Pressure and Hydrostatic Pressure
This topic covers pressure, which is the concentration of a force on a surface. You will learn to calculate the pressure exerted by solid objects and the pressure at a specific depth within a fluid, which are fundamental concepts in mechanics and fluid dynamics.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- Pressure from a solid is inversely proportional to the contact area; a smaller area results in higher pressure for the same force.
- Pressure within a fluid (liquid or gas) acts equally in all directions.
- The pressure in a fluid increases linearly with depth.
- The shape of a container does not influence the hydrostatic pressure at a given depth; only the depth, fluid density, and gravity matter.
- The total pressure at a point in a fluid open to the air is the sum of the hydrostatic pressure and the atmospheric pressure acting on the surface.
Diagram
› Why does this happen?
Why does pressure increase with depth? (The 'column of water' idea)
Imagine a specific point deep inside a swimming pool. The pressure at that point is caused by the weight of all the water in a column directly above it, pushing down. The deeper you go, the taller this column of water is, and therefore the more it weighs. This greater weight pushing on the same area results in a higher pressure. The formula P = h × rho × g is derived from this idea: Pressure = Force / Area = (Weight of the fluid column) / (Area of the column base). When you work this through using Weight = mass × g and mass = density × volume, the area term cancels out, which is also why the shape of the container doesn't matter, only the vertical depth.
Why does fluid pressure act in all directions?
Unlike a solid block that just pushes downwards due to its weight, a fluid is made of countless tiny particles in constant, random motion. These particles are constantly colliding with each other and with any surface they touch (like the sides of a container or an object submerged in the fluid). Each collision exerts a tiny force. Because the particles are moving randomly in every possible direction, the forces they exert are also in every direction – up, down, and sideways. Pressure is the overall effect of these forces, so it also acts equally in all directions.
Formulae
P = F / A To find the pressure (P) exerted by a solid object on a surface, where F is the force (often the object's weight, mg) and A is the contact area.
P = h × rho × g To find the hydrostatic pressure (P) at a depth (h) within a fluid of density (rho). 'g' is the gravitational field strength.
Definitions
- Pressure
- The amount of force applied perpendicular to a surface, divided by the area over which the force is distributed.
- Pascal (Pa)
- The SI unit of pressure, defined as one newton of force per square metre (N/m2).
- Hydrostatic Pressure
- The pressure exerted by a fluid at rest due to the weight of the fluid column above the point of measurement.
Worked example
A storage tank is a cylinder with a base radius of 2 m. It rests on the ground and is filled with oil to a height of 5 m. The density of the oil is 800 kg/m3. Calculate the pressure exerted by the oil on the base of the tank. (Use g = 10 N/kg).
- 1
Identify the formula for pressure in a liquid:
P = h × rho × g - 2
The radius of the tank is extra information and not needed for this specific question.
- 3
Substitute the given values into the formula.
- 4 P = 5 m × 800 kg/m3 × 10 N/kg
- 5
Calculate the result:
P = 5 × 8000 = 40000 Pa - 6
The pressure on the base due to the oil is 40,000 Pa or 40 kPa.
Answer: 40000 Pa
Common mistakes
- ×Forgetting to sum the areas of all contact points when an object rests on multiple supports, like a table with four legs. This leads to overestimating the pressure.
- ×Making a unit conversion error with area. Always convert lengths to metres *before* calculating area. Remember 1 m2 = 10,000 cm2, not 100 cm2.
- ×Confusing total pressure with hydrostatic pressure. The formula P = h*rho*g only gives the pressure from the liquid. If asked for total pressure, you must add atmospheric pressure if the container is open.
- ×Using a diameter instead of a radius when calculating the area of a circular base. Always check the question and halve the diameter if necessary before using A = pi × r2.
No-calculator tips
- ✓When calculating P = F/A where A is a small decimal, multiply the numerator and denominator by a power of 10 to make the division easier. For example, 500 / 0.02 is the same as 50000 / 2 = 25000.
- ✓For hydrostatic pressure (h*rho*g), rearrange the multiplication to group easy numbers. For h=5, rho=800, g=10, calculate (5 × 800) × 10 or 5 × (800 × 10) = 5 × 8000.
- ✓Be confident with standard form. Many pressure calculations involve large numbers. Keeping numbers as powers of 10 simplifies multiplication and division.