not Newtonian (paint, ketchup, blood), and during the first moments after the plate starts moving.
Easy To Mix Up
- Fluid is not the same as liquid. Gases are fluids too.
- Fluids do resist shearing while they move (viscous stress). What they cannot do is hold a shear stress while at rest.
- Thick does not mean solid. Honey and pitch both flow. Honey is simply very viscous; pitch is viscoelastic: it shatters under a sudden blow but flows over years.
- Some materials, like toothpaste, flow only after a minimum push (a yield stress). They are special non-Newtonian materials, covered later.
9. Quiz
Four quick questions: a concept, a calculation and an interpretation. Each answer comes with an explanation. Score 3 or more to mark this lesson completed.
Check Your Understanding
Four questions: a concept, a calculation and an interpretation. Every answer comes with an explanation. Score 3 of 4 to mark the lesson completed.
Fluids are everywhere. So what exactly does fluid mechanics study?
Go to Lesson 2: What Does Fluid Mechanics Study? →Read More
- Cengel and Cimbala, Fluid Mechanics: Fundamentals and Applications, "Introduction and Basic Concepts" (what is a fluid, the no-slip condition) and "Properties of Fluids" (viscosity).
- NPTEL, Introduction to Fluid Mechanics (Prof. Suman Chakraborty, IIT Kharagpur): Weeks 1 and 2.