Physics: Pressure and Fluid Principles

2.1 Tekanan Cecair (Liquid Pressure)

• Formula for Liquid Pressure:     The pressure in a liquid is calculated using the formula:     $P = h\rho g$

  • $P$ = Tekanan cecair (Liquid pressure), measured in Pascals ($Pa$).

  • $h$ = Kedalaman cecair (Depth of liquid), measured in meters ($m$).

  • $\rho$ = Ketumpatan (Density of liquid), measured in $kg\,m^{-3}$.

  • $g$ = Pecutan graviti (Acceleration due to gravity), taken as $9.81\,ms^{-2}$.

• Factors Affecting Liquid Pressure:

  • Depth ($h$): Pressure is directly proportional to depth ($P \propto h$). As the depth increases, the liquid pressure increases, and vice versa.

  • Density ($\rho$): Pressure is directly proportional to the density of the liquid ($P \propto \rho$). A higher density liquid exerts a higher pressure at the same depth.

  • Gravity ($g$): Under constant conditions, pressure depends on the gravitational field strength.

• Points at the Same Level:     In a continuous static liquid, points at the same horizontal level experience the same pressure.

  • $P_A = P_B$ implies $h_A\rho_Ag = h_B\rho_Bg$.

• Actual Pressure (Tekanan Sebenar):     The total pressure acting on an object submerged in a liquid is the sum of the liquid pressure and the atmospheric pressure.

  • $\text{Tekanan sebenar} = \text{tekanan cecair} + \text{tekanan atmosfera}$

• Applications of Liquid Pressure:

  • Water Tanks: Placed at high elevations. The height difference between the faucet and the tank generates high liquid pressure, ensuring water flows out quickly when the tap is opened.

  • Intravenous (IV) Therapy: The IV bag is hung higher than the patient's body. The height difference creates sufficient liquid pressure to push the fluid into the patient's bloodstream.

  • Dams: The wall at the base of a dam is significantly thicker than at the top to withstand the much higher liquid pressure at greater depths. Water outlets are positioned low so the high pressure can turn turbines effectively.

  • Siphons: Water flowing out at point C creates a low-pressure zone at point B. Atmospheric pressure then pushes water through the tube from point A.

2.2 Tekanan Atmosfera (Atmospheric Pressure)

• General Concept:     Atmospheric pressure is caused by the weight of the thick layer of air acting upon the Earth's surface.

• Measurement Instruments:

  • Mercury Barometer: A glass tube inverted into a bowl of mercury. At sea level, the height of the mercury column ($h$) is approximately $760\,mm$. Higher atmospheric pressure results in a higher $h$.

  • Fortin Barometer: A more accurate mercury barometer ($\pm 0.1\,mmHg$) but is bulky and difficult to transport. It takes time to provide a reading.

  • Aneroid Barometer: Functions based on the change in volume of a partial-vacuum metal box. It is small, portable, and provides direct readings, though with lower accuracy ($\pm 1\,mmHg$).

• Units of Pressure:

  • Pascal ($Pa$)

  • $mmHg$

  • $m\,H_2O$

  • millibar ($mbar$), where $1\,mbar = 1\,hPa$.

• Altitude and Depth Effects:

  • High Altitude: Air density and atmospheric pressure decrease as altitude increases ($P_A < P_B$ if A is higher than B). This affects mountain climbers and aircraft (requires cabin pressurization).

  • Extreme Depth (Undersea): Pressure increases significantly. For every $10\,m$ of water depth, the pressure increases by approximately $1\,atm$ ($10\,m\,H_2O = 1\,atm$). Specialized suits for divers and reinforced hulls for submarines are required to survive the pressure.

2.3 Tekanan Gas (Gas Pressure)

• Manometer Usage:     Gas pressure is typically measured using a manometer, which consists of a U-shaped tube containing liquid (usually mercury or water).

  • Before connection: Liquid levels in both arms of the U-tube are equal because both are exposed to atmospheric pressure ($P_{\text{atm}}$).

  • After connection: If gas is connected to one arm, the liquid level shifts. The gas pressure is calculated as:         $P_{\text{gas}} = P_{\text{atm}} + P_L$ (where $P_L$ is the pressure exerted by the height difference of the liquid column).

2.4 Prinsip Pascal (Pascal's Principle)

• Definition:     Pressure applied to an enclosed fluid is transmitted uniformly in all directions throughout the fluid.

• The Hydraulic System:     Hydraulic systems use liquids to transmit pressure and act as a force multiplier.

  • Formula: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$

  • $P_1 = P_2$ because the pressure is uniform.

