Liquids
Pressure
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Pressure = force / area
Standard International (SI) units are Pascals
1N/m2 = 1 Pa about pressure of dollar bill on a table.
Pressure
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Liquid pressure = weight density x depth
– Weight density = weight/volume
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– Independent of volume!!!
For fresh water density is 1000 kg/m3
For water, weight density is 1000*9.8 = 9800N/m3
(liquid density is almost constant – Liquids are almost incompressible!)
Pressure
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Liquid density is about same for any given depth.
Force of liquid is perpendicular to a surface.
Buoyancy – Greater pressure against the bottom
of submerged object produces an upward
buoyant force! This is due to pressure being
depth dependent.
Archimedes’ Principle
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An immersed body is buoyed up by a force equal to the weight of the
fluid it displaces.
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True for Liquids and Gases
Objects weigh more in air than in liquid!
If an object is denser than fluid, it will sink.
If an object is less dense it will float.
If an object has equal density it will neither float or sink – like a fish.
If a 25 kg object displaces 20 kg fluid, it’s apparent weight is 5 kg
Archimedes Principle
Archimedes Principle
Archimedes Principle
Buoyant forces
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What is density of a fish? Of a person?
A diver will have greater pressure of water on them and increased
density, so must swim to surface.
Life jackets increase volume with little weight – reduces your density!
Buoyant Forces
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An equally sized block of lead and aluminum are submerged – which
has the greater buoyant force?
How about a lead block and a wood one of same size?
What is buoyant force on a ten-ton ship in fresh water, salt water, or a
lake of mercury?
What happens to the water line in a ship when it is loaded?
Buoyant Forces
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A ship captain throws you a life preserver filled with lead pellets – he
says it will give you a greater buoyant force than the Styrofoam filled
ones. Will you take it?? Is he correct??
Pascal’s Principle
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A change in pressure at any point in an enclosed fluid at rest is
transmitted undiminished to all points in the fluid.
Pascal’s Principle
Surface Tension & Capillary Action
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Liquid surfaces tend to contract and force each drop into shape having
least surface area.
On the space shuttle, water drops are spherical!
Attraction of unlike surfaces is called Adhesion, like water in thin glass
tubes. Molecules act as sticky balls on the glass.
Attraction of like surfaces is cohesion.
Capillary Action
Class Problem
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Compared to an empty ship, will a ship
loaded with a cargo of styrofoam float
lower or higher in water?
1) lower
2) higher
3) same
Class Problem
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Compared to an empty ship, will a ship loaded
with a cargo of Styrofoam float lower or higher
in water?
The ship loaded with Styrofoam will float lower
in water. A ship will float highest when its
weight is least—that is, when it is empty.
Loading any cargo will increase its weight and
make it float lower in the water. Whether the
cargo is a ton of Styrofoam or a ton of iron, the
water displacement will be the same.
Class Problem
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Everybody knows that water "seeks its own
level," but very few people know why water
seeks its own level. The reason has most to do
with
1) atmospheric pressure
2) water pressure depending on depth
3) water's density
Class Problem
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The answer is b:
Water pressure depends on depth, so only at
equal depths of water will the pressure be
equal. Consider the U-tube. If water is at rest
where each X is, the pressure must be equal—
otherwise a flow would occur from the region of
higher to the region of lower pressure until the
pressures equalize. For this to happen, the
depths below the surfaces must be equal.
This is true whatever the density of water or
whether or not there is atmospheric pressure.
Class Problem
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Consider a boat loaded with scrap iron in a
swimming pool. If the iron is thrown overboard
into the pool, will the water level at the edge of
the pool
1) rise,
2) fall,
3) remain unchanged?
Class Problem
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The water level at the side of the pool will fall, because the iron will
displace less water submerged than when floating. When floating it
displaces its weight of water (a lot!)—when submerged it displaces only
its volume (less, because iron is more dense than water). The more
exaggerated view shows cases for a very heavy but small cannonball—
note the differences in water level.
Class Problem
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A block of balsa wood with a rock tied to it floats
in water. When the rock is on top as shown,
exactly half the block is below the water line.
When the block is turned over so the rock is
underneath and submerged, the amount of block
below the water line is
1) less than half
2) half
3) more than half
And the water level at the side of the container
will
1) rise
2) fall
3) remain unchanged
Class Problem
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The answers are a and f:
When the rock is on top, its whole weight
pushes the wood into the water. But when
the rock is submerged, buoyancy on it
reduces its effective weight and less than
half the block is pulled beneath the water
line. Or by the law of flotation: the rock and
wood unit displaces its combined weight and
the same volume of water whether the rock
is on the top or the bottom, less wood is
below the water line than when the rock is
on top.
Since the same volume of water is
displaced, no matter how it floats, the water
level at the side of the container remains
unchanged.
Class Problem
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The density of the block of wood floating in
water is
1) greater than the density of water
2) equal to the density of water
3) less than half that of water
4) more than half the density of water
5) … not enough information is given
Class Problem
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The answer is d:
A very low-density object, like an inflated balloon, floats high on the water, and a
denser object like a piece of hardwood, floats lower into the water. An object half
as dense as water floats half way into the water (because it weighs as much as
half its volume of water). Wood that floats 3/4 submerged, is 3/4 as dense as
water—like the block in question—more than half the density of water.
The density of the block compared to the density of water is the same as the
fraction of the block below the water line.
Class Problem
1. Water pressure is greatest against the
1) top of a submerged object.
2) bottom of a submerged object.
3) sides of a submerged object.
4) is the same against all surfaces
5) none of these
2. The reason that buoyant force acts upward on a submerged object
is that
1) it acts in a direction to oppose gravity.
2) if it acted downward, nothing would float.
3) the weight of fluid displaced reacts with an upward force.
4) upward pressure against the bottom is greater than downward
pressure against the top of the submerged object.
Class Problem
3. What is the weight of water displaced by a 100-ton floating ship?
1) less than 100 tons
2) 100 tons
3) more than 100 tons
4) 100 cubic meters
5) depends on the ship's shape
4. The buoyant force on an object is least when the object is
1) partly submerged.
2) submerged near the surface.
3) submerged near the bottom.
4) none of these
Class Problem
5. When holes are drilled through the wall of a water tower , water will
spurt out the greatest horizontal distance from the hole closest to
1) the bottom of the tower.
2) the middle of the tower.
3) the top of the tower.
4) The horizontal distance will be the same for all holes.
6. Buoyant force is greatest on a submerged
1) 1-kg block of lead.
2) 1-kg block of aluminum.
3) is the same on each
Class Problem
7. Compared to the buoyant force that acts on you when you float in
fresh water, the buoyant force that acts on you when you float in the
dense water of the Dead Sea is
1) less, because less of your volume is displaced.
2) more, because of the greater density of fluid displaced.
3) the same.
8. A hydraulic press multiplies a force by 100. This multiplication is done at
the expense of
1) energy, which is divided by 100.
2) the distance through which the force acts.
3) the time through which the force acts, which is multiplied by 100.
4) the mechanism providing the force.
5) none of these