15.2.1 Atmospheric pressure and height

Air particles create atmospheric pressure

1. Earth is surrounded by an atmosphere, which is a layer of gases held around the planet by gravity.
2. Air particles are in constant random motion and repeatedly collide with exposed surfaces.
3. Each collision changes a particle's momentum, so the particle exerts a small force on the surface.
4. The combined normal force from many collisions acting on each unit area is atmospheric pressure.
5. Atmospheric pressure acts in all directions because air particles move and collide in all directions.

Gravity creates a pressure gradient

1. Gravity pulls every air particle towards Earth, so the particles have weight.
2. Air near Earth's surface supports the weight of the air above it.
3. This weight compresses the lower layers of the atmosphere, pushing their particles closer together.
4. The lower atmosphere therefore contains more particles in each cubic metre and has a greater density.
5. A denser layer produces more particle collisions with each square metre of surface each second.
6. More frequent collisions produce a greater total force per unit area, so atmospheric pressure is greatest near Earth's surface.

Pressure decreases as height increases

1. At a greater height, there is a shorter column of atmosphere above a surface.
2. The shorter column contains less air, so the weight of air pressing on the layers below is smaller.
3. With less compression, the air particles are farther apart and the air density is lower.
4. Fewer particles are available to strike each unit area, so collisions occur less frequently.
5. The total force per unit area is therefore smaller, which means atmospheric pressure decreases with height.
6. The decrease is not uniform because air density also changes continuously with height.

The atmosphere thins gradually

1. The atmosphere has no sharp upper edge at which pressure suddenly becomes zero.
2. Air becomes progressively less dense with height because the weight and compression from overlying air progressively decrease.
3. Although gravity becomes slightly weaker with height, it still acts strongly enough over ordinary mountain and aircraft heights to keep pulling air towards Earth.

Pressure changes have visible effects

1. A sealed flexible packet taken to a high altitude can expand because the external atmospheric pressure decreases while its internal pressure initially remains higher.
2. A flexible container moved to lower altitude can be compressed because the external atmospheric pressure increases.
3. A barometer gives a lower reading at greater height because the atmosphere exerts a smaller pressure.
4. Aircraft cabins are pressurised so the pressure inside does not fall to the much lower atmospheric pressure outside at cruising height.

15.2.2 Pressure in fluids

Fluids exert pressure in every direction

1. Liquids and gases are fluids because their particles can move past one another and the substance can flow.
2. Within a fluid, moving particles and the weight of fluid above create pressure.
3. At a point in an open fluid, the total pressure includes both the fluid's pressure and the atmospheric pressure acting on its surface.

Pressure produces a normal force

1. Fluid pressure exerts a force normal to a surface, meaning perpendicular to that surface.
2. The force acts on every surface in contact with the fluid, including horizontal, vertical and curved surfaces.
3. Because the force is normal locally, its direction changes around a curved object.

Open and sealed fluids differ

1. For an open container, atmospheric pressure is transmitted through the liquid as part of the total pressure.
2. A pressure gauge may show gauge pressure, which is the amount above atmospheric pressure, rather than total pressure.

15.2.3 Pressure, force and area

Pressure depends on normal force and area

1. Pressure is calculated using $P=\frac{F}{A}$.
2. Here, $P$ is pressure in pascals, $F$ is the force normal to the surface in newtons, and $A$ is the contact area in square metres.
3. One pascal is one newton per square metre: $1Pa=1{N\; m}^{-2}$.

Force and area have opposite effects

1. At constant area, a larger normal force produces a larger pressure, so $P\propto F$.
2. At constant force, a larger contact area spreads the force and produces a smaller pressure, so $P\propto \frac{1}{A}$.
3. A sharp blade creates high pressure through a small area, while wide tyres reduce pressure on soft ground by increasing area.

Rearrange and convert areas correctly

1. Use $F=PA$ to find force and $A=\frac{F}{P}$ to find area.
2. For areas, square the length conversion: $1{cm}^2=1\times 10^{-4}{m}^2$ and $1{mm}^2=1\times 10^{-6}{m}^2$.

