Grade 10 physics Mechanics and Thermal Physics – Pressure Notes

1.0 Mechanics and Thermal Physics — Subtopic 1.2: Pressure

Subject: Physics — Target age: 15 (Kenyan secondary school). These notes cover the specific learning outcomes for sub-strand 1.2 Pressure and give simple demonstrations, worked examples and suggested classroom/field activities.

Specific learning outcomes (by end of sub-strand)

1. Describe atmospheric pressure as used in Physics.
2. Demonstrate the existence of atmospheric pressure in nature.
3. Investigate factors affecting pressure in fluids.
4. Apply the equation P = ρ g h to determine pressure in liquids.
5. Demonstrate transmission of pressure in fluids (Pascal's law).
6. Appreciate applications of pressure in fluids (drinking straw, syringe, syphon, hydraulic machines, bicycle pump).
7. Explain mechanisms of water pumping.

Key concepts and definitions

• Pressure (P) — force per unit area: P = F / A. SI unit is pascal (Pa) where 1 Pa = 1 N/m².
• Atmospheric pressure — pressure exerted by the weight of air above a surface. At sea level ≈ 101 325 Pa (≈101.3 kPa ≈1 atm).
• Fluid pressure in a liquid — depends on depth and fluid density: P = ρ g h (see below).
• Gauge pressure — pressure relative to atmospheric pressure. Absolute pressure = gauge pressure + atmospheric pressure.
• Pascal’s law — pressure applied to a confined fluid is transmitted undiminished to every part of the fluid and container.

Atmospheric pressure — description and demonstrations

Atmospheric pressure is the pressure from the weight of air. It acts on all surfaces and may be demonstrated by simple experiments:

1. Inverted glass and card: Put a little water in a glass, place a card on top and invert the glass while holding the card. Remove your hand — the card stays because atmospheric pressure on the card is greater than the weight of the water + card.
2. Crushed can (simple): Heat a little water in an empty aluminium can until steam forms, quickly invert the can into cold water. Steam condenses, internal pressure drops, atmospheric pressure crushes the can. (Teacher demonstration; follow safety rules.)
3. Barometer (explanation): A mercury barometer shows atmospheric pressure by supporting a column of mercury about 760 mm at sea level. In class, a simple water manometer can be used to show pressure changes.

Pressure in fluids — factors and the formula P = ρ g h

Pressure at depth h in a liquid of density ρ (rho) under acceleration due to gravity g is:

P = ρ g h

- P is the pressure due to the liquid at depth h (Pa).
- ρ is the density of the liquid (kg/m³). For fresh water ρ ≈ 1000 kg/m³.
- g ≈ 9.81 m/s² (take 10 m/s² in rough classroom calculations if advised).
- h is the vertical depth (m) below the free surface.

Notes on the formula

• Pressure increases with depth and with density; it does not depend on the shape of the container.
• The total (absolute) pressure at depth is atmospheric pressure + ρ g h.
• Use gauge pressure (ρ g h) when measuring extra pressure due to the fluid only.

Worked examples

Example 1 — Pressure at 5 m depth in water

Use ρ = 1000 kg/m³, g = 9.81 m/s², h = 5 m.

P = ρ g h = 1000 × 9.81 × 5 = 49 050 Pa ≈ 4.905 × 10^4 Pa (≈ 49.05 kPa).

Absolute pressure = atmospheric + 49.05 kPa ≈ 101.3 kPa + 49.05 kPa ≈ 150.35 kPa (at sea level).

Example 2 — Pressure difference between salt and fresh water

Salt water has slightly higher density (≈1025 kg/m³). For the same depth, salt water gives a slightly higher pressure because ρ is larger.

Transmission of pressure — Pascal’s law and hydraulic machines

Pascal’s law: A change in pressure applied to a confined fluid is transmitted undiminished to every part of the fluid and the walls of its container. This is the principle behind hydraulic jacks and brakes.

For two pistons connected by fluid: P1 = P2 → F1/A1 = F2/A2. If A2 > A1, a small force F1 on piston 1 produces a larger force F2 on piston 2.

Applications of pressure in fluids (simple explanations)

• Drinking straw: Sucking lowers the pressure inside the straw, atmospheric pressure on the surface of the drink pushes liquid up the straw.
• Syringe: Pulling the plunger reduces pressure inside; fluid rises. Pushing transmits pressure to eject fluid.
• Siphon: Liquid flows from a higher container to a lower one over a hump because the pressure at the free surface and gravity create a continuous flow once started.
• Hydraulic machines: Use Pascal’s law to multiply force (hydraulic lifts, brakes).
• Bicycle pump: Compressing air increases pressure, forcing air into the tyre; pressure gauge shows gauge pressure above atmosphere.

