Fluids and Their Properties: Density, Pressure, Specific Gravity, and Buoyancy - Prof. A. | Study notes Physics

Chapter 10 – Fluids

Vocabulary

Phases – the three common states of matter, solid, liquid, and gas.

Solid – maintains a fixed shape and a fixed size; even if a large force is applied to a solid,

it does not readily change its shape or volume.

Liquid – does not maintain a fixed shape, it takes on the shape of its container, but is not

readily compressible, and its volume can be changed significantly only by a very

large force.

Gas – has neither a fixed shape nor a fixed volume – it will expand to fill its container.

Fluids – liquids and gases because they do not maintain a fixed shape, they both have the

ability to flow.

Plasma – a fourth state of matter. It occurs only at very high temperatures and consists

of ionized atoms (electrons separated from the nuclei).

Density (ρ) ρ) ) – the mass of an object per unit volume. ρ = m/V.

Specific Gravity (ρ) SG) – the ratio of the density of a substance to the density of water at

4.0ºC. It has no dimensions or units.

Pressure – force per unit area. F is understood to be acting perpendicular to the surface

area A. pressure = P = F/A. The SI unit of pressure is N/m².

Pascal – the official name of the unit for pressure, N/m², in honor of Blaise Pascal.

Pressure Head – the height h is sometimes called the pressure head.

Atmosphere – a unit of pressure. 1 atm = 1.013  10^5 N/m² = 101.3 kPa.

Bar – another unit of pressure. 1 bar = 1.00  10^5 N/m² = 100 kPa.

Gauge Pressure – pressure over and above atmospheric pressure. PG = P – PA.

Pascal’s Principle – pressure applied to a confined fluid increases the pressure

throughout by the same amount. Fout/Fin = Aout/Ain.

Mechanical Advantage - Fout/Fin. It is equal to the ratio of the areas.

Open-tube Manometer – a device invented to measure pressure. It is a U-shaped tube

partially filled with a liquid, usually mercury or water. The pressure P being

measured is related to the difference in height h of the two levels of the liquid by the

relation P = P0 + ρgh where P0 is atmospheric pressure and ρ is the density of the

liquid.

Torr – the unit mm-Hg is also called the torr in honor of Evangelist Torricelli who

invented the barometer.

Barometer – a modified kind of mercury manometer with one end closed. The glass

tube is completely filled with mercury and then inverted into the bowl of mercury.

The level of the mercury will drop, leaving a vacuum at the top of the tube.

Buoyant Force (ρ) FB) – the net force due to the fluid pressure, which is the buoyant force.

This force acts upward and has the magnitude FB = F2 – F1 = ρFgV.

Archimedes’ Principle – the buoyant force on a body immersed in a fluid is equal to the

weight of the fluid displaced by that object.

Fluid Dynamics – the study of fluids in motion.

Hydrodynamics – the study of water in motion.

Streamline (ρ) Laminar Flow) – when the flow is smooth such that neighboring layers of

the fluid slide by each other smoothly.

