Pressure in Liquids

Overview

Pressure in Liquids is one of the most elegantly connected topics in the OCR GCSE Physics specification. At its heart, it asks a deceptively simple question: why does it hurt your ears when you dive to the bottom of a swimming pool? The answer — that the weight of the water column above you creates a force pressing inward from every direction — unlocks a chain of understanding that leads from a single formula all the way to explaining why ships float, why submarines must be built with reinforced hulls, and why deep-sea fish would be crushed at the surface.

OCR assesses this topic through both quantitative and qualitative questions. Candidates at Foundation tier are expected to recall and apply the formula P = hρg and describe qualitatively how pressure varies with depth. Higher tier candidates must additionally explain the origin of upthrust in terms of pressure differences, apply Archimedes' Principle, and evaluate floating and sinking scenarios using force comparisons. Typical exam question styles include short-answer calculations (2–4 marks), explain questions requiring mechanistic reasoning (3–4 marks), and extended response questions linking pressure to upthrust and buoyancy (5–6 marks).

This topic connects directly to forces and Newton's Laws (Topic 5), density (Topic 2.8), and atmospheric pressure (Topic 2.9 extension). Understanding pressure in liquids also underpins the study of hydraulic systems in engineering contexts. Examiners consistently report that the most common source of lost marks is unit conversion errors and vague explanations of upthrust — both of which this guide addresses in detail.

Key Concepts

Concept 1: Pressure Increases with Depth

The fundamental principle of pressure in liquids is that pressure increases as depth increases. To understand why, consider a horizontal layer of liquid at depth h below the surface. The liquid above this layer has a certain weight, and that weight must be supported by the pressure at depth h. The greater the depth, the greater the weight of liquid above, and therefore the greater the pressure.

This relationship is not merely qualitative — it is precisely linear. Doubling the depth exactly doubles the pressure (assuming constant density and gravitational field strength). This linearity is captured in the formula P = hρg, where every variable has a direct proportional effect on pressure.

A critical qualitative point that OCR tests regularly is that pressure at a given depth acts equally in all directions — upward, downward, and sideways. This is a property of fluids that distinguishes them from solids. If you place a small sensor at a depth of 2 m in a tank of water, it will register the same pressure regardless of which direction it faces. This omnidirectional nature of fluid pressure is why a submarine hull must be equally strong in all directions, and why a balloon inflated underwater is compressed uniformly rather than squashed from one side.

Real-world example: A diver at 10 m depth in seawater (density ≈ 1025 kg/m³) experiences a pressure of approximately 100,500 Pa above atmospheric — roughly equivalent to an additional atmosphere of pressure pressing in from every direction.

Concept 2: The Formula P = hρg

The pressure due to a column of liquid is calculated using:

P = hρg
where P = pressure (Pa), h = depth below the liquid surface (m), ρ = density of the liquid (kg/m³), g = gravitational field strength (N/kg, use 10 N/kg unless told otherwise)

Each variable must be in SI units before substitution. This is the single most important practical requirement for this topic. OCR frequently provides data in non-SI units specifically to test whether candidates can convert correctly.

Unit conversion table:

Note: The formula sheet provided by OCR in the examination includes P = hρg, so candidates do not need to memorise the formula itself — but they must know what each symbol represents and be able to apply it correctly.

The critical distinction for h: h is always the vertical distance from the free surface of the liquid down to the point of interest. It is not the height of any object placed in the liquid, and it is not the distance from the bottom of the container. If a 0.4 m tall block rests on the floor of a tank filled to 1.2 m depth, the pressure at the top of the block is calculated using h = 0.8 m (the depth of the top of the block below the surface), not h = 0.4 m.

Concept 3: Upthrust and Its Origin

Upthrust is the net upward force exerted on any object submerged (fully or partially) in a fluid. It arises directly from the pressure difference between the bottom and top surfaces of the object.

Consider a rectangular block fully submerged in water. The water exerts pressure on all six faces of the block. The pressures on the left and right faces are equal (both faces are at the same average depth), so their horizontal forces cancel. Similarly, the front and back faces cancel. However, the bottom face is deeper than the top face. Since pressure increases with depth, the upward pressure force on the bottom face is greater than the downward pressure force on the top face. The difference between these two forces is the upthrust — a net upward force.

This is the mechanistic explanation OCR requires. Candidates who write only "the water pushes the object up" will not receive credit for an explain question. The full chain of reasoning must be present: greater depth → greater pressure → greater force on bottom face → net upward force = upthrust.

Concept 4: Floating, Hovering, and Sinking

The behaviour of an object in a fluid depends entirely on the comparison between its weight (W, acting downward) and the upthrust (U, acting upward):

For a floating object, the upthrust always adjusts to equal the weight. As the object rises and less of it is submerged, it displaces less fluid, reducing the upthrust until equilibrium is reached. This is why a heavy ship floats: its hull displaces an enormous volume of water, generating an upthrust equal to the ship's entire weight.

An object sinks when its weight exceeds the maximum possible upthrust — that is, the upthrust when the object is fully submerged. If even at full submersion the upthrust is less than the weight, the object will sink to the bottom.

Higher tier — Archimedes' Principle: The upthrust on an object equals the weight of fluid displaced by that object. Mathematically: U = ρ_fluid × V_displaced × g. This principle allows calculation of upthrust without knowing the pressure distribution directly.

Mathematical Relationships

Formula Summary

Rearranging P = hρg

The formula can be rearranged to find any unknown:

• To find depth: h = P ÷ (ρg)
• To find density: ρ = P ÷ (hg)
• To find pressure: P = h × ρ × g (standard form)

Always state which rearrangement you are using before substituting values.

Practical Applications

Pressure in liquids has direct applications in engineering, medicine, and everyday life. Dam walls are built thicker at the base than at the top because the water pressure is greatest at the bottom — engineers must account for P = hρg when calculating the structural requirements at each depth. Hydraulic systems in car brakes and construction equipment exploit the fact that pressure is transmitted equally in all directions through a fluid (Pascal's Law). Blood pressure in the human body varies with height — blood pressure in the legs is higher than in the head because the column of blood above the measurement point is taller. Deep-sea submersibles must withstand pressures exceeding 60,000,000 Pa at the deepest ocean trenches, requiring specially engineered titanium spheres.

Listen to the 10-minute revision podcast above for a full audio walkthrough of all key concepts, exam tips, and a quick-fire recall quiz.