Fluid Mechanics · Unit 1 · Lesson 4 of 13
Why Does Water Take The Shape Of Its Glass?
Pour water into a glass and it takes the glass's shape. Drop a stone in and it keeps its own. Let a little perfume out and it fills the whole room. What is different inside each one?
1. Real-World Problem
Car brakes use a liquid to pass the driver's push to the wheels. Tyres use air to cushion bumps. Why would the brakes fail if they were filled with air?
2. Predict
Make your guess before you try the experiment. You will see the answer after the next step.
Predict
3. Experiment
Switch between Solid, Liquid and Gas. Press Tilt and Push sideways: which one keeps its own shape? Change the container to Flask and Funnel and watch where each state ends up.
In Engineering mode, choose the Box and drag the squeeze slider to 100 kPa. Compare how much 1 L of air and 1 L of water shrink. Remember that the dots are a conceptual illustration: the numbers come from measured properties.
4. Understand
Whether a substance is a solid, liquid or gas depends on a balance: attractive interactions between molecules pull them together and hold them in place, while thermal motion (which grows with temperature) shakes them apart. The arrangement that results decides how the substance behaves.
- Solid: interactions hold each molecule near a fixed position; it can only vibrate. The arrangement can be ordered (crystalline: metals, salt, ice) or disordered (amorphous: glass, many plastics).
- Liquid: molecules are packed about as closely as in a solid, but thermal motion lets them slip past one another, so the liquid flows while keeping its volume.
- Gas: thermal motion wins. Molecules are far apart (about 10 molecule widths in air at room conditions) and interact mainly when they collide.
| Property | Solid | Liquid | Gas |
|---|---|---|---|
| Shape | Keeps its own | Takes the container's | Takes the container's |
| Volume | Fixed | Fixed | Fills the whole container |
| Arrangement | Fixed positions; ordered (crystalline) or disordered (amorphous) | Close together, disordered, neighbours keep changing | Far apart, random |
| Typical spacing | About one molecule width | About one molecule width | About 10 molecule widths (air, room conditions) |
| What wins | Interactions hold positions | Interactions keep it together; thermal motion lets molecules slide | Thermal motion; interactions matter mainly in collisions |
| Shear stress at rest | Can hold it with a fixed deformation | Cannot hold it; flows | Cannot hold it; flows |
| Free surface | Not applicable | Yes | No |
| Ease of compression | Very hard | Very hard | Easy |
| Example density (kg/m³) | Steel 7850 | Water 1000 | Air 1.2 (20 °C, sea level) |
An interesting exception: ice floats. For most substances the solid is denser than the liquid. Water is different: ice is about 917 kg/m³ and liquid water about 1000 kg/m³, because hydrogen bonds lock ice into an open, hexagonal arrangement. That is why ice floats and lakes freeze from the top down.
The deciding test from Lesson 1 still holds: a solid can hold a shear stress at rest, liquids and gases cannot, which is why both are fluids.
5. Derive
Step 1. How hard a substance is to squeeze is measured by its bulk modulus K:
K = -\frac{dp}{dV/V}dp is the increase in pressure (Pa) and dV/V the fractional change in volume (the minus sign makes K positive, because volume shrinks).
Step 2. For a small change in a liquid, ΔV/V ≈ −Δp/K.
Step 3. For an ideal gas squeezed slowly at constant temperature, pV = constant. Differentiate: p dV + V dp = 0, so dp/(dV/V) = −p, which gives:
K_{gas,\ isothermal} = pSo air at atmospheric pressure has K of about 0.1 MPa, while water's K is about 2.2 GPa: roughly 20,000 times larger.
6. Calculate
Add 100 kPa (about 1 bar) to 1 L of each.
- Water: ΔV/V = −100,000 ÷ 2,200,000,000 = −4.5 × 10⁻⁵. The litre shrinks by only 0.045 mL.
- Air, starting at 101.3 kPa: p₁V₁ = p₂V₂, so V₂ = 1 × 101.3 ÷ 201.3 = 0.50 L. The air halves in volume.
- Note: for the air we used pV = constant, not ΔV/V = −Δp/K, because the change is large and K itself changes as the air is squeezed.
7. Apply
- Car brakes use liquid, not air, because a liquid passes a push on without squashing. Air in a brake line is dangerous for exactly this reason ("spongy brakes").
- Tyres use air because it squashes and cushions bumps.
- A gas cylinder holds a lot of gas because gas compresses easily.
- Rivers and lakes have a flat free surface; the atmosphere has none.
- Pipes burst in freezing weather because water expands about 9% when it turns to ice.
8. Validate
In the Squeeze panel set Δp = 100 kPa: water must show about −0.0045% and air about −50%. Where these numbers stop applying: fast compression heats air, so it resists more than the slow (isothermal) value; at very high pressures water's K rises slightly.
Easy To Mix Up
- Liquids are not perfectly incompressible. We treat them that way because the change is tiny.
- Not every solid is crystalline. Glass is a solid with a disordered arrangement.
- The solid is not always denser than the liquid. Ice floats on water.
- Gas taking any shape does not make it weaker. A compressed gas can push enormously hard.
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.
If solids and fluids are both made of molecules, why do engineers study them as two different subjects?
Go to Lesson 5: Why Do Engineers Study Fluids Separately From Solids? →Read More
- Cengel and Cimbala, "Properties of Fluids" (density, compressibility).
- NPTEL, Introduction to Fluid Mechanics (Prof. Suman Chakraborty, IIT Kharagpur): Weeks 2 and 3.