Comparisons must control one variable

1. When comparing designs, identify whether force or area is unchanged, then link the changed quantity to pressure.
2. Show the equation, conversion, substitution and unit because a correct numerical value without $Pa$ can lose a unit mark.

15.2.4 Pressure and depth

Fluid pressure increases with depth and density

1. A deeper point has a taller column of fluid above it, so a greater weight of fluid presses down.
2. This produces a larger pressure and therefore a larger normal force on the same area.
3. At the same depth, a denser fluid has more mass and weight in the same volume, so it produces greater pressure.
4. At the same horizontal level in one stationary connected liquid, the pressure is the same.

Jet distance provides qualitative evidence

1. Water from a lower hole leaves faster and travels farther because the pressure difference between the inside and outside is greater.
2. A fair comparison uses holes of equal size in the same container and measures their horizontal jet distances under the same conditions.

Pressure difference drives motion

1. A fluid moves from higher pressure towards lower pressure when a path is available.
2. The quantitative equation and pressure differences are developed in the next article.

15.2.5 Pressure in liquids: depth and density

A liquid column produces calculable pressure

1. The pressure due to a liquid column is $P=h\rho g$.
2. Here, $P$ is pressure in pascals, $h$ is the vertical height of liquid above the point in metres, $\rho$ is density in kilograms per cubic metre, and $g$ is gravitational field strength in newtons per kilogram.
3. The equation gives the pressure caused by the liquid column, not automatically the total pressure including the atmosphere.

The equation follows from weight per area

1. For a column with area $A$ and height $h$, its volume is $V=Ah$.
2. Its mass is $m=\rho V=\rho Ah$, so its weight is $F=mg=\rho Ahg$.
3. Using $P=F/A$ gives $P=\rho Ahg/A=h\rho g$.

Pressure differences use changes in depth

1. Between two depths in the same liquid, $\Delta P=\Delta h\rho g$.
2. Use the vertical difference in depth, even if the container is sloping or irregularly shaped.
3. At fixed density and gravitational field strength, pressure due to the liquid is directly proportional to depth.

Density changes the pressure gradient

1. On a pressure against depth graph, the gradient is $\rho g$.
2. A denser liquid gives a steeper graph because pressure rises more rapidly with depth.

15.2.6 Upthrust

A pressure difference produces upthrust

1. Fluid pressure acts normal to every surface of an immersed object.
2. Because pressure increases with depth, the upward force on the lower surface is greater than the downward force on the upper surface.
3. The resultant of the fluid-pressure forces is an upward force called upthrust.
4. Sideways pressure forces cancel for a symmetrical object in a stationary fluid.

Upthrust equals displaced-fluid weight

1. The magnitude of upthrust equals the weight of fluid displaced by the immersed part of the object.
2. For fluid density $\rho$, displaced volume $V$ and gravitational field strength $g$, this can be written as $U=\rho Vg$.
3. A fully immersed object with fixed volume displaces the same volume wherever it is in an incompressible liquid, so its upthrust is unchanged with depth.
4. A partially immersed object displaces only the volume below the surface.

Gases also provide upthrust

1. A balloon displaces air, so the surrounding air exerts upthrust equal to the weight of the displaced air.
2. Upthrust increases when more fluid is displaced or when the fluid is denser.

15.2.7 Floating and sinking

Floating depends on upthrust and weight

1. An object initially accelerates upward when upthrust is greater than weight and downward when weight is greater than upthrust.
2. A floating object at rest is in equilibrium, so upthrust equals its weight and the resultant force is zero.
3. As a floating object sinks farther into a liquid, it displaces more liquid and upthrust increases until it balances weight.

Density predicts floating and sinking

1. An object with a lower average density than the fluid can float because it can displace its own weight of fluid before becoming fully submerged.
2. An object with a greater average density than the fluid sinks because even when fully submerged, the maximum upthrust is less than its weight.
3. If the object and fluid have equal densities, a fully immersed object can remain suspended when upthrust equals weight.
4. A hollow steel ship floats because its large air-filled volume makes its overall average density less than that of water.