Pressure

Scenarios

• Submarines and marine exploring vehicles must be designed to withstand very great pressures. This is because the ocean provides upthrust, which can push objects back to the surface. The deeper an object goes, the greater the pressure acts on it.
  • Submarines have curved surfaces, which are much stronger under pressure. They are also made of thick metal.
• Any object under water is pressed down on by the weight of water above it. The deeper you go, the greater the amount of water pressing down on you.
  • The pressure caused by water is much greater than that caused by air because water is much denser than air.
    • In order for dams to withstand the water’s pressure, the base would need to be the thickest because pressure is the greatest at the bottom of the water.
• The atmosphere exerts pressure on us, though we are not very aware of it. The Earth’s gravity pulls it downwards, so that the atmosphere presses downwards on our heads.
  • Mountaineers climbing to the top of Mount Everest rise through $\frac{2}{3}$ of the atmosphere, so the pressure is only about $\frac{1}{3}$ of the pressure down at sea level. There is much less air above them, pressing down.
• In a fluid such as water or air, pressure does not simply act downwards. It acts equally in all directions.
  • This is due to the molecules of the fluid moving around in all directions. This causes pressure on every surface they collide with.

Calculating pressure

• Pressure is the force acting per unit area at right angles to a surface.
• Pascal is the SI unit of pressure, equivalent to one newton per square meter.
  • $1\text{Pa}=1{\text{N/m}}^2=1\text{Pa}$

Formula

$$P=\frac{F}{A}$$

• Where:
  • $P$ is the pressure
  • $F$ is the force
  • $A$ is the area.

Pressure, depth and density

• Remember that the deeper an object is in water, the greater the pressure.
• Pressure $p$ is proportional to depth $h$ ($h$ is used for height).
  • Twice the depth means twice the pressure.
• Pressure also depends on the density $\rho$ (rho) of the material.
  • For example, if an object is submerged in mercury, which is more than ten times as dense as water, the pressure will be more than ten times as great.

Formula

$$\Delta p=\rho g\Delta h$$

• Where:
  • $\Delta p$ is change in pressure
  • $\rho$ is density
  • $g$ is acceleration due to gravity
  • $\Delta h$ is depth.