LiquidsLiquids

PressurePressure

• Pressure = force / areaPressure = force / area

• Standard International (SI) units are PascalsStandard International (SI) units are Pascals

• 1N/m1N/m22 = 1 Pa about pressure of dollar bill on a table. = 1 Pa about pressure of dollar bill on a table.

PressurePressure

• Liquid pressure = weight density x depthLiquid pressure = weight density x depth– Weight density = weight/volume

– Independent of volume!!!

• For fresh water density is 1000 kg/mFor fresh water density is 1000 kg/m33

• For water, weight density is 1000*9.8 = 9800N/mFor water, weight density is 1000*9.8 = 9800N/m33

• (liquid density is almost constant – Liquids are almost incompressible!)(liquid density is almost constant – Liquids are almost incompressible!)

PressurePressure

• Liquid density is about same for any given depth.Liquid density is about same for any given depth.

• Force of liquid is perpendicular to a surface.Force of liquid is perpendicular to a surface.

• Buoyancy – Greater pressure against the bottom Buoyancy – Greater pressure against the bottom of submerged object produces an upward of submerged object produces an upward buoyant force! This is due to pressure being buoyant force! This is due to pressure being depth dependent.depth dependent.

Archimedes’ PrincipleArchimedes’ Principle

• An immersed body is buoyed up by a force equal to the weight of the An immersed body is buoyed up by a force equal to the weight of the fluid it displaces.fluid it displaces.

– 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 PrincipleArchimedes Principle

Archimedes PrincipleArchimedes Principle

Archimedes PrincipleArchimedes Principle

Buoyant forcesBuoyant forces

• What is density of a fish? Of a person?What is density of a fish? Of a person?

• A diver will have greater pressure of water on them and increased A diver will have greater pressure of water on them and increased density, so must swim to surface.density, so must swim to surface.

• Life jackets increase volume with little weight – reduces your density!Life jackets increase volume with little weight – reduces your density!

Buoyant ForcesBuoyant Forces

• An equally sized block of lead and aluminum are submerged – which An equally sized block of lead and aluminum are submerged – which has the greater buoyant force?has the greater buoyant force?

• How about a lead block and a wood one of same size?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 What is buoyant force on a ten-ton ship in fresh water, salt water, or a lake of mercury?lake of mercury?

• What happens to the water line in a ship when it is loaded?What happens to the water line in a ship when it is loaded?

Buoyant ForcesBuoyant Forces

• A ship captain throws you a life preserver filled with lead pellets – he 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 says it will give you a greater buoyant force than the Styrofoam filled ones. Will you take it?? Is he correct??ones. Will you take it?? Is he correct??

Pascal’s PrinciplePascal’s Principle

• A change in pressure at any point in an enclosed fluid at rest is A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid.transmitted undiminished to all points in the fluid.

Pascal’s PrinciplePascal’s Principle

Surface Tension & Capillary ActionSurface Tension & Capillary Action

• Liquid surfaces tend to contract and force each drop into shape having Liquid surfaces tend to contract and force each drop into shape having least surface area. least surface area.

• On the space shuttle, water drops are spherical!On the space shuttle, water drops are spherical!

• Attraction of unlike surfaces is called Adhesion, like water in thin glass Attraction of unlike surfaces is called Adhesion, like water in thin glass tubes. Molecules act as sticky balls on the glass.tubes. Molecules act as sticky balls on the glass.

• Attraction of like surfaces is cohesion.Attraction of like surfaces is cohesion.

Capillary ActionCapillary Action

Class ProblemClass Problem

• Compared to an empty ship, will a ship Compared to an empty ship, will a ship loaded with a cargo of styrofoam float loaded with a cargo of styrofoam float lower or higher in water?lower or higher in water?1) lower

2) higher

3) same

Class ProblemClass Problem

• Compared to an empty ship, will a ship loaded Compared to an empty ship, will a ship loaded with a cargo of Styrofoam float lower or higher with a cargo of Styrofoam float lower or higher in water? in water?

• The ship loaded with Styrofoam will float lower The ship loaded with Styrofoam will float lower in water. A ship will float highest when its in water. A ship will float highest when its weight is least—that is, when it is empty. weight is least—that is, when it is empty. Loading any cargo will increase its weight and Loading any cargo will increase its weight and make it float lower in the water. Whether the make it float lower in the water. Whether the cargo is a ton of Styrofoam or a ton of iron, the cargo is a ton of Styrofoam or a ton of iron, the water displacement will be the same. water displacement will be the same.

