FluidsChapter 11

Why Does Something Float?

11.1 Mass Density• In this chapter, we discuss the behavior of fluids.• Fluids by definition, include both gases and

liquids• Mass density is the mass per unit volume of a

liquid or gas• Greek letter rho (ρ) is the symbol. kg/m3 is the

unit

Remember Chemistry• The relative closeness of particles of solids and

liquids lead to greater densities than gases.• In chemistry you learned that changes in

temperature, volume, and pressure can change the density of a substance.

• That is TRUE!• However, for the range of temperatures and

pressures used in this course, the densities of solids and liquids will not differ much from those given on page 322, Table 11.1.

Mass vs Weight

• Fg=mg

• Mass, not weight, is part of the definition of mass density.

• When weight is needed, you must solve using mass density, volume, and g.

Specific Gravity

• Specific Gravity can be used to compare the densities of substances

• Specific Gravity is density of a substance divided by the density of a standard reference material, usually water at 4⁰C.

• Since specific gravity is a ratio, no unit is involved!

Mass density

can be used

to help

determine

pressure.

11.2 Pressure

• Pressure exerted by gases and liquids comes from collisions between molecules and container walls.

• Pressure, technically, is defined as magnitude F of the force acting perpendicular to a surface divided by the area over which the force acts.

Units of Pressure and Conversions• SI unit: N/m2 referred to as a Pascal• 105 Pa = one bar• Pounds per square inch (psi)

1.010 x 105 Pa 1 atm

14.70 lbs/in2 760 mmHg

Atmospheric Pressure

Force is a vector, pressure is NOT!

The FORCE generated by the pressure of a static fluid is always perpendicular to the surface that the fluid contacts.

11.3 Pressure and Depth in a Static Fluid• As a diver descends to deeper water, more pressure will be

exerted on his or her body.• Since more water is supported by the same horizontal area of

water at greater depths (namely the weight of the water above it) there is more force per unit area or pressure.

• Check the derivation on pg. 325 of your text.

• P1 is the “higher level”

• Equation assumes an incompressible fluid (reasonable for liquids)• With gases, this equation can only be used for values of h where

differences in ρ are negligible.• Horizontal distances in fluids DO NOT affect pressure.

Time for a Dork Break!

Click on the professor for a video lesson

recap and then some!

More Pressure and Depth• Problem Solving Insight: The pressure at any

point in a fluid depends on the vertical distance (h) of the point beneath the surface. However, for a given vertical distance, the pressure is the same, no matter where the point is located horizontally on the fluid.

• The pressure on the surface of water at sea level is the atmospheric pressure of the air above it.

• Try this self-assessment test!

11.4 Pressure Gauges• Mercury Barometer measures atmospheric pressure

with respect to the height of mercury in an *evacuated column.

Patm = 0 Pa + ρgh

• Open – tube manometer contains one open side of a U-tube.

P2 – Patm = ρgh

• Changes in air pressure cause changes in the height of the mercury in both cases.

• The gauge pressure is the amount by which the container pressure differs from atmospheric pressure. Gauge pressure is proportional to height.

• The actual value for P2 is the absolute pressure.

SPHYGMOMANOMETER • This word deserves it’s own title!• Fancy word for device used to measure blood

pressure.

Learn more by clicking the

picture!

11.5 Pascal’s Principle• Deals with completely enclosed fluids and the

pressure resulting from external forces.• Any change in the pressure applied to a

completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls.

because the pressure is equal

• This relationship only works when points 1 and 2 lie at the same depth (h = 0m) in the fluid.

Hydraulic Lifts• Use Pascal’s Principle to apply small forces in

order to move objects with large weight.• The same amount of work is done by both the

input and output forces (in this magical world of no friction!)

• The larger output force moves through a smaller distance while the smaller input force moves through a larger distance.

• http://www.explainthatstuff.com/hydraulics.html• http://

www.wfu.edu/physics/demolabs/demos/avimov/bychptr/chptr4_matter.htm#FluidPressure

11.6 Archimedes’ Principle• The upward force supplied by a fluid is called the

buoyant force.• All fluids apply such a force to objects immersed in them

(similar to normal force from solids).• Exists because fluid pressure is larger at greater depths.• Not a new type of force; simply the name given to the net

upward force exerted by the fluid on the object.

Any fluid applies a buoyant force to an object that is partially or completely immersed in it; the magnitude

of the buoyant force equals the weight of the fluid that the object displaces.

