Chapter 8

Fluid Mechanics – how fluids flow and how forces and energy are transmitted through fluids

Fluid – able to take the shape of their containers – gases and liquids

Pressure – a ratio of force to area – how much pressure (force) is this area under? Formula: Pressure = force/area P = F/A Pressure is measured in N/m2 (Newtons per meter squared) The smaller your area, the greater your pressure will be

Fluid Pressure – Any point within a fluid has an equal amount of pressure coming from all angles

Pressure is measured in N/m2. This is also called the pascal (Pa). 1 N/m2 = 1 Pa. Pascal can also be called atmosphere (atm). 100,000 Pa = 1 atm. Millibars (mb) may also be used by meteorologists.

Hydrostatic pressure means that the deeper you go into water, the more pressure you will have. This happens because there is more weight as you go deeper into water.

The pressure in a liquid does not change if the liquid is compressed (squeezed) because liquid does not squeeze much. The pressure of gas increases the more it is compressed.

Several instruments can be used to measure pressure. Evangelista Torricelli made the first barometer (thing to measure pressure) in

1643. This was a mercury barometer. It was a tube with mercury inside that

went up and down as the atmosphere’s pressure changed.

Today we use aneroid barometers (barometer with a gauge and needle)

because they are more sensitive to lower pressures in the atmosphere.

Gauges are used to measure fluid pressure within a system, like in a

car’s tires.

Gauge pressure measures the absolute pressure within a system minus

the atmospheric pressure. Bourdon Tubes are used to measure atmospheric pressure in extreme

environments, and are made of C-shaped coils.

Buoyancy – the ability of an object to float in a given liquid or gas; usually the fluid to measure buoyancy is water

Archimedes’ principle says that an immersed (in a fluid) object is lifted or buoyed up by a force equal to the weight of the fluid that is dispersed (moved).

Buoyant force is the force from the dispersed water that is pushing the object up. It applies to both floating (sitting on top of fluid) and submerged (totally covered by fluid) objects.

If I move 1.0 g/cm3 of water by an object that whose density is 0.5 g/cm3, the object will float. If I move 1.0 g/cm3 of water by an object whose density of 1.5 g/cm3, the object will sink.

Only 1/2 of the volume of an object must be immersed (put in the fluid) to make buoyant force.

More water = more density of water = more buoyant force. The shape of an object can decrease the object’s density by increasing the

amount of air in the object. This is why ships can float even though they are heavy.

Some objects will match their density to the density of the fluid around them – when this happens they neither sink nor rise, but stay exactly where they are. Hot air balloons and submarines do this.

Specific gravity measures relative density – it compares the density of the object to the density of water. It has no unit of measure.

Specific gravity formula is density of object/density of water. S.g. = density of object/density of water If the density of a piece of wood is 0.5 g/cm3 and the density of water is

1.0 g/cm3 the specific gravity would be: S.g. = density of object/density of water S.g. = 0.5 g/cm3/1.0 g/cm3

S.g = 0.5

Specific gravity is measured by a hydrometer.

Hydraulics and Fluid Flow

Pascal’s Principle – Changes of pressure on the surface of a confined (trapped) fluid are exerted (felt, used) equally throughout the fluid and at all points on the fluid’s container.

Pascal’s Principle only works in liquids because they cannot be compressed. Pascal’s principle can be used to make hydraulic machines (machines that

use the increased distance of liquid to decrease effort). Hydraulics means using liquid to do a job. Hydraulic lifts are used in car mechanic shops to lift cars – these are the

most common hydraulic machines. Oil is the best fluid for this. See page 183 for a picture.

The flow (movement) of all fluids can be controlled by putting them under pressure.

Pneumatics is the study of flowing and stationary (not moving) gasses. Aerodynamics is the study of objects moving through gasses. Hydrodynamics is the study of flowing and stationary liquids.

Daniel Bernoulli was a scientist who studied fluids. Bernoulli’s Principle says that if a pipe is narrow on one end and wide on the other, the water’s pressure + the water’s kinetic energy + the water’s potential energy must be equal at all places in the pipe.This is expressed (shown) mathematically as P1+KE1+PE1 = P2+KE2+PE2

This does not account for any friction from the water moving through the pipe.Remember that potential energy changes as height changes, so you will see a great difference in pressure in a pipe that is laid flat than you will see in a pipe that is vertical. See page 185 for pictures.Remember that pressure dictates (decides) the speed of the liquid.

The Coanda effect is for gasses moving around an object. The Coanda effect says that gasses moving around an object follow the shape of an object instead of going in a straight line. This causes air foils, which are changes in pressure around an object moving through a gas. Air foils + lift (supporting upward pressure force) are what allow an airplane to fly.

