Section 3: Fluids Preview Key Ideas Bellringer Pressure Buoyant Force Comparing Weight and Buoyant Force Pascal’s Principle Math Skills Fluids in Motion

Key Ideas How do fluids exert pressure? What force makes a rubber duck float in a bathtub? What happens when pressure in a fluid changes? What affects the speed of a fluid in motion? GLOBAL NOTE: Section 2 at top of slide needs to be changed to Section 3

Bellringer Although you may not be familiar with the specific details, you have seen buoyant forces at work. You know from experience that certain objects float in air or in water. This is because of the force that pushes, or buoys the object up. This force, which is always in the upward direction, opposes the weight of the object. Examine each of the drawings shown on the next slide. Then answer the questions that follow.

Bellringer, continued 1. Is the buoyant force on the lump of gold greater than, less than, or equal to the gold’s weight? 2. Is the buoyant force on the balloon greater than, less than, or equal to the balloon’s weight? 3. Is the buoyant force on the boat greater than, less than, or equal to the boat’s weight? 4. Is the buoyant force on the submarine greater than, less than, or equal to the submarine’s weight?

Pressure How do fluids exert pressure? Fluids exert pressure evenly in all directions. pressure: the amount of force exerted per unit area of a surface example: when you pump up a bicycle tire, air particles constantly push against each other and against the tire walls

Pressure, continued Pressure can be calculated by dividing force by the area over which the force is exerted: The SI unit for pressure is the pascal. pascal: the SI unit of pressure; equal to the force of 1 N exerted over an area of 1 m2 (symbol, Pa)

Visual Concept: Equation for Pressure

Buoyant Force What force makes a rubber duck float in a bathtub? All fluids exert an upward buoyant force on matter. buoyant force: the upward force that keeps an object immersed in or floating on a fluid

Buoyancy

Buoyancy in a Liquid The downward weight of an object (force due to gravity) is not as great as an upward force on that object called the buoyant force or buoyancy Weight

Buoyancy in a Liquid The force of pressure is greater at the bottom of the object than the force of pressure exerted on the top of the object.

Therefore, the buoyant force is due to the pressure differences between the top and the bottom of object.

Buoyancy arises from the fact that: fluid pressure increases with depth the increased pressure is exerted in all directions there is an unbalanced upward force on the bottom of a submerged object

Buoyant Force Equals Weight of Liquid Displaced any object placed in water displaces a certain amount of water think about how the water level in the bathtub rises when you get in you can use the weight of the displaced water to determine the buoyant force

Buoyant Force Equals Weight of Liquid Displaced What is the buoyant force on the weight? To calculate, figure out the weight of the displaced water.

http://www.youtube.com/watch?v=JDjA6oiXXJQ&feature=player_embedded

Archimedes’ Principle Archimedes lived over 2000 years ago in Greece. He discovered the fact that: The buoyant force on an object is equal to the weight of the fluid displaced by the object.

Sink or Float? The buoyant force determines whether an object will sink or float. If the buoyant force is greater than the weight of the object, then the object will float If the buoyant force is less than the weight of the object, then the object will sink.

Sink or Float? An object floats when it displaces a volume of fluid whose weight is greater than or equal to its own weight. An object will float in a fluid if the density of that object is less than the density of the fluid.

Why is the tip of the iceberg the only part seen out of the ocean?

Isostasy The buoyant force of the ocean pushes the iceberg upwards, but the volume of the ice is only slightly less than the same volume of salt water it displaces, so almost 90% of the iceberg remains submerged.

Why do some objects sink while others float? Density (the object’s mass divided by it’s volume - how much space it takes up) In order for an object to float, the water it displaces must weigh more than the object itself Or to put in density terms, the object must have a density lower than the density of the water

If the density of water is 1g/cm3, then . . . will wood (D = 0.8 g/cm3) float? will aluminum (D = 2.7 g/cm3) float? will steel (D = 7.8 g/cm3) float?

Didn’t you just say steel would sink?!? Then why is this ship made of steel floating on top of the water?

The shell of the ship may be made of steel, but most of the space inside the hull is filled with air that has a very low density.

Some creatures in the sea have gas filled bladders whose volume can be changed to adjust for the buoyant force at various depths.

This is how submarines work too This is how submarines work too. They can take in sea water to submerge or discharge sea water to rise up to the surface.

