8.1 - Pressure in Fluids

Concept of Pressure in Fluids in an Enclosed System

• A fluid is a liquid or gas.
• An enclosed system is a physical system where matter cannot enter or leave the system.
• Water from the bottommost hole of a water-filled bottle shoots out the furthest because water pressure is greater at a greater depth.
• When the closed plastic bottle is compressed, water from every hole shoots an equal additional distance farther.
• The additional pressure is transmitted uniformly throughout the water and in all directions.

Pascal’s principle: The transmission of pressure exerted on a fluid (liquid or gas) in an enclosed system is uniform throughout the fluid and in all directions.

Activity 8.1: Pascal’s Equipment

Aim: To explain Pascal’s principle using Pascal’s equipment.

Apparatus: Round-bottom flask with fine pores and piston, and large beaker

1. Fill the beaker with water.
2. Immerse the flask and pull the piston upwards until water fills the flask.
3. Remove the flask from the beaker.
4. Push the piston into the flask.
5. Observe and sketch the direction of water shooting from the fine pores.

Observation: Water shoots out from all the fine pores in all directions.

Explanation: Pressure exerted by the piston is transmitted uniformly throughout the water and in all directions.

Conclusion: The observation demonstrates Pascal’s principle.

Operating Principle of a Hydraulic System

• A hydraulic system transmits pressure in all directions based on Pascal’s principle.
• It produces a large output force from a small input force, enabling heavy work such as lifting a heavy load.
• It consists of two cylindrical pistons with different surface areas connected by a fluid.
• Water or oil is commonly used because it:
  • has no fixed shape; and
  • cannot be compressed.
• Pressure exerted by the small piston equals pressure produced at the large piston.

Force Multiplication

• The same pressure acts on both pistons.
• A large piston with a greater surface area produces a greater output force.

Example: Input force $=10\text{N}$, area of small piston $=2{\text{cm}}^2$, area of large piston $=100{\text{cm}}^2$.

Thus, an input force of $10\text{N}$ produces an output force of $500\text{N}$.

Applications of Pascal’s Principle in Daily Life

Hydraulic systems perform heavy work using a small force. The three applications are the hydraulic jack, hydraulic brake and dental chair.

Hydraulic Jack System

• Function: Lifts heavy loads such as cars in workshops.
• Main parts: lever, pivot, small piston, large piston, liquid reservoir, air hole, valve A, valve B and release valve.
• Repeated downward and upward movements of the lever raise the loaded large piston when the release valve is closed.
• Opening the release valve lowers the loaded large piston to its original position.

Raising the loaded large piston

1. Keep the release valve closed.
2. Move the lever downwards: valve A closes and valve B opens.
3. The small piston exerts pressure on the liquid.
4. The liquid transmits the pressure to the loaded large piston and pushes it upwards.
5. Move the lever downwards and upwards repeatedly until the load reaches the desired height.

Maintaining the height of the large piston

1. Move the lever upwards while the release valve remains closed.
2. Valve A opens and valve B closes.
3. Liquid from the reservoir flows below the small piston through valve A.
4. Constant liquid pressure acts on the large piston, so its position is maintained.

Lowering the large piston

1. Open the release valve: valve A opens and valve B closes.
2. The loaded large piston exerts pressure on the liquid beneath it.
3. The liquid flows back into the liquid reservoir through the release valve.
4. The large piston returns to its original position.

Hydraulic Brake System

• Function: Slows down or stops a moving wheeled vehicle such as a car.
• The front wheels use disc brakes; the back wheels use drum brakes.

1. The pressed brake pedal pushes the piston into the master cylinder and exerts pressure on the brake oil.
2. The brake oil transmits this pressure uniformly through metal pipes to the brake cylinders at the front and back wheels.
3. At the disc brake, the brake-cylinder piston presses the brake pad against the steel plate.
4. At the drum brake, the brake-cylinder piston presses the brake shoe and brake lining against the brake drum.
5. Friction slows down or stops the rotation of the wheels.

Brake	Braking surfaces that produce friction
Disc brake	Brake pad and steel plate at the front wheel
Drum brake	Brake lining and brake drum at the back wheel

Dental Chair

• Its operation is related to the hydraulic system and Pascal’s principle.

Relationship Between Fluid Velocity and Pressure

• In a fluid that is not flowing, the pressure at $P_1$, $P_2$ and $P_3$ is the same.
• A Venturi tube is a non-uniform tube with a narrower centre.
• When fluid flows through the tube:
  • velocity at the narrow part, $P_2$, is higher than at the wider parts, $P_1$ and $P_3$;
  • pressure at $P_2$ is lower than at $P_1$ and $P_3$.
• The narrower the part of the Venturi tube, the higher the fluid velocity and the lower the fluid pressure. This is the Venturi effect.

Bernoulli’s principle: A fluid moving at a higher velocity produces a lower pressure in that region.

Activity 8.2: Venturi Tube

Aim: To explain Bernoulli’s principle using a Venturi tube.

Material: Tap water
Apparatus: Venturi tube with vertical tubes $X$, $Y$ and $Z$, rubber tube and clip

1. Connect the Venturi tube to a tap and direct its outlet to a sink.
2. Close the clip, turn on the tap and allow tubes $X$, $Y$ and $Z$ to fill with water.
3. Compare and sketch the water levels in $X$, $Y$ and $Z$.
4. Open the clip so water flows continuously through the glass tube into the sink.
5. Compare and sketch the water levels again.

Condition	Observation and inference
Clip closed	Water does not flow; velocity is zero and the water levels in $X$, $Y$ and $Z$ are equal, showing equal pressure.
Clip open	Water flows fastest through the narrow part at $Y$; the water level at $Y$ is lowest, showing the lowest pressure.

• The pressure change at the narrower part is the Venturi effect.
• The result when water flows demonstrates Bernoulli’s principle.

Applications of Bernoulli’s Principle in Daily Life

Aerofoil-shaped Wings of an Aeroplane

• Air flows at high velocity and low pressure above the wing.
• Air flows at lower velocity and higher pressure below the wing.
• The pressure difference produces an upward lift.
• Lift is produced by the aerofoil shape and angle of attack of the wing.

Helicopter and Drone

• Airflow above the blades has high velocity and low pressure.
• Air below the blades has lower velocity and higher pressure.
• The pressure difference produces lift.

Bunsen Burner

• Gas flows at high velocity and low pressure.
• Surrounding air at higher pressure is drawn into the burner.
• The air mixes with the gas and the mixture flows upwards.

Safety Lines Near Railway Tracks

• A moving train produces high-velocity, low-pressure airflow in the space between the train and a nearby person.
• Air on the other side of the person has lower velocity and higher pressure.
• The pressure difference produces a force towards the moving train.
• Stand behind the safety line to avoid being pushed towards the train.

Activity 8.3: Studying Applications in Daily Life

1. Gather information on applications of Bernoulli’s principle in sports such as sailing and windsurfing.
2. Discuss the information gathered.
3. Present the findings in a report.

Activity 8.4: Designing a Tool Using the Principle of Pressure in Fluids

Aim: To design a tool using the principle of pressure in fluids.

1. Design a tool such as a crane that uses a hydraulic system to lift a heavy load.
2. Present the design and explain how its hydraulic system functions.

Operating sequence: