Properties and mechanics of fluids
A fluid is a liquid or a gas. Its parts slide over each other, so it can flow. Three things matter for machines:
- Density (ρ): how heavy it is for its size. Water is about 1000 kg per m³. Air is about 1.2 kg per m³.
- Pressure (p): the push on each square metre. p = F / A. Unit: pascal (Pa), 1 Pa = 1 N per m².
- Flow rate (Q): how much fluid passes each second. Q = A × v, where A is pipe area and v is speed. Unit: m³ per second.
A liquid is almost impossible to squeeze. A gas is easy to squeeze. This one difference decides which machine we use.
Pascal's law: a push on a fluid in a closed container goes equally in every direction. Pressure is the same everywhere inside.
Water turbines and pumps
A pump gives energy to a liquid. A common one is the centrifugal pump. A motor spins the impeller. The water in the blades is thrown outward, leaves at high speed, and is pushed up the pipe. New water comes in at the centre.
A water turbine does the opposite. Moving or falling water hits the blades and spins the wheel. The wheel turns a generator. Chemical or stored energy in the water becomes electric energy.
- Impulse turbine (for tall dams, high head): a fast jet of water hits cups on the rim.
- Reaction turbine (for low head, big flow): the whole wheel sits in the water, and the water pushes the blades as it passes.
Pump power needed: P = ρ g Q H (H is the height lifted). Turbine power out is η ρ g Q H, where η is efficiency (less than 1).
Fans and compressors
These machines handle gas (air).
- Fan: turns blades to move a lot of air with a very small rise in pressure. Used for cooling and ventilation.
- Blower: a stronger fan with a medium rise in pressure.
- Compressor: squeezes air to a much higher pressure. It may use a piston (reciprocating) or spinning blades (centrifugal or axial).
When air is squeezed, its volume gets smaller and its pressure goes up. It also gets hot, so big compressors have coolers. A cycle pump and the air-conditioner outdoor unit both have a small compressor.
Hydraulic and pneumatic equipment
Hydraulic equipment uses a liquid (oil). Pneumatic equipment uses compressed air.
Take two pistons joined by a tube of oil. A small force F₁ on a small piston of area A₁ makes pressure p = F₁ / A₁. The same pressure pushes the big piston of area A₂, so
F₂ = F₁ × (A₂ / A₁)
The big piston gives a big force, but it moves a short distance. You get no free energy: force × distance stays the same (ignoring losses).
- Hydraulic: very big forces, smooth and slow. Examples: car lift, press, excavator arm, brakes.
- Pneumatic: clean, fast, light. Air can be squeezed, so it feels springy. Examples: bus air-brakes, dentist drill, factory clamps.
Main parts: a pump or compressor (supply), valves (control the direction), pipes and an actuator (cylinder or motor that does the work).
Try it: feel pressure at home
Take two plastic syringes (no needle) of different sizes and a short tube. Fill both and the tube with water. Push the small syringe with one finger and hold the big one with your other hand. Feel how the big one pushes back harder but moves less. Check with the slider in the 3D: the force on the big piston is 10 times, but it rises one-tenth as far. Predict first, then check.
Key formulas and definitions
- Q = A × v (flow rate)
- p = F / A (pressure)
- F₂ / F₁ = A₂ / A₁ (hydraulic lift)
- P = ρ g Q H (pump power); turbine: P = η ρ g Q H
Worked examples
1. Water flows at 3 m/s in a pipe of area 0.02 m². Find the flow rate.
Q = A × v = 0.02 × 3 = 0.06 m³/s. That is 60 litres every second.
2. A force of 40 N pushes a small piston of area 2 cm². The big piston has area 50 cm². Find the force on the big piston.
Ratio of areas = 50 / 2 = 25. F₂ = 40 × 25 = 1000 N. The big piston gives 1000 N but moves 25 times less distance.
3. A pump lifts 0.01 m³ of water every second to a height of 10 m. Find the power the water receives. (ρ = 1000 kg/m³, g = 9.8 m/s²)
P = ρ g Q H = 1000 × 9.8 × 0.01 × 10 = 980 W, about 1 kW. The motor needs more than this because of losses.
4. A turbine gets 2 m³ of water each second from a height of 50 m. Its efficiency is 80%. Find the electric power. (g = 9.8)
P = η ρ g Q H = 0.8 × 1000 × 9.8 × 2 × 50 = 784 000 W = 784 kW.
Common mistakes
- Thinking a pump makes water. A pump only moves water and gives it energy.
- Using diameter instead of area in the hydraulic ratio. Area depends on the square of the diameter: double the diameter gives 4 times the area.
- Believing a hydraulic jack gives extra energy. The big piston moves less, so work in = work out (minus losses).
- Mixing up fan and compressor. A fan moves air easily; a compressor squeezes air to high pressure.