What floats?• Compare the weight of a floating object to the

maximum possible buoyant force. • Since the Fg =ρVg, and V and g are the same for

both the floating object and the water, the comparison depends ONLY ON DENSITY.

• Any object that is solid throughout will float in a liquid of the density of the object is less than or equal to the density of the liquid.

Large Boats Floating is Really Cool• Boats float because it is NOT a solid material. • Large, steel boats contain A LOT of “empty space”

and because of their shape, displace enough water to balance their own weight.

• Watch this! http://science.howstuffworks.com/science-vs-myth/everyday-myths/question254.htm

• Try this problem. http://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=6796&itemId=0470879521&resourceId=26562&chapterId=73116

11.7 Fluids in Motion

Steady Flow• The velocity of the

fluid particles at any point is constant as time passes.

• Within a stream, all particles passing through one point will that the same velocity. Other particles at other points may have a different velocity.

Unsteady Flow• The velocity at a point

in the fluid changes as time passes.

• Turbulent flow occurs when the velocity at a point changes erratically from moment to moment, both in magnitude and direction.

Compressible vs Incompressible

Compressible• Gases are highly

compressible.• Most gases will change

density very easily when they are subject to changes in pressure.

Incompressible• Most liquids are nearly

incompressible.• Density remains

almost constant as pressure changes.

• Liquids flow in an incompressible manner.

Viscosity

High Viscosity• Honey does not flow

very readily• Flow of a viscous fluid

is said to be energy dissipating.

• Viscosity of one layer hinders the flow of nearby layers.

No Viscosity• Ideal fluids are

incompressible, nonviscous fluids.

• Flow in an unhindered manner.

• No dissipation of energy.

Streamlines• Used to represent the trajectories of the fluid

particles.• A line (like a vector) drawn in a fluid such that a

tangent to the streamline at any point is parallel to the fluid velocity.

• Remember: velocity is a vector quantity.• While fluid velocity can vary from point to point,

the velocity is constant in time.• Steady flow is often referred to as streamline flow.• Liquids use colored dye.• Gases use smoke streamers.

11.8 The Equation of Continuity• If a fluid enters one end of a pipe at a certain rate,

then the fluid must also leave at the same rate, assuming that there are no places between the entry and exit point to add or remove fluid.

• Mass flow rate (ρAv) is the mass of fluid per second that flows through a tube. SI unit kg/s.

ρ = fluid density (kg/m3)A = cross-sectional area of tube (m2)

v = fluid speed (m/s)

Volume Flow Rate• Since the density of a flowing fluid doesn’t

change, it can be eliminated from previous equation.

• For an incompressible fluid

• Av represents the volume flow rate (Q) passing through the tube at any second.

• Be careful: if the fluid density changes due to compression, you must use previous equation!

11.9 Bernoulli’s Equation• The work-energy theorem leads us to Bernoulli’s

equation (helps us relate concepts and derive equation)

• Wnc = ΔE is the work energy -theorem.• Conditions necessary for equation to work: steady

flow, incompressible, nonviscous fluid.• Pressure on a fluid is caused by collision forces

which are nonconservative.• When a fluid is accelerated because of a

difference in pressures, work is being done by nonconservative forces.

• Total mechanical energy is NOT conserved.

Bernoulli’s Observations of Moving FluΔids• When a fluid is flowing in a horizontal pipe and

meets a region of reduced cross-sectional area, the pressure drops.

• When moving from wider region to narrower region, the fluid speeds up (accelerates) consistent with equation of continuity.

• According to 2nd Law of Motion, if something accelerates, an unbalanced force exist. (ΔP)

• Also, if fluid moves to higher elevation, P2 > P1

Bernoulli’s Equation• In the steady flow of a nonviscous, incompressible

fluid of density ρ, the pressure P, the fluid speed v, and the elevation y at any two points (1 and 2) are related by

• For a static fluid, this equation reduces when the speed of the fluid is uniform throughout. (A is constant)

11.10 Applications of Bernoulli’s Equation• If a moving fluid is in a horizontal pipe, all parts

have the same elevation, so simplify Bernoulli’s equation to eliminate ρgy. DUH!

• Watch this video. It is basically a review of the nature of fluids in motion.

• Bernoulli’s equation is summarized here. Applications, including airplane flight are included.

• Physics of a curveball.