Can you think of something else that uses changes in the density within a chamber to make it rise or fall in our atmosphere?

Buoyant Force, continued Archimedes’ principle is used to find buoyant force. The buoyant force on an object in a fluid is an upward force equal to the weight of the fluid that the object displaces.

Comparing Weight and Buoyant Force

Buoyant Force, continued An object will float or sink based on its density. If an object is less dense than the fluid in which it is placed, it will float. If an object is more dense than the fluid in which it is placed, it will sink.

Density

Pascal’s Principle What happens when pressure in a fluid changes? Pascal’s principle states that a change in pressure at any point in an enclosed fluid will be transmitted equally to all parts of the fluid. In other words, if the pressure in a container is increased at any point, the pressure increases at all points by the same amount. Mathematically, Pascal’s principle is stated as P1 = P2. Because P = F/A, Pascal’s principle can also be expressed as F1/A1 = F2/A2.

Pascal’s Principle, continued Hydraulic devices are based on Pascal’s principle. Because the pressure is the same on both sides of the enclosed fluid, a small force on the smaller area (left) produces a much larger force on the larger area (right). The plunger travels through a larger distance on the side that has the smaller area.

Hydraulic Devices produce enormous forces with the application of only a very small force hydraulic devices multiply forces example = hydraulic brakes on a car

Allows us to lift and rotate people without effort or stop cars just by pushing a brake pedal

How it Works:

1. A small force is applied to the smaller piston. #1

2. The pressure created by the force pushes against the liquid. #2

3. The piston moves a large distance as it presses on the liquid. #3

4. The pressure is transmitted equally throughout the liquid. #4

5. The transmitted pressure pushes upward against the larger piston, but over a smaller distance. #5

6. The pressure on every square cm of the larger piston is equal to the pressure on every square cm. #6

7. Since the # of square cm (or area) is greater on the larger piston, the force is greater. #7

Math Skills Pascal’s Principle A hydraulic lift uses Pascal’s principle to lift a 19,000 N car. If the area of the small piston (A1) equals 10.5 cm2 and the area of the large piston (A2) equals 400 cm2, what force needs to be exerted on the small piston to lift the car? 1. List the given and unknown values. Given: F2 = 19,000 N A1 = 10.5 cm2 A2 = 400 cm2 Unknown: F1

Math Skills, continued 2. Start with Pascal’s principle, and substitute the equation for pressure. Then, rearrange the equation to isolate the unknown value. P1 = P2

Math Skills, continued 3. Insert the known values into the equation, and solve. F1 = 500 N

Fluids in Motion What affects the speed of a fluid in motion? Fluids move faster through small areas than through larger areas, if the overall flow rate remains constant. Fluids also vary in the rate at which they flow.

Fluids in Motion, continued Viscosity depends on particle attraction. viscosity: the resistance of a gas or liquid to flow Fluid pressure decreases as speed increases. This is known as Bernoulli’s principle.

What you have just demonstrated is . . . Formulated by the Swiss mathematician who lived in late 1600’s

Bernoulli’s Principle The pressure in a moving stream of fluid is less than the pressure in the surrounding fluid

How do birds fly? the wing is round in the front, thickest in the middle, and narrow at the back the bulge at the top make this surface area longer than the bottom surface the air traveling above the wing must travel a longer distance but is moving faster therefore, the faster the air on top is moving, the less pressure on the top of the wing

Bird is moving in this direction How do birds fly?

Other Ways to Use Bernoulli’s Principle

What is Happening? Bernoulli's principle tells us that air that is moving at high speed has lower pressure than still air. The air that moves around the ball creates a pocket around the ball of low pressure air. When the ball moves to the side of the pocket, it will be pushed back in. The upward force from the air stream keeps the ball aloft.

How does an airplane fly?

OBJECTIVES Understand the concept of pressure. Explain Bernoulli's principle as it pertains to lift. Demonstrate how airplanes fly

LIFT THRUST DRAG GRAVITY an airplane must CONTROL forces Air on top of the wing moving faster than the air below (Bernoulli effect). THRUST DRAG The force necessary to overcome gravity and drag. Resistance created by air. GRAVITY

an airplane must CONTROL forces LIFT THRUST DRAG GRAVITY

Bernoulli's principle: concept stating that as a fluid's speed increases, its pressure decreases. lift: force exerted on the underside of a wing by air moving over the surfaces of the wing.

Visual Concept: Viscosity