Liquids

1
Chapter 19

• Liquids

2
Liquid Pressure

• A liquid in a container exerts forces on the
  walls and bottom of the container
• Pressure is force/area
• How much pressure depends on the density of the
  liquid
• For the same volume, a denser liquid exerts more
  pressure
• For liquids of the same density, the pressure
  will be greater at the bottom of a deeper liquid
• Think of diving deep into a pool, you feel the
  increased pressure in your ears

3
Liquid Pressure

• Pressure of a liquid at rest only depends on the
  density of the liquidnot on the shape of the
  container or the size of its bottom surface
• This is because liquids are incompressible
  (cannot be squeezed into a smaller volume)
  therefore their density is the same at all depths
• Pressure due to liquid weight density x depth
  ?gh
• Total pressure pressure due to liquid
  atmospheric pressure
• Normal atmospheric pressure is 1.01 x 105 Pa
• Pressure due to a liquid depends on DEPTH, not
  volume!
• Forces produced by pressure are equally exerted
  in all directions
• Net force exerted by a liquid against a surface
  is perpendicular to the surface
• If there is a hole in the surface the liquid will
  initially move perpendicular to the surface

4
Liquid Pressure

• Where is the pressure the greatestat the bottom
  of the large, shallow lake or at the bottom of
  the small, deep pond?
• Wanda watches the fish in her fish tank and
  notices that the angel fish like to feed at the
  waters surface, while that catfish feed 0.300 m
  below at the bottom of the tank. If the average
  density of the water in the tank is 1000. kg/m3,
  what is the pressure on the catfish?

5
Liquid Pressure

• Why is the water level the same in each vase?
• Water seeks its own levelbecause of pressure!
• Which teapot can hold more tea?

6
Buoyancy

• Why is it easier to lift something that is
  submerged in water?
• The object has an apparent weight loss due to an
  upward force exerted on the object by the
  waterthis upward force is called the buoyant
  force
• Why does buoyant force push upward when forces
  are exerted all around the object?
• Horizontal forces cancel out
• Upward forces (against the bottom of the object)
  are greater than downward forces (against the top
  of the object) because the bottom of the object
  is deeper

7
Buoyancy

• When the weight of the submerged object
• is greater than the buoyant force, the object
  will sink to the bottom
• is equal to the buoyant force, the object will
  remain at any level (like a fish)
• is less than the buoyant force, the object will
  rise to the surface and float
• In terms of density, if the object is
• denser than the fluid, it will sink
• the same density as the fluid, it will neither
  sink or float
• less dense than the fluid, it will float

8
Buoyancy

• What happens to water level when something is
  placed in it?
• It rises
• How much does it rise?
• The amount of displaced water is equal to the
  volume of the submerged object
• A completely submerged object always displaces a
  volume of liquid equal to its own volume.
• This is a good way to find the volume of
  irregular shapes

9
Archimedes Principle

• An object completely or partially immersed in a
  fluid is pushed up by a force that is equal to
  the weight of the displaced fluid
• Buoyant force equals the weight of the fluid
  displaced by the object
• In general cases Fb ?g?V
• Buoyant Force density x acceleration due to
  gravity x volume
• In terms of Newtons third law If you put
  something in water that pushes 100 N of water out
  of the way, then the water pushes back with a
  force on 100 N.
• The buoyant force is equal and opposite to the
  weight of water you displace.
• 1 liter of water 1000 cm3 1 kg 9.8 N

10
Archimedes Principle

• A object weighs less in water than air
• A 500 gram mass weighs about 5 N in air. Suppose
  the mass displaces 3 N of water when it is
  submerged. The buoyant force on the mass will
  also measure 3 N (pointing up). The mass will
  weigh only 2 N in the water (5 N 3N).
• What happens it the mass is in deeper waterwhere
  there is greater pressure?
• As long as it is submerged completely, the depth
  will not make a difference because the difference
  in pressure between the bottom and top of the
  mass at different depth will be the same
• The difference in the upward and downward force
  acting on the submerged object is the same at any
  depth.
• The density of water near the surface is
  practically the same as the density of the water
  far beneath the surface. Greater variation
  occurs due to temperature difference.
• Waterlogged objects that lie submerged, yet above
  the bottom, are slightly denser than the warmer
  surface water and not quite as dense as the
  cooler water at the bottom.
• Object that are much denser than water will
  always sink to the bottom regardless of the depth
  of the water.

11
Archimedes Principle

• Palmer drops an ice cube into his glass of water.
  The ice, whose density is 917 kg/m3, has
  dimensions 0.030 m x 0.020 m x 0.020 m. What is
  the buoyant force acting on the ice?
• Williams wedding ring, presumed to be pure gold,
  has a mass of 0.1 kg. When submerged in water
  its apparent mass is 0.080 kg. The density of
  water is 1000 kg/m3 which is equivalent to 1
  kg/L.
• What is the buoyant force in Newtons?
• What volume of water (in liters) is displaced?
• Is the ring made of pure gold (? 19.3 kg/L)?
• Pine is 0.50 as dense as water and therefore
  floats in water. Weight density of water is 9800
  N/m3 or 9.80 N/L.
• What weight of water will be displaced by 25 kg
  of floating pine?
• What additional force would be required to poke
  the pine beneath the surface so it is completely
  submerged?

12
Sink or Float?

• An object more dense than the fluid in which it
  is immersed sinks.
• Fb Fg (displaced fluid) mfg ?fVfg
• An object less dense than the fluid in which it
  is immersed floats.
• Fb Fg (object) mog ?oVog
• An object with density equal to the density of
  the fluid in which it is immersed neither sinks
  or floats

13
Apparent Weight

• Apparent weight depends on the density
• Apparent weight Fg Fb ?fVfg ?oVog
• For a submerged object
• A piece of metal weighs 50.0 N in air, 36.0 N in
  water, and 41.0 N in an unknown liquid. Find the
  densities of the following
• The metal
• The unknown liquid

14
Flotation

• How can a ship be made of iron if a solid block
  of iron sinks?
• It has to do with the shape of the ship
• Principle of Flotationa floating object
  displaces a weight of fluid equal to its own
  weight
• The ship must be shaped to displace enough water
  to equal its own weight
• The deeper the ship is immersed, the more water
  it displacesa loaded ship will ride lower in the
  water than an unloaded ship

15
Flotation

• What is the buoyant force on a 10 ton ship
  floating in fresh water?
• In salt water?
• In a lake of mercury?
• 10 tons in each case the weight of the ship is
  constant, so the weight of the water displaced
  must also be constant. The volume of the liquid
  displaced will differ based on the density of the
  liquid.

16
Pascals Principle

• The change in pressure on one part of a confined
  fluid is equal to the change in pressure on any
  other part of the confined fluid.
• A small force exerted over a small area will
  result in a large force exerted over a large
  area.
• Used in hydraulic liftsa force is exerted on a
  smaller piston providing a pressure that is
  applied, undiminished, to the larger piston
  enabling it to lift the car

17
Pascals Principle

• Every Sunday morning, Dad takes the family trash
  to the trash compactor in the basement. When he
  presses the button on the front of the compactor,
  a force of 350 N pushes down on the 1.3 cm2 input
  piston, causing a force of 22,076 N to crush the
  trash. What is the area of the output piston
  that crushes the trash?