Introduction to Hydrostatics: Fluids and Liquids

• Hydrostatics focuses on water at rest and is crucial for understanding buoyancy, fluid pressure, and hydraulic machine design
• It finds applications in engineering, medicine, and technology

Fluids

• Fluids adapt to the shape of their containers; this property is called fluidity
• Both liquids and gases are fluids
• Gases differ from liquids in expansion, compression and resistance to sliding:
• Liquids occupy a certain level of their container and are hardly compressed
• Gases expand to fill the entire container and are easily compressed

Properties of Liquids

• Cohesion is the force that holds molecules of the same substance together
• This is demonstrated when two nearby drops of water merge into one
• Adherence is the attraction between molecules of different substances in contact
• Most liquids adhere to solid surfaces like glass, while mercury doesn't
• Viscosity is a liquid's resistance to flow; more viscous liquids take longer to flow
• Liquids are incompressible, meaning their volume doesn't decrease when force is applied
• Liquids have a defined volume but take the shape of their container
• Surface tension causes the free surface of a liquid to act like a thin elastic membrane, due to attraction between liquid molecules
• Capillarity is seen when a liquid contacts a solid wall in a thin tube, causing the liquid to rise within the tube (like water in a capillary tube)

Density and Specific Weight

• Density (ρ) is a material property representing mass per unit volume
• Determined by dividing the mass of a substance by the volume it occupies
• ρ = m/V, measured in kg/m³
• Specific weight is another characteristic property, determined by dividing weight by volume
• It's an intensive property used to identify and differentiate substances
• P = W/V, measured in N/m³
• Viscosity is sometimes confused with density in everyday language
• Mass refers to the amount of substance a body possesses, while the weight measures the force of attraction
• Density remains constant anywhere in the universe, despite changes in gravitational force

Pressure

• Pressure is the force applied per unit area, essentially "how much something presses"
• P = F/A, measured in Pascals (Pa) or N/m²
• Pressure is directly proportional to the magnitude of the applied force and indirectly proportional to the area over which it acts
• Hydrostatic pressure in liquids increases with the height of the liquid column
• Liquids apply pressure not only on the walls and bottom of a container, but also at every point within
• Hydrostatic pressure exerted by a liquid depends on the liquid's density, the gravity, and the depth
• Ph = ρ * g * h

Atmospheric Pressure

• Air has weight, and the weight of the air above exerts atmospheric pressure
• Atmospheric pressure lowers as altitude increases, because the amount of air above is less
• Lower pressure correlates with a lower boiling temperature
• Warming air causes it to rise, lowering atmospheric pressure
• Cooling air causes it to contract, raising atmospheric pressure
• Wind flows from areas of high pressure to areas of low pressure
• Storms (low-pressure zones) have air that rises and cools, causing condensation, rain, and unstable weather and rotate counterclockwise in the Northern hemisphere because of rising air
• High-pressure zones called anticyclones have descending air, causing heating, evaporation of clouds, and stable weather, also rotating clockwise in the Northern hemisphere

General Theorem of Hydrostatics

• The pressure difference between two points in a liquid depends only on the depth difference

Pressure at a Depth

• Pressure increases with depth
• The formula that relates everything is P= dgh (pressure = density * gravity * depth)
• Pressure at a depth is also exerted in every direction like on the sides of submarines

Pascal's Law

• Pascal's principle states that if pressure is applied at one point in a mass of liquid, this pressure is transmitted to the entire mass of the liquid.

Hydraulic press

• The hydraulic press is a machine that allows forces to be amplified, and is present in the operation of elevators, brakes and other mechanisms
• If a force is exerted on the smaller cylinder the pressure will be transmitted via the liquid which generates an equal force in the larger diameter cylinder

Tubes in U

• Tubes in U are used to hold at least two different types of liquids
• The two liquids must be different enough that they don't mix
• To find the relationship between the heights used specific weights
• The formula indicates that the equality of pressures is posed in the place where the separation between both liquids is.

Buoyancy

• Archimedes’ principle: Everything experiences an upward thrust
• Whether a body floats of sinks depends on the weight of the body, the volume of the fluid displaced and the material’s density
• The formula: E = m₁ • g = V₁・d₁・g or Pa = P - E = mg – E