Fluid Mechanics · Unit 1 · Lesson 5 of 13
Why Do Engineers Study Fluids Separately From Solids?
A steel shaft and the oil film around it are both being sheared. Why do engineers need two different subjects to describe them?
1. Real-World Problem
A designer checking a journal bearing must check two things: will the steel shaft twist too much under its torque, and will the oil film around it carry the load without the metal touching? Both are sheared by the turning motion, the steel by its torque and the oil film by the spinning shaft, yet the two checks use different subjects.
2. Predict
Make your guess before you try the experiment. You will see the answer after the next step.
Predict
3. Experiment
The same shear stress acts on a rubber block (left) and a layer of honey (right). Drag the stress slider and press Double the stress.
Watch what doubles: the rubber leans twice as far and stops, while the honey flows twice as fast. On the graph, one line goes flat and the other keeps rising.
4. Understand
Solid mechanics links stress to how much a body deforms. Fluid mechanics links stress to how fast a fluid deforms. The two simplest models are:
- Linear elastic solid: shear stress proportional to shear strain, τ = Gγ.
- Newtonian fluid: shear stress proportional to the rate of shear strain, τ = μ du/dy.
These are models, not universal laws. Many real materials are more complicated: rubber at large stretch is nonlinear, metals yield and deform permanently, polymers and body tissues are viscoelastic (part solid, part fluid), and paint, ketchup, blood and toothpaste are non-Newtonian fluids. The two simple models are the starting point of each subject, and they work very well for steel at normal loads and for water, air and oils.
| Solid mechanics | Fluid mechanics | |
|---|---|---|
| Asks | How much does it deform? | How fast does it flow? |
| Stress is linked to | Strain (deformation) | Strain rate (velocity gradient) |
| Simplest model in shear | τ = Gγ (linear elastic solid) | τ = μ du/dy (Newtonian fluid) |
| Where that model fails | Large strain, yielding, viscoelastic materials | Non-Newtonian fluids such as paint, ketchup, blood |
| Main unknowns | Displacement, strain, stress | Velocity, pressure |
| Stresses carried at rest | Tension, compression, shear | Pressure only (ordinary fluids) |
| Usual way to describe it | Follow the same piece of material | Watch fixed points in space as fluid passes |
| Typical problems | Beam bending, shaft twisting | Pipe flow, drag, pumps |
| BTech subject | Strength Of Materials | Fluid Mechanics |
What they share: both are part of continuum mechanics. Both use Newton's laws, both use stress (force per area), and both treat matter as continuous (Lesson 8 explains why that is allowed).
5. Derive
Step 1. Solid block of thickness H: for a small lean, the top moves sideways by x, and γ ≈ x/H. With τ = Gγ:
x = \frac{\tau H}{G}Step 2. Fluid layer of thickness h: from Lesson 1, τ = μU/h, so:
U = \frac{\tau h}{\mu}Step 3. Both are linear in τ, so doubling τ doubles x (solid) or U (fluid). But the solid's x is a fixed distance, while the fluid's top surface keeps moving: its displacement after time t is U t.
6. Calculate
Apply τ = 200 Pa to both.
- Rubber, H = 10 mm, G = 0.5 MPa: γ = 200 ÷ 500,000 = 0.0004 rad; x = 0.0004 × 10 mm = 0.004 mm. It stays there.
- Honey, h = 1 mm, μ = 10 Pa·s: U = 200 × 0.001 ÷ 10 = 0.02 m/s. After 10 s the top has moved 0.2 m (200 mm), and it is still going.
7. Apply
- A car's suspension spring is designed with solid mechanics; the shock absorber's oil with fluid mechanics.
- A dam wall is checked with solid mechanics; the water pushing on it with fluid mechanics.
- A pump's casing is a solid problem; the water inside it is a fluid problem.
- A journal bearing: shaft twist is solid mechanics, the oil film is fluid mechanics.
8. Validate
In compare mode set τ = 200 Pa: the rubber panel must show γ = 0.0004 rad and the honey panel U = 0.02 m/s. Where the models stop working: rubber stretched by more than a few tens of percent no longer follows τ = Gγ; a yield-stress material like toothpaste does not flow at all below a minimum stress, so τ = μ du/dy does not describe it.
Easy To Mix Up
- Fluids can carry stress. At rest it is pressure; in motion they carry viscous shear stress too.
- τ = Gγ and τ = μ du/dy are models for linear elastic solids and Newtonian fluids, not laws for every material.
- "Fluid" and "solid" mechanics use the same physics. Only the material behaviour, and so the main question, differs.
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.
A fluid can sit still, flow, or be pushed into flowing. Engineers split the subject into three parts to match. What are they?
Go to Lesson 6: Still, Moving Or Pushed: Three Ways To Look At A Fluid →Read More
- Cengel and Cimbala, "Properties of Fluids" (viscosity); Gere and Goodno, Mechanics of Materials, chapter on tension, compression and shear (shear strain, Hooke's law in shear).
- NPTEL, Introduction to Fluid Mechanics (Prof. Suman Chakraborty, IIT Kharagpur): Week 2.