Physics Chapter 13: Forces in Fluids Section 13.2 Forces and Pressure in Fluids

Objectives 13.2 Describe how pressure is transmitted in a fluid according to Pascal's principle. Explain how a hydraulic system works to change a force. Explain how the speed and pressure of a fluid are related according to Bernoulli's principle.

Vocabulary Hydraulic system Lift

Transmitting Pressure in a Fluid Remember that a fluid exerts pressure equally in all directions at a given depth. Also, that the pressure exerted depends upon the depth and the type of fluid. Take a look at the 2-liter soda bottle. Take out your Cartesian Divers if you have them. I want you to think about these concepts when trying to describe how the pressure forces act against the inside of the bottle.

Pascal’s Principle According to Pascal's principle, a change in pressure at any point in a fluid is transmitted equally and unchanged IN ALL DIRECTIONS throughout the fluid. What Pascal’s principle really says is that a force applied to one part of a fluid are transmitted all throughout the fluid equally. Observe the following illustrations and note the sizes of the force vectors…they indicate in which directions the forces are applied and what magnitude they are.

Pascal’s Principle What do you think that is? That if you apply a force in one part of a fluid it is distributed throughout the fluid? Think about how the chips reacted when you pushed one into a row of touching chips.

Pressure Remember that pressure is caused form molecules moving around, running into each other. If there is a force, such as the container being squeezed, then the pressure will increase due to increased numbers of collisions. The force is transferred because it’s an instant chain reaction (these molecules are really close together).

Recall Pressure & Volume Remember that as volume changes, so does the pressure The plunger acts as the force. Does pressure go up or down?

Illustrating Pascal’s Principle Observe the following illustrations and note the sizes of the force vectors…they indicate in which directions the forces are applied and what magnitude they are.

Illustrating Pascal’s Principle

Illustrating Pascal’s Principle Pressure Increases Notice that the force vectors are smaller at the top compared to those at the bottom. Why? Correct! That the amount of pressure depends only on the type of fluid (in this case it’s all the same…water) and the depth.

Illustrating Pascal’s Principle Now what happens when a force is applied in the middle of the bottle?

Illustrating Pascal’s Principle Notice that all the force vectors increased by the same magnitude. Pascal’s principle states that this force is distributed evenly and unchanged throughout the container.

Input Pressure = Output Pressure Pascal’s Principle Pascal’s principle is simple stated as: & if pressure = force/area then… Input Pressure = Output Pressure Force/area = Force/area (Input) (Output)

Pascal’s Principle Summary Complete your illustrations on the bottle. Explain why the “diver” (the straw) dives when the bottle is squeezed in terms of Pascal’s principle. You have 5 minutes and then we will discuss.

Hydraulic Systems Pascal’s principle is the underlying science behind hydraulic systems. A hydraulic system is a device that uses pressurized fluid acting on pistons of different sizes to change a force. In a hydraulic lift system, an increased output force is produced because a constant fluid pressure is exerted on the larger area of the output piston.

Hydraulic Systems Hydraulic systems Output Force Input Force Remember that the pressure is evenly distributed throughout the fluid but the observable change is in the pistons. When the pistons are the same size (same area), the input force isn’t magnified but it’s transmitted to a different place. Input Force Transmitted Force

Hydraulic System Multiplication Hydraulic systems can be used to change the direction of a force like in the previous example but they are usually used to multiply a force because it magnifies the input force. A force is applied to the piston on the left. The force is transmitted equally through the fluid and pushes on the piston on the right. The distance for piston 1 has to be large to have to right piston to move a little, but the force is magnified relative to the different diameters of the pistons.

The Equation to Calculate the Benefit of a Hydraulic System The benefit, the extra output force, is calculated by dividing the output piston area by the input piston area. Output Piston Area = Hydraulic benefit Input Piston Area

Hydraulic Benefit To calculate the benefit of the hydraulic system simply divide the output piston area by the input piston area. Output area/input area 500cm2 / 100cm2 = 5 The hydraulic system will increase the input force by 5 times. Output 500cm2 Input 100cm2

Hydraulic Systems In order to really see why hydraulic systems can increase a force you can also apply Pascal's principle to the math of the pressure equation. Forceinput = 10N Input area (the size of the piston) = 10cm2 Pressureinput = 10N/10m2 = 1Pa. Pressureinput = Pressureoutput Output area = 50cm2 Forceoutput = Pressureinput x output area Forceoutput = 1Pa x 50cm2 = 50N Pascal’s principle

Hydraulic Systems If the input force is 10N then the output force will be magnified to 50N relative to the size of the output piston. The tradeoff is the distance that the input piston has to move. This is because of the work equation. Work input = work output & what you will learn is work = force x distance!

