Transcript Solids and Fluids

Solids and Fluids
Chapter 9
Phases of Matter
 Solid – definite shape and volume
 Liquid – definite volume but assumes the
shape of its container
 Gas – assumes the shape and volume of its
container.
 Liquids and Gases are collectively referred to
as FLUIDS.
 Fluid – A substance that can flow.
Fluid Pressure
 Pressure = Force / Area
 Units of [Newtons/m2] or [pounds/in2]
 p= F / A to find pressure, use the
component of force normal to the surface area
 Pressure is commonly measured in [Pascals] =
[Pa] = [N/m2]
Density
 Density = Mass / Volume
 Density is measured in [kg/m3] or [g/cm3]
 Density of Water = 1 g/cm3 = 1000 kg/m3
 Density is symbolized with ρ
Pressure and Depth
 Water pressure increases with depth.
 Water Pressure =
 Water pressure at
height, h is
F/A
mg/A
(ρhA)g/A
ρgh [N/m2]
Water Pressure and Depth
 Pressure of a liquid at
a depth of h is
p = po + ρgh
where po is the
pressure at the surface
of the liquid.
Water Pressure and Depth
 po is pressure at the surface
 Often surface pressure is air pressure, pa
 Standard air pressure at sea level is
[1 atmosphere] = [1 atm] = [1.013 X 105
N/m2] = [101.3 kPa]
Scuba Diver Example
 What is the total pressure on the back of
a scuba diver in a lake at a depth of 8.0
meters?
 What is the force on the divers back due
to the water alone, taking the surface of
the back to be a rectangle 60.0 cm by
50.0 cm?
Pascal’s Principle
 Pressure which is
applied to an
enclosed
incompressible fluid
is transmitted to
every point in the
fluid and to the walls
of the container.
Pascal’s Principle
 Pressure applied to
an incompressible
fluid is transmitted
instantaneously
throughout the fluid.
 Pressure is the same
throughout.
Pascal’s Principle
 Hydraulic systems
make use of Pascal’s
Principle.
 An applied force can
be multiplied and
made to lift a large
load.
 (F/A) remains
constant
Example
 A garage lift has input and lift (output)
pistons with diameters of 10cm and 30
cm. The lift is used to hold up a car with
a weight of 1.4 X 104 N.
a) what is the magnitude of the input
force on the piston?
b) what pressure is applied to the input
piston?
Archimedes Principle
 A body immersed wholly or partially in a
fluid experiences a buoyant force equal
in magnitude to the weight of the volume
of fluid that is displaced.
Examples
 A spherical helium filled balloon was a radius of
1.10m. Does the buoyant force on the balloon
depend on the density of 1) helium 2) air or 3)
the weight of the rubber skin?
 Compute the magnitude of the buoyant force on
the balloon. ρair = 1.29 kg/m3 and ρHe = 0.18
kg/m3.
 If the rubber skin of the balloon has mass of 1.2
kg, find the balloon’s initial acceleration when
released if it carries a load of 3.52 kg.
Fluid Flow
Conditions of molecules in a flowing fluid may be
unpredictable - difficult to quantify. Therefore it is
helpful to identify several conditions of an ideal
fluid:
Condition 1: Steady flow means that all particles
have the same velocity as they pass a given
point.
Condition 2: Irrotational flow means that a fluid
element has not angular velocity. (no whirlpools)
Condition 3: Nonviscous flow means viscosity is
negligible.
Condition 4: Incompressible flow means the fluid’s
density is constant.
Continuity of Fluid Flow
Consider fluid flowing in a tube with different
diameters…
Equation of Continuity
 Mass of fluid flowing into the tube in a
given time must equal the mass flowing out
of the tube…
 Δm1 = ρV1= ρA1Δx1 = ρA1v1Δt
 Δm2 = ρV2= ρA2Δx2 = ρA2v2Δt
 Since Δm1= Δm2, A1v1 = A2v2
 Equation of Continuity: A1v1 = A2v2
Bernoulli’s Equation
 Work – Energy Formula become
Bernoulli’s Equation:
 Wnet = ΔKE + ΔU
 p1 + ½ρv12 + ρgy1 = p2 + ½ρv22 + ρgy2
Bernoulli’s Equation
Special Cases
 p1 + ½ρv12 + ρgy1 = p2 + ½ρv22 + ρgy2
 p + ½ρv2 + ρgy = constant
 If the fluid is at rest, then the formula becomes
the pressure depth relationship:
p2 – p1 = ρg(y2 – y1)
 If y1 = y2, then p1 + ½ρv12 = p2 + ½ρv22 which
says if the velocity of a fluid increases, the
pressure it exerts decreases.
Examples
 A cylindrical tank containing water has a
small hole punched in its side below the
water level, and water runs out. What is
the approximate initial flow rate of water out
of the tank?