Pressure in Fluids and Atmospheric Pressure Notes

Pressure in Fluids and Atmospheric Pressure

Change of Pressure with Depth

Pressure in fluids increases with depth due to the weight of the liquid above. The increase in pressure is linear, meaning that for every unit of depth added, the pressure rises uniformly.

Formula: $P = hpg$

Where:
$P$ = pressure
$h$ = depth
$p$ = density of the fluid
$g$ = acceleration due to gravity

For example, if you go underwater, the pressure will increase by approximately $9.81 kPa$ for every meter you descend, based on the density of water and assuming standard gravity.

Thrust and Pressure

Thrust:

A force acting normally (perpendicular) on a surface, which in practical terms could be thought of as force applied over an area.

Example: A person's weight on sand exerts thrust downward, causing a certain pressure on the sandy surface, which could lead to sinking.

Pressure:

Defined as thrust per unit area. The concept of pressure is crucial in various physical applications, including engineering and meteorology.

Formula: $P = \frac{F}{A}$

Where $F$ = Thrust, $A$ = Area

Thrust is a vector quantity (it has a direction), whereas Pressure is a scalar quantity (it does not have a direction). This distinction is essential in analyzing forces in fluid dynamics and other physics fields.

Units of Thrust and Pressure

Thrust:

• SI Unit: Newton (N); CGS Unit: dyne (1 N = 10^5 dyne)

Pressure:

• SI Unit: Pascal (Pa), defined as $1 Pa = 1 \frac{N}{m^2}$. This unit is commonly used to express pressure in scientific contexts.
• Other units: bar (1 bar = 10^5 N/m²), millibar (1 millibar = 10⁻³ bar) which is frequently used in meteorology.

Atmospheric Pressure

Defined as the pressure exerted by the weight of air above a surface, atmospheric pressure plays a crucial role in weather patterns and aviation.

Average atmospheric pressure at sea level: $1 atm = 1.013 × 10^5 Pa$

Barometric height of mercury: 76 cm or 760 mm at sea level, which can be measured using various barometer types. Understanding how this pressure varies with altitude has implications in numerous fields such as aviation and mountaineering.

Factors Affecting Pressure

Pressure depends on:

• Area the thrust is applied to. A larger area will decrease the pressure for the same amount of thrust.
• Magnitude of the thrust: More thrust = Greater pressure on the same area.

Examples:

• A brick on its longest side exerts more pressure than on its shortest side due to the distribution of weight across different surface areas, demonstrating the fundamental relationship between area and pressure.

Laws of Liquid Pressure

1. Pressure in a liquid increases with depth, which is critical for underwater construction and diving.
2. Pressure is the same at all points on a horizontal plane in a stationary liquid, an essential factor in fluid static conditions.
3. Pressure is exerted in all directions in a fluid, affecting fluid dynamics and engineering designs.
4. Pressure at the same depth is different for different liquids based on their densities, an important consideration in various scientific applications.
5. A liquid seeks its own level, a principle utilized in devices like manometers and barometers.

Consequences of Liquid Pressure

• Pressure increases with depth leading to specific engineering needs such as divers needing specialized suits.
• The size of gas bubbles changes as depth changes due to pressure changes (Boyle's Law), explaining the phenomenon of decompression sickness in divers.

Pascal's Law

States that when pressure is applied to a confined liquid, it is transmitted equally in all directions.

Demonstrated using hydraulic systems like hydraulic presses or car lifts:

$\text{Pressure on Piston A} = \text{Pressure on Piston B}$

This principle is central to the function of hydraulic systems, enabling the lifting of heavy loads with minimal manual effort.

Applications of Pascal's Law

• Hydraulic Press: Used for compressing materials (e.g., cotton bales) and is a common tool in factories and recycling centers.
• Hydraulic Jack: Lifts heavy objects using a smaller force, a must-have tool in automotive repairs.
• Hydraulic Brakes: Used in vehicles to apply brakes evenly, ensuring safety and efficiency in stopping.

Atmospheric Pressure and Its Measurement

Measured using barometers (simple, Fortin's, aneroid), it provides essential information about weather conditions.

Normal atmospheric pressure changes with altitude due to the decrease in density and air column height, affecting both meteorology and aviation.

Example of barometer: A simple barometer consists of a glass tube filled with mercury inverted in a dish of mercury; the height of mercury indicates atmospheric pressure, showcasing the relationship between air pressure and liquid height in barometers.

Variation of Atmospheric Pressure

Decreases with altitude:

• Higher altitude → lower atmospheric pressure.
• Weather changes linked to atmospheric pressure variations allow for forecasting (e.g., storms