Pressure in Fluids

IGCSE Edexcel Physics
5.5–5.7 Pressure from force, and pressure with depth in fluids
Key Concepts: Pressure = force ÷ area: $p = F/A$ (pascals, Pa). Pressure in a fluid increases with depth: $p = h\rho g$. Pressure in a fluid acts equally in all directions at the same depth.

Section A — Pressure Concepts

1. Define pressure and write its equation, defining all symbols and units. [3]
2. Explain why a sharp knife cuts more easily than a blunt one, even when the same force is applied. [2]
3. Explain why pressure in a liquid acts equally in all directions at a given depth. [2]

Section B — p = F/A Calculations

4. A force of 300 N acts on an area of $0.6\,\text{m}^2$. Calculate the pressure. [2]
5. A 500 N block rests on a surface. The pressure exerted is 2500 Pa. Calculate the area in contact with the surface. [2]
6. A rectangular book of dimensions 0.3 m × 0.2 m weighs 12 N. Calculate the pressure when it lies flat. [3]

Section C — Pressure with Depth: p = hρg

7. Write the equation for pressure due to a column of fluid. Define all symbols. [2]
8. Calculate the pressure at 5 m depth in water. ($\rho_{water} = 1000\,\text{kg/m}^3$, $g = 9.8\,\text{N/kg}$) [2]
9. Calculate the pressure at 20 m depth in seawater. ($\rho = 1025\,\text{kg/m}^3$, $g = 9.8\,\text{N/kg}$) [2]
10. Explain why a dam wall is built thicker at the bottom than at the top. [2]

Total marks: 22

Mark Scheme

1. Pressure is force per unit area [1]; $p = F/A$ [1]; $p$ in pascals (Pa), $F$ in newtons (N), $A$ in m² [1] [3]
2. A sharp blade has a smaller contact area [1]; for the same force, smaller area gives greater pressure, which cuts more effectively [1] [2]
3. Fluid particles move randomly in all directions [1]; they collide with surfaces from all angles, exerting the same pressure in all directions at the same depth [1] [2]
4. $p = F/A = 300/0.6 = 500\,\text{Pa}$ [2]
5. $A = F/p = 500/2500 = 0.2\,\text{m}^2$ [2]
6. $A = 0.3 \times 0.2 = 0.06\,\text{m}^2$ [1]; $p = F/A = 12/0.06 = 200\,\text{Pa}$ [2] [3]
7. $p = h\rho g$ [1]; $h$ = depth (m), $\rho$ = density of fluid (kg/m³), $g$ = gravitational field strength (N/kg) [1] [2]
8. $p = h\rho g = 5 \times 1000 \times 9.8 = 49\,000\,\text{Pa}$ (49 kPa) [2]
9. $p = 20 \times 1025 \times 9.8 = 200\,900\,\text{Pa}$ (≈ 201 kPa) [2]
10. Pressure increases with depth ($p = h\rho g$) [1]; so the water exerts greater pressure lower down, requiring a thicker wall to withstand it [1] [2]