Mechanisms of water pumping (overview)

Common pumps used in Kenya for domestic and small-scale water supply:

• Hand (reciprocating) pumps: A piston and one-way valves lift water (suction + delivery strokes). Suitable for shallow boreholes and wells.
• Suction/force pumps: Suction lifts water to a limited height (~7–10 m maximum theoretical suction at sea level); force pumps push water to higher levels using pressurised delivery stroke.
• Hydraulic ram: Uses water hammer (pressure surge) to pump a portion of flowing water uphill without external power.
• Centrifugal pumps: Use a rotating impeller to give water kinetic energy which converts to pressure; common in borehole and motorised pumps.
• Deep-well submersible pumps: Electric pumps placed down the borehole push water upward; avoid suction limit issues.

Investigations and suggested learning experiences (practical, class & field)

Each activity includes materials, steps and points for observation/explanation. Use local, low-cost materials where possible.

1. Demonstrate atmospheric pressure — inverted glass/card
   • Materials: glass, water, stiff card, sink or bucket.
   • Steps: Fill glass a little, place card, invert, remove hand and observe. Explain forces and atmospheric pressure pushing the card up.
   • Safety: Do over sink. Discuss limitations and why it works.
2. Crushed can demo (teacher-led)
   • Materials: empty aluminium can, small flame or hot plate, tongs, cold water container.
   • Steps: Heat a little water in can until steam appears; quickly invert into cold water. Observe implosion. Explain condensation reduces internal pressure so atmosphere crushes can.
   • Safety: Teacher demonstration; wear eye protection and gloves.
3. Investigate P = ρ g h (class experiment)
   • Materials: a tall clear plastic tube or cylinder with scale, water, salt (optional), pressure sensor or simple manometer (U-tube with coloured water).
   • Steps: Measure pressure (manometer height) at different depths h. Plot P vs h and verify linear relation; repeat with salt solution to show density effect.
   • Observation: Slope gives ρ g; students can calculate density from slope and compare to known value.
4. Pascal’s law and hydraulic lift (model)
   • Materials: 2 syringes of different size connected by tubing and filled with water (no air), wooden board as support.
   • Steps: Push the small syringe and observe the large syringe moving. Measure forces/displacements and show F1/A1 = F2/A2.
   • Link to real life: hydraulic car jacks, brakes.
5. Siphon demonstration
   • Materials: tube, two containers with different heights, water.
   • Steps: Fill tube with water, place one end in the higher container and the other end lower; observe flow. Explain role of atmospheric pressure and gravity.
6. Bicycle pump and tyre pressure
   • Materials: bicycle pump with gauge, tyre or small inflatable.
   • Steps: Show how pushing increases pressure; read gauge (gauge pressure). Discuss safe tyre pressures for Kenyan road types.

Assessment ideas

• Short written questions: define atmospheric pressure; explain why pressure increases with depth.
• Practical test: students measure pressure at several depths using a manometer and calculate ρ from the slope.
• Design task: sketch and explain a simple hydraulic lift for lifting a 200 N object using available syringe sizes.
• Field question: Explain why house water taps in low-lying areas of Nairobi may have higher pressure than taps at higher altitudes (link to elevation and supply systems).

Summary — key formulas and numbers

• P = F / A (pressure from force on area). Unit: Pa (N/m²).
• P (liquid at depth) = ρ g h (g ≈ 9.81 m/s²; water ρ ≈ 1000 kg/m³).
• Total (absolute) pressure at depth = atmospheric pressure + ρ g h.
• Pascal’s law: pressure applied to confined fluid is transmitted equally; F1/A1 = F2/A2 in connected pistons.
• Atmospheric pressure at sea level ≈ 101 325 Pa (≈ 101.3 kPa ≈ 1 atm). At higher altitude (e.g., Nairobi ≈ 1 795 m) atmospheric pressure is lower.

Practical tips for Kenyan classrooms

• Use local materials (plastic bottles, syringes from clinics with permission, tubing, jerrycans) to build cheap apparatus.
• Discuss real Kenyan applications: borehole hand pumps, rooftop water tanks (pressure from head), bicycle pumps for boda boda tyres, hydraulic lifts in vehicle repair shops.
• Encourage students to observe pressure effects in daily life: why taps at house bottoms run faster than those on roofs, why deep wells require submersible pumps.

If you want, I can generate printable worksheets, step-by-step experiment instructions with materials list, or a short quiz for learners (with answers).