Class ProblemClass Problem

• Everybody knows that water "seeks its own Everybody knows that water "seeks its own level," but very few people know level," but very few people know whywhy water water seeks its own level. The reason has most to do seeks its own level. The reason has most to do withwith

1) atmospheric pressure1) atmospheric pressure2) water pressure depending on depth2) water pressure depending on depth3) water's density 3) water's density

Class ProblemClass Problem

• The answer is The answer is bb::

Water pressure depends on depth, so only at Water pressure depends on depth, so only at equal depths of water will the pressure be equal depths of water will the pressure be equal. Consider the U-tube. If water is at rest equal. Consider the U-tube. If water is at rest where each X is, the pressure must be equal—where each X is, the pressure must be equal—otherwise a flow would occur from the region of otherwise a flow would occur from the region of higher to the region of lower pressure until the higher to the region of lower pressure until the pressures equalize. For this to happen, the pressures equalize. For this to happen, the depths below the surfaces must be equal.depths below the surfaces must be equal.

This is true whatever the density of water or This is true whatever the density of water or whether or not there is atmospheric pressure. whether or not there is atmospheric pressure.

Class ProblemClass Problem

• Consider a boat loaded with scrap iron in a Consider a boat loaded with scrap iron in a swimming pool. If the iron is thrown overboard swimming pool. If the iron is thrown overboard into the pool, will the water level at the edge of into the pool, will the water level at the edge of the pool the pool

1) rise,

2) fall,

3) remain unchanged?

Class ProblemClass Problem

• The water level at the side of the pool will fall, because the iron will 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 displace less water submerged than when floating. When floating it displaces its weight of water (a lot!)—when submerged it displaces only displaces its weight of water (a lot!)—when submerged it displaces only its volume (less, because iron is more dense than water). The more its volume (less, because iron is more dense than water). The more exaggerated view shows cases for a very heavy but small cannonball—exaggerated view shows cases for a very heavy but small cannonball—note the differences in water level. note the differences in water level.

Class ProblemClass Problem

• A block of balsa wood with a rock tied to it floats A block of balsa wood with a rock tied to it floats in water. When the rock is on top as shown, in water. When the rock is on top as shown, exactly half the block is below the water line. exactly half the block is below the water line. When the block is turned over so the rock is When the block is turned over so the rock is underneath and submerged, the amount of block underneath and submerged, the amount of block below the water line isbelow the water line is

1) less than half     2) half     3) more than half1) less than half     2) half     3) more than half

And the water level at the side of the container And the water level at the side of the container willwill

1) rise     2) fall     3) remain unchanged1) rise     2) fall     3) remain unchanged

Class ProblemClass Problem

• The answers are a and f:The answers are a and f:

When the rock is on top, its whole weight When the rock is on top, its whole weight pushes the wood into the water. But when pushes the wood into the water. But when the rock is submerged, buoyancy on it the rock is submerged, buoyancy on it reduces its effective weight and reduces its effective weight and less than less than half the blockhalf the block is pulled beneath the water is pulled beneath the water line. Or by the law of flotation: the rock and line. Or by the law of flotation: the rock and wood unit displaces its combined weight and wood unit displaces its combined weight and the same volume of water whether the rock the same volume of water whether the rock is on the top or the bottom, less wood is is on the top or the bottom, less wood is below the water line than when the rock is below the water line than when the rock is on top.on top.

Since the same volume of water is Since the same volume of water is displaced, no matter how it floats, the water displaced, no matter how it floats, the water level at the side of the container remains level at the side of the container remains unchangedunchanged. .

Class ProblemClass Problem

• The density of the block of wood floating in The density of the block of wood floating in water iswater is

1) greater than the density of water1) greater than the density of water2) equal to the density of water2) equal to the density of water3) less than half that of water3) less than half that of water4) more than half the density of water4) more than half the density of water5) … not enough information is given 5) … not enough information is given

Class ProblemClass Problem

• The answer is d:The answer is d:

A very low-density object, like an inflated balloon, floats high on the water, and a 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 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 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 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.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 The density of the block compared to the density of water is the same as the fraction of the block below the water line. fraction of the block below the water line.

Class ProblemClass 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 ProblemClass 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 ProblemClass 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 ProblemClass Problem

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

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.