Gas Laws

Important people: Guillaume Amontons – built the first thermometer and found absolute

zero (the temperature where it is so cold that atoms can’t move) John Dalton – figured out that the total pressure in a gas is equal to

the sum of all the pressures of the individual gasses within that gas This concept (idea) us called the Law of Partial Pressures

Formula: Total gas pressure = pressure of gas 1 + pressure of gas 2

(and gas 3 and gas 4, etc)

Joseph Gay-Lussac – helped us understand that gasses combine in ratios (2 hydrogens and 1 oxygen make a water. If you have 30 hydrogens and only 10 oxygens, you can only make 10 waters)

Amedeo Avogadro – discovered that the same amount of gas will have the same amount of particles

Three things affect gasses – temperature, pressure, and volume.If you know 2 of these things, you can find the third using one of three laws.

If temperature is constant, pressure and volume are inversely related (if one goes up, the other goes down). Use Boyle’s Law (if temperature is unknown).

If pressure is constant, temperature and volume are directly related (if one goes up, the other goes up). Use Charles’s Law (if pressure is unknown).

If volume is constant, pressure and temperature are directly related (if one goes up, the other goes up. Use Gay-Lussac’s Law (if volume is unknown).

Boyle’s Law is used when temperature is constant (stays the same). If you know

the pressure and volume, but you don’t know the temperature, use Boyle’s Law.

Math formula: PV = k (pressure times volume = constant)K means constant, in this case the constant is the temperature.

If pressure is 30 and Volume is 20: PV = k, 30 times 20 = 60, temperature = 60

You can also use Boyle’s Law to find another gas’s pressure or volume if that gas has the same temperature as your gas.Math formula: P1V1 = P2V2

If gas one and two are at the same temperature, and gas 1 has a pressure of 30 and volume of 20, and gas 2 has a pressure of 20 and volume unknown:P1V1 = P2V2, 30 times 20 = 20 times ?, 600 = 20xX = 30 (volume of gas 2 = 30)If gas one and two are at the same temperature and gas 1 has a pressure of 30 and a volume of 20, and gas 2 has a pressure unknown and a volume of 30:P1V1 = P2V2, 30 times 20 = ? times 30, 600 = 30xX = 20 (pressure of gas 2 = 20)

Charles’s Law is used when the pressure of a gas is constant. If you know the volume and temperature, but don’t know the pressure, use Charles’s Law.

Math formula: V/T = k (volume over temperature = constant)In Charles’s Law, the pressure is the constant

If the volume of the gas is 20 and the temperature is 500:V/T = k20/500 = kk = 0.04 (pressure of the gas = 0.04

Charles’s Law can also be used to find an unknown volume or temperature of a second gas if the pressure between two gasses is the same.Math formula: V1/T1 = V2/T2

If the pressures between gas 1 and gas 2 are the same, and the volume of gas 1 is 10 and the temperature of gas 1 is 5, and the volume of gas 2 is 5 and the temperature is unknown:V1/T1 = V2/T2

10/5 = 5/?Cross multiply and divide10x = 25Divide by 10 on both sides

10x/10 = 25/10X = 2.52.5 is the temperature of gas 2

If the pressures between gas 1 and gas 2 are the same, and the volume of gas 1 is 10 and the temperature of gas 1 is 5, and the volume of gas 2 is unknown and the temperature of gas 2 is 10:V1/T1 = V2/T2

10/5 = ?/10Cross multiply and divide100 = 5xDivide by 5 on both sides100/5 = 5x/5X = 2020 is the volume of gas 2

Gay-Lussac’s Law is used when the volume of a gas is constant. If you know the pressure and temperature, but don’t know the volume, use Gay-Lussac’s Law.

Math formula: P/T = k (pressure over temperature = constant)(The constant is the volume)

If the pressure of the gas is 30 and the temperature is 600:P/T = k30/600 = 0.050.05 = the volume of the gas

Gay-Lussac’s Law can also be used to find a pressure or temperature if one gas and the pressure is already known.P1/T1 = P2/T2

If the volume of gas 1 and gas 2 are the same, and the pressure of gas 1 is 10 and the temperature is 5, and the pressure of gas 2 is 20 and the temperature is unknown:P1/T1 = P2/T2

10/5 = 20/?Cross multiply and divide100 = 10xDivide by 10 on both sides100/10 = 10x/10X = 1010 is the temperature of gas 2

If the volume of gas 1 and gas 2 are the same, and the pressure of gas 1 is 10 and the temperature is 5, and the pressure of gas 2 is unknown and the temperature of gas 2 is 10:P1/T1 = P2/T2

10/5 = ?/10Cross multiply and divide100 = 5x

Divide by 5 on both sides100/5 = 5x/5X = 2020 is the pressure of gas 2

For Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law:Temperature is always measure in KelvinVolume is measured in millilitersPressure is measured in Pascal or Atmosphere