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Chapter 10 – Fluids

Vocabulary

Phases – the three common states of matter, solid, liquid, and gas. Solid – maintains a fixed shape and a fixed size; even if a large force is applied to a solid, it does not readily change its shape or volume. Liquid – does not maintain a fixed shape, it takes on the shape of its container, but is not readily compressible, and its volume can be changed significantly only by a very large force. Gas – has neither a fixed shape nor a fixed volume – it will expand to fill its container. Fluids – liquids and gases because they do not maintain a fixed shape, they both have the ability to flow. Plasma – a fourth state of matter. It occurs only at very high temperatures and consists of ionized atoms (electrons separated from the nuclei). Density (ρ) ρ) ) – the mass of an object per unit volume. ρ = m / V. Specific Gravity (ρ) SG) – the ratio of the density of a substance to the density of water at 4.0ºC. It has no dimensions or units. Pressure – force per unit area. F is understood to be acting perpendicular to the surface area A. pressure = P = F / A. The SI unit of pressure is N/m². Pascal – the official name of the unit for pressure, N/m², in honor of Blaise Pascal. Pressure Head – the height h is sometimes called the pressure head. Atmosphere – a unit of pressure. 1 atm = 1.013  10^5 N/m² = 101.3 kPa. Bar – another unit of pressure. 1 bar = 1.00  10^5 N/m² = 100 kPa. Gauge Pressure – pressure over and above atmospheric pressure. P G = P – P A. Pascal’s Principle – pressure applied to a confined fluid increases the pressure throughout by the same amount. F out/ F in = A out/ A in. Mechanical Advantage - F out/ F in. It is equal to the ratio of the areas. Open-tube Manometer – a device invented to measure pressure. It is a U-shaped tube partially filled with a liquid, usually mercury or water. The pressure P being measured is related to the difference in height h of the two levels of the liquid by the relation P = P 0 + ρ gh where P 0 is atmospheric pressure and ρ is the density of the liquid. Torr – the unit mm-Hg is also called the torr in honor of Evangelist Torricelli who invented the barometer. Barometer – a modified kind of mercury manometer with one end closed. The glass tube is completely filled with mercury and then inverted into the bowl of mercury. The level of the mercury will drop, leaving a vacuum at the top of the tube. Buoyant Force (ρ) F B ) – the net force due to the fluid pressure, which is the buoyant force. This force acts upward and has the magnitude F B = F 2 – F 1 = ρF gV. Archimedes’ Principle – the buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by that object. Fluid Dynamics – the study of fluids in motion. Hydrodynamics – the study of water in motion. Streamline (ρ) Laminar Flow) – when the flow is smooth such that neighboring layers of the fluid slide by each other smoothly.

Turbulent Flow – characterized by erratic, small, whirlpool-like circles called eddy currents or eddies. Viscosity – internal friction in a liquid. Mass Flow Rate – the mass Δ m of fluid that passes a given point per unit time Δ t : mass flow rate = Δ m /Δ t. Equation of Continuity – ρ 1 A 1 v 1 = ρ 2 A 2 v 2 Bernoulli’s Principle – where the velocity of a fluid is high, the pressure is low, and where the velocity is low, the pressure is high. Bernoulli’s Equation – P 1 + ½ρρ v 1 ² + ρ gy 1 = P 2 + ½ρρ v 2 ² + ρ gy 2 or P + ½ρρ v ² + ρ gy = constant Torricelli’s Theorem – the liquid leaves the spigot with the same speed that a freely falling object would attain falling the same height. v 1 = √2 g ( y 2 – y 1 ). Dynamic Lift – when the air pressure above the wing is less than that below, there is a net upward force called the dynamic lift. Venturi Tube – a pipe with a narrow constriction. Venturi Meter – used to measure the flow speed of fluids.

Notes

10-1 Density and Specific Gravity Objects made of a given pure substance, such as pure gold, can have any size or mass, but the density will be the same for each. The SI unit for density is kg/m³. Temperature and pressure affect the density of substances (although the effect is slight for liquids and solids). 10-2 Pressure in Fluids A fluid exerts a pressure in all directions. At any point in a fluid at rest, the pressure is the same in all directions. If the fluid is not flowing, then the pressures must be equal. The force due to fluid pressure always acts perpendicular to any surface it is in contact with. The pressure due to the liquid at a depth h is due to the weight of the column of liquid above it. P = ρ gh. Pressure at equal depths within a uniform liquid is the same. Gasses are very compressible, and density can vary significantly with depth. Δ P = ρgg Δ h 10-3 Atmospheric Pressure and Gauge Pressure The density of air varies greatly with altitude, but there is no distinct top surface to the atmosphere from which h can be measured. Living cells maintain an internal pressure that closely equals the external pressure. 10-4 Pascal’s Principle External pressure acting on a fluid is transmitted throughout that fluid. Pascal’s principle states that pressure applied to a confined fluid increases the pressure throughout by the same amount. 10-5 Measurement of Pressure; Gauges and the Barometer P = P 0 + ρggh where P 0 is atmospheric pressure and ρg is the density of the liquid.

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Chapter 10 – Fluids

Vocabulary

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