Fluids

Honors Physics

Liquids

In a liquid, molecules flow freely from position to position by sliding over each other

Have definite volume

Do not have definite shape – conform to their container

Density

Mass Densityρ = m/VUnits – kg/m3

Common densitiesAir – 1.29 kg/m3

Fresh water – 1.00 x 103 kg/m3

Ice - 0.917 x103 kg/m3

Densities of Common Substances

BuoyancyThe apparent loss of weight of an object that is submerged

The water exerts an upward force that is opposite the direction of gravity called the buoyant force.

Submerged

An object placed in water will displace, or push aside, some of the water

The volume of water displaced, is equal to the volume of the object

This method can be used to easily determine the volume of irregularly shaped objects

Archimedes’ Principle

An immersed object is buoyed up by a force equal to the weight of the fluid it displaces.

This principle is true for all fluids.

This means that the apparent weight of an immersed object is its weight in air minus the weight of the water it displaces

For floating objects FB = Fg (object)

Examples

A brick with a mass of 2kg weighs 19.6N If it displaces 1L of water, what is the buoyant force exerted on the brick?

Buoyant force = weight of water displaced

1L displaced = 9.8N

Buoyant force = 9.8N

Sink or Float?

If the buoyant force acting on an object is greater than its weight force, the object will float

A submerged objects’ volume, not mass determines buoyant force

3 Rules An object more

dense than the fluid it is immersed in will sink

An object less dense than the fluid it is immersed in will float

An object with equal density to the fluid will neither sink nor float.

Density & Buoyant Force

The buoyant force and apparent weight of an object depends on density

fB

g

F

objF

)(

Sample Problem 9A

A bargain hunter purchases a “gold” crown at a flea market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is the crown make of pure gold? Explain.

Floatation

Why is it possible for a brick of iron to sink, but an equal mass of iron shaped into a hull will float?

When the iron is shaped, it takes up more space (volume)

Principle of Flotation – A floating object displaces a weight of fluid equal to its own weight

Liquid Pressure

Pressure for solids is determined by the equation P=F/A

In this equation, the force is simply the weight of the object.

The same principle can be used for liquids

Pascal’s Principle

Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container.

F2 = A2 F1

A1

Sample Problem 9B

The small piston of a hydraulic life has an area of 0.20 m2. A car weighing 1.20 x 104 N sits on a rack mounted on the large piston. The large piston has an area of 0.90 m2. How large a force must be applied to the small piston to support the car?

Pressure

More dense liquids will produce more force and, therefore, more pressure.The higher the column of liquid the more pressure also.For liquids, Pressure = density x g x depth

AKA Gauge Pressure = ρghTotal pressure = density x g x depth +

atmospheric pressureP = PO + ρgh

Examples

Is there more water pressure at 3m or at 9m of depth?

Calculate the pressure exerted by a column of water 10m deep.

9m

=98000 Pa

)10)(/8.9)(/1000( 23 msmmkgP

Sample Problem 9C

Calculate the absolute pressure at an ocean depth of 1.00 x 103 m. Assume that the density of the water is 1.025 x 103 kg/m3 and that PO=1.01 x 105 Pa.

Pascal’s PrincipleChanges in pressure at any point in an enclosed fluid at rest are transmitted undiminished to all points in the fluid and act in all directions.Hydraulic systems operate using this principle.

Gasses

Have neither definite volume nor shape

The atmosphere is a good example of a gas.

In the atmosphere, the molecules are energized by sunlight and kept in continual motion

Atmosphere

The density of the atmosphere decreases with altitude

Most of the Earth’s atmosphere is located close to the planets surface.

Atmospheric Pressure

The atmosphere all around us exerts pressure just as if we were submersed in a liquid

At sea level, air has a density of about 1.2 kg per cubic meter

A column of air, of 1 sq. meter that extends up through the atmosphere weighs about 100,000 NThe avg atmospheric pressure a sea level is 101.3 kPa

Measuring Pressure

A barometer is used to measure atmospheric pressure

Air pressure forces mercury up the glass tube, to display the pressure

This process is similar to that of drinking out of a straw

Boyle’s Law

For a gas, the product of the pressure and the volume remain constant as long as the temperature does not change.P1V1 = P2V2

Examples

If you squeeze a balloon to 1/3 its original volume, what happens to the pressure inside?

3x

A swimmer dives down, until the pressure is twice the pressure at the waters surface. By how much does the air in the divers lungs contract?

2x

Charles’ Law

The volume of a definite quantity of a gas varies directly with the temperature, provided the pressure remains constant.

V1T2 = V2T1

Combined Gas Law

When Boyle’s and Charles’ laws are combined the equation looks like this.

P1V1T2 = P2V2T1

Sample Problem 9E

Pure helium gas is contained in a leakproof cylinder containing a movable piston. The initial volume pressure and temperature of the gas are 15 L, 2.0 atm and 310 K, respectively. If the gas is rapidly compressed to 12 L and the pressure increased to 3.5 atm, find the final temperature of the gas.

Ideal Gas Law

Compares volume, pressure, and temperature of a gasPV = NkBTP = pressure, V = volume, N = # of mols of

gas particles, kB = Boltzman’s Constant (1.38x10-23 J/K), T = temperature

Fluid Flow

Smooth flow is said to be laminar flow

Particles all follow along a smooth path Streamline path

Streamlines never cross

Irregular flow is said to be turbulent

Irregular motion produced are called eddies

Continuity

Continuity says that the mass of and ideal fluid flowing into a pipe must equal to mass flowing out of the pipe.

Or m1 = m2

Because the mass flowing is determined by the cross-sectional area of the pipe and how fast it flows, we can also say

A1v1 = A2v2

Bernoulli’s Principle

Pressure in a fluid decreases as the fluid’s velocity increases.

Bernoulli’s Principle can be seen in birds in flight and airplanes

Pressure above the wing is less than pressure below the wing, creating lift

Bernoulli’s Equation

This is an expression of conservation of energy in a fluid.

P + ½ρv2 + ρgh = constant

Pressure + kinetic energy per unit volume + gravitational potential energy per unit volume = constant along a given streamline

Sample Problem 9DA water tank has a spigot near its bottom. If the top is open to the atmosphere, determine the speed at which the water leaves the spigot when the water level is 0.500m above the spigot.We’ll use (P + ½ρv2 + ρgh)1 = (P + ½ρv2 + ρgh)2

we assume the water level is dropping slowly, so v2, at the top, = 0

Also, since both ends are open to the atmosphere P1 = P2

That simplifies the equation to

P + ½ρv12 + ρgh1 = P + ρgh2 and subtract P

½ρv12 + ρgh1 = ρgh2 ρ is the same throughout, so

½v12 + gh1 = gh2 solve for v

v = √(2g(h2-h1)) plug & chug

v = √(2(9.8 m/s2)(.5m))

v = 3.13 m/s

Pg. 344: 17, 18, 23, 25, 29, 36, 39, 44, 47, 48

Test on Fluids:Thursday