Chapter 11
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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
𝑚
𝜌=
𝑉
• 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.
• 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 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.
𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝒐𝒇 𝒔𝒖𝒃𝒔𝒕𝒂𝒏𝒄𝒆
𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒈𝒓𝒂𝒗𝒊𝒕𝒚 =
𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝒐𝒇 𝑯𝟐 𝑶 𝒂𝒕 𝟒°𝑪
• Since specific gravity is a ratio, no unit is involved!
• 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.
𝑭
𝑷=
𝑨
• SI unit: N/m2 referred to as a Pascal
• 105 Pa = one bar
• Pounds per square inch (psi)
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.
1.010 x 105 Pa
1 atm
Atmospheric
Pressure
14.70 lbs/in2
760 mmHg
• 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.
𝑃2 = 𝑃1 + 𝜌𝑔ℎ
• 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.
Click on the professor
for a video lesson
recap and then some!
• 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!
• 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.
• This word deserves it’s own title!
• Fancy word for device used to measure blood pressure.
Learn more by
clicking the picture!
• 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.
𝐹2
𝐴2
=
𝐹1
𝐹2
because the pressure is equal
• This relationship only works when points 1 and 2 lie at the same
depth (h = 0m) in the fluid.
• 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/bychpt
r/chptr4_matter.htm#FluidPressure
• 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.
𝐹𝐵 = 𝜌𝑔ℎ𝐴 = 𝜌ℎ𝑉
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.
• 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.
• 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-vsmyth/everyday-myths/question254.htm
• Try this problem. http://bcs.wiley.com/hebcs/Books?action=resource&bcsId=6796&itemId=047087952
1&resourceId=26562&chapterId=73116
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
• 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.
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.
• 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.
• 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.
𝜌1 𝐴1 𝑣1 = 𝜌2 𝐴2 𝑣2
ρ = fluid density (kg/m3)
A = cross-sectional area of tube (m2)
v = fluid speed (m/s)
• Since the density of a flowing fluid doesn’t change, it can be
eliminated from previous equation.
• For an incompressible fluid
𝐴1 𝑣1 = 𝐴2 𝑣2
• 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!
• 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.
• 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
• 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
1 2
1 2
𝑃1 + 𝜌𝑣1 + 𝜌𝑔𝑦1 = 𝑃2 + 𝜌𝑣2 + 𝜌𝑔𝑦2
2
2
• For a static fluid, this equation reduces when the speed of the
fluid is uniform throughout. (A is constant)
𝑃2 = 𝑃1 + 𝜌𝑔 𝑦1 − 𝑦2 = 𝑃1 + 𝜌𝑔ℎ
• 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.