Fluid Forces

Fluid Forces

A fluid is anything that flows: a liquid or a gas. Fluids press on everything they touch, and that push is pressure. The same idea explains why a sharp knife cuts and a blunt one does not, why a diver's ears hurt, why a crisp packet puffs up on a mountain, and why there is a limit to how long a drinking straw can be. All of that comes out of two short equations.

The words for it

Five terms. The first equation is the one to recall; the second is given to you in the exam:

Find the pressure

A force of 200 N presses evenly on an area of 4 m². What is the pressure, in pascals (Pa)?

Same force, different area

Because pressure is force divided by area, you can change the pressure enormously without changing the force at all. Engineers and designers use this in both directions:

Why snowshoes work?

A walker sinks into deep snow in ordinary boots, but not when wearing snowshoes. What has changed?

• Nothing about their weight: the same force is now spread over a much larger area, so the pressure on the snow is far lower and the snow can support it
• The snowshoes make the walker lighter, so there is less force on the snow
• The snowshoes grip the snow, holding the walker up by friction
• The snowshoes compress the snow beneath them, making it harder

Find the force

A fluid exerts a pressure of 50 Pa on a surface of area 2 m². What force acts on that surface, in newtons (N)?

Deeper means more

(Higher tier) The deeper you go into a fluid, the more fluid there is above you pushing down, so pressure increases with depth: p = h ρ g. Notice what the equation does not contain: the shape of the container, and how much fluid there is sideways. Only the depth, the density and gravity matter, which is why a narrow pipe of water 3 m tall gives exactly the same pressure at its base as a swimming pool 3 m deep. And in a fluid at rest, the pressure at a given depth acts equally in all directions, not just downwards. That fact does more work than it looks, as the next question shows.

Pressure at depth

A diver is 3 m below the surface of fresh water, of density 1000 kg/m³, where g = 10 N/kg. What is the pressure due to the water, in pascals (Pa)?

Crushed from where?

A sealed empty can is lowered deep into the sea. It is crushed inwards evenly from every side, rather than being flattened from the top down. Why?

• In a fluid at rest the pressure at a given depth acts equally in all directions, so the water pushes on the sides and even upwards on the base just as hard as it pushes down on the top
• The weight of the water above pushes down, and the can buckles sideways as a result
• The vacuum inside the can pulls the walls inwards equally
• The cold water at depth makes the metal contract evenly

The air is pressing too

Atmospheric pressure is caused by air molecules colliding with a surface, and at sea level it is about 100,000 Pa: roughly the weight of a small car spread over every square metre of you. You do not notice, because it acts equally on all sides and from within. Higher up there is less air above you, so the air is less dense, there are fewer collisions, and atmospheric pressure falls. Which explains a familiar thing. Carry a sealed crisp packet up a mountain and it puffs up like a balloon. Nothing has been added to it. The air inside is still at the pressure it was sealed at, the air outside is now pushing in less hard, and the packet expands until the two balance again.

Four fluid puzzles

Each of these follows from p = F ÷ A, p = h ρ g, or pressure acting in all directions.

• A diver doubles their depth. What happens to the pressure from the water above them?
• Two divers are both at exactly 10 m, one in a fresh-water lake and one in the sea. Sea water is denser. Who is under greater pressure?
• The crisp packet on the mountain has puffed up. What would happen if the walker carried it back down again?
• However hard you suck, you cannot drink water through a straw more than about ten metres long. Why not?

Which are true?

Select ALL THREE statements that are TRUE.

• The same force produces a greater pressure when it acts on a smaller area, which is why a sharp blade cuts and a blunt one does not
• At a given depth in a fluid at rest, the pressure is the same in every direction
• You do not suck a drink up a straw: reducing the pressure in your mouth allows atmospheric pressure to push it up
• Pressure in a fluid acts only downwards, because it is caused by gravity
• Atmospheric pressure increases as you climb a mountain
• Doubling your depth in water quadruples the pressure

Fluids summary

Pressure is force per unit _____, so the same force gives a greater pressure on a smaller area, which is why a sharp knife cuts. In a fluid at rest, pressure acts equally in all _____, and it increases with depth according to p = h ρ g, where ρ is the _____. Atmospheric pressure comes from air molecules colliding with a surface, and it _____ as altitude increases because the air becomes less dense.