Deformation & Fluid Pressure
Explain elastic and inelastic deformation, thermal expansion and contraction, and how pressure in still fluids acts in all directions and increases with depth
What a learner can do afterwards
- Distinguishes elastic deformation (returns to shape) from inelastic/plastic deformation (permanently changed)
- Explains how expansion gaps in some bridges and jointed railway tracks allow thermal expansion and contraction
- Explains how pressure grows with depth in still water, compares extra pressure at fixed density, and compares equal-depth pressures when water density, gravity and surface pressure match
- Gives an everyday example of thermal expansion causing a problem or being used usefully
- Uses equal added pressure to calculate added forces on ideal, frictionless hydraulic pistons at the same height, ignoring piston weights
- Finds total absolute pressure by adding air pressure of about 101 kPa to gauge water pressure
1 · Read
You have worked out how forces add up and cancel out. Push, pull, bend, or squeeze an object hard enough and you deform it: you change its shape. What happens once you stop pushing depends on how far you went.
Stretch a rubber band gently and let go. It returns to its original shape. That is elastic deformation: the shape change is reversed once the force is gone.
Now bend a paperclip a little. It springs back too, same as the rubber band. But bend it too far and it stays bent. Past a certain point the material cannot return to normal. That permanent change is called inelastic, or plastic, deformation.
Most solids expand when warmed and contract when cooled. Their particles move farther apart on average as they warm. A warmed metal lid can expand and loosen. Some bridges and jointed railway tracks use gaps to allow expansion. If expansion is blocked, thermal stress can buckle metal. Other tracks use special engineering instead of gaps.
Pressure is perpendicular force per area. In still water, it acts in every direction and increases with depth. With constant density, extra pressure = density x gravity x depth. Doubling depth doubles this extra pressure. At fixed depth and surface pressure, the pool's shape does not matter. Higher pressure near a dam's bottom calls for more support. A submarine needs a hull strong enough for its diving depth.
In an ideal enclosed liquid, an added pressure spreads equally (Pascal's principle). With frictionless pistons at the same height, added force / area is equal. A 100 N added push gives 1000 N on ten times the area. We ignore piston weights. Absolute pressure = air pressure + gauge pressure: 101 kPa of air plus 50 kPa of extra water pressure gives 151 kPa.
Elastic changes reverse; plastic changes remain. Most materials expand when warmed. In still water, pressure acts in every direction and increases with depth.
The rewritten readings were written for this dataset.
More to read
Pressure beneath the surface
In still water, pressure is greater farther down because more water weighs on the water below. In a denser fluid, each extra metre adds more pressure. Because water is denser than air, its pressure changes more rapidly with depth. Submarine hulls must resist the pressure where they dive.
Passing pressure through a liquid
An ideal liquid in a closed container transmits an applied pressure increase throughout, with no loss. This is Pascal's principle. Pressure differences caused by depth still remain. For frictionless hydraulic pistons at equal heights, dividing added force by area gives the same result for either piston. Increasing piston area increases its added force. Lifts and hydraulic brakes use this relationship.
Measuring changes in materials
Forces can lengthen or compress a material. Dividing force by area gives stress; strain compares deformation with the starting dimensions or shape. Elastic changes disappear after the force stops, while plastic changes remain. Elastic moduli describe stiffness: Young's modulus concerns length changes, shear modulus concerns shearing, and bulk modulus concerns pressure-driven volume changes.
Calculating water pressure
Atmospheric pressure varies with height; pressure in resting water rises downward. Near Earth's surface, water with constant density obeys extra pressure = density x gravity x depth. Add the pressure of air above the surface to find absolute pressure. Twice the depth gives twice the extra pressure. Container shape makes no difference when depth, density, gravity and surface pressure match. The greater pressure below helps explain why many dams have thicker bases.
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