  • Multiplication Factor: $\frac{A_2}{A_1}$. A small force ($F_1$) applied to a small input piston ($A_1$) produces a large force ($F_2$) at the large output piston ($A_2$).

• Applications:

  • Hydraulic Jack: Uses a handle to pump fluid through valves, raising a large piston to lift heavy loads.

  • Hydraulic Brakes: Pressure from the brake pedal is transmitted through brake fluid to the pistons on the wheels to slow the vehicle.

• Operational Note: Air bubbles in a hydraulic system reduce efficiency because air is compressible; part of the applied force is wasted on compressing the air rather than moving the liquid.

2.5 Prinsip Archimedes (Archimedes' Principle)

• Definition:     An object that is partially or completely submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object.

• Buoyant Force ($F_B$):     $F_B = \rho V g$

  • $\rho$ = Density of the fluid ($kg\,m^{-3}$).

  • $V$ = Volume of fluid displaced ($m^3$), which is equal to the volume of the submerged portion of the object.

  • $g$ = Acceleration due to gravity ($9.81\,ms^{-2}$).

• Weight Relationships:

  • $\text{Apparent Weight} = \text{Actual Weight} - \text{Buoyant Force}$

  • $\text{Weight of displaced fluid} = \text{Buoyant Force}$

• Conditions for Flotation:

  • Object Floats and Stationary: $W = F_B$. The forces are in equilibrium ($F_{\text{net}} = 0$).

  • Object Sinks: $W > F_B$. The net force is downward, leading to downward acceleration.

  • Object Rises: $W < F_B$. The net force is upward, leading to upward acceleration.

• Applications:

  • Hydrometer: Measures liquid density. It sinks deeper in less dense liquids to displace more mass to equal its own weight.

  • Submarines: Use ballast tanks. When tanks fill with water, the submarine's weight exceeds the buoyant force and it sinks. When water is pumped out (replaced by air), it rises.

  • Hot Air Balloons: Heating air increases its volume, displacing more surrounding air and increasing the buoyant force. When $F_B > W$, the balloon rises.

2.6 Prinsip Bernoulli (Bernoulli's Principle)

• Definition:     As the velocity of a moving fluid (liquid or gas) increases, the pressure within that fluid decreases.

• Venturi Tube:     In a tube with varying cross-sections, water flows fastest through the narrowest part. Consequently, the pressure is lowest at the narrowest point and highest at the widest point.

• Aerofoils and Lift Force:     An aerofoil shape (like an airplane wing) causes air to move faster over the curved top surface and slower across the flat bottom surface.

  • Top: High velocity, low pressure.

  • Bottom: Low velocity, high pressure.

  • Result: A pressure difference generates a net upward force called Lift.

• Applications in Daily Life:

  • Racing Cars: Rear spoilers are designed as inverted aerofoils to create downforce (high pressure on top, low pressure underneath), increasing stability and tire grip.

  • Soccer (Curve Balls): A spinning ball drags air with it. On one side, the air moves faster (lower pressure); on the other, it moves slower (higher pressure). The ball curves toward the low-pressure side.

  • Bunsen Burner: Gas flows at high velocity through a nozzle, creating a low-pressure zone. This sucks outside air into the chimney to mix with the gas for combustion.

Questions & Discussion (Latihan)

• Liquid Pressure Calculation:

  • Scenario: A fish is $20\,cm$ from the bottom of a $50\,cm$ deep aquarium. Calculate the pressure on it (Density = $1000\,kg\,m^{-3}$).

  • Calculation: Depth $h = 0.50\,m - 0.20\,m = 0.30\,m$. $P = 0.3 \times 1000 \times 9.81 = 2943\,Pa$.

• Submarine Depth:

  • Scenario: Calculate depth where pressure is $3.5 \times 10^5\,Pa$ (Sea density = $1029\,kg\,m^{-3}$).

  • Calculation: $h = \frac{P}{\rho g} = \frac{3.5 \times 10^5}{1029 \times 9.81} \approx 34.67\,m$.

• Pascal's Principle Exercise:

  • Scenario: Input force $100\,N$, input area $0.5\,m^2$, output area $2.5\,m^2$.

  • Multiplication Factor: $2.5 / 0.5 = 5$.

  • Output Force: $100\,N \times 5 = 500\,N$.

• Safety Lines (Bernoulli):

  • Question: Why must passengers stand behind the yellow line at train stations?

  • Answer: A fast-moving train creates a low-pressure zone. An individual near the track would be pushed by the higher atmospheric pressure behind them toward the train.

• Storms and Roofs:

  • Question: Why do roofs lift off during strong winds?

  • Answer: High-velocity wind over the roof creates low pressure. The higher static pressure inside the house creates a net upward force that can lift the roof.