Hydraulic Systems It is here that you can see the benefit of hydraulic systems. The input force is 1/3 the output force but because it is applied over 3 times the distance, the force gets multiplied by 3 but the distance the force travels is merely 1/3. A useful tradeoff.

Common Hydraulic Systems Floor jacks Dump trucks Power steering systems Hydraulic breaks Bike pumps Your heart

Hydraulics Summary Complete your illustrations for the bike pump. Explain how the force applied is transmitted through the pump so that a greater force is pushed out of the nozzle. You have 5 minutes then we will discuss.

Introduction to Pressures in the Air What would you predict to happen if I put this ping pong ball in the stream of air coming from this hair dryer. The principles that are at work in this situation directly relate to the transmission of pressure and how fluid pressures work. Hair Dryer suspends ping pong ball.

Bernoulli’s Principle Bernoulli’s principle states as the speed of a fluid increases (this includes air too), the pressure within the fluid decreases. Try a simple experiment. Take a piece of paper as I show you and blow across the top side of the paper. What happened? What did you expect to happen? Why did the paper behave the way it did?

Bernoulli’s Principle According to Bernoulli’s Principle, the air you are blowing has less pressure than the air below the paper. The greater pressure below the paper pushes the paper up. Re-observe the ping pong ball demonstration. This principle accounts for why the ball stays in one spot rather then flying up to the ceiling because of the low pressure area above the ball.

Bernoulli’s Principle This principle is the reason why birds and planes can get lift. Lift is the upward force caused by the difference in pressures between the top and bottom of a wing. LIFT

Bernoulli’s Principle Bernoulli’s principle is the main reason why planes and birds can get lift but it’s also used in reverse sometimes. But why do some cars have a spoiler on the back? Right, to create a downward force. This is because of Bernoulli's principle.

Spray Bottles Bernoulli's principle is used to create a spray system too. Observe the following illustrations.

A Hose-End Sprayer

A Hose-End Sprayer

A Hose-End Sprayer This creates a vacuum at the top of the tube in the sprayer can that pulls the solution up.

A Hose-End Sprayer

A Hose-End Sprayer

Is the green “fertilizer” solution pushed up the tube or pulled? A Hose-End Sprayer Where is the Pressure Highest? Where is Pressure Lowest? A B C D Is the green “fertilizer” solution pushed up the tube or pulled?

Other Bernoulli Affects The Magnus affect with the Bernoulli affect This gives a baseball or soccer ball the ability to curve.

Other Bernoulli Affects Can you pick up a ping pong ball with air being blown?

Bernoulli’s Principle Summary Complete your illustrations. Explain how Bernoulli’s principle will keep the ball from flying away. You have 5 minutes then we will discuss.

Journal Entry List the top 3 things you learned today & yesterday. Please write minimum 3 sentences, maximum 5 or so. Quiz tomorrow.

Summary Section 13.2 According to Pascal’s principle, a change in pressure at any point in a fluid is transmitted equally and unchanged in all directions. In a hydraulic lift system, an increased output force is produced by a constant fluid pressure exerted on the larger area of the output piston. According to Bernoulli's principle, as the speed of a fluid increases, the pressure within the fluid decreases.

Section 13.2 Worksheet Due tomorrow. Thursday you’ll have quiz 13.2.

Quiz 13.2 (2 pts each = 20pts) Summarize Pascal’s principle. Describe how a hydraulic system is able to increase force. Describe the relationship between fluid speed and fluid pressure. How does a plane wing produce lift? What would happen to a blow-up balloon that is held as you sink down to the bottom of a pool? The area of an output piston is 25x greater than the input piston. If the input force is 40N, what is the output force? How does the output distance compare to the input distance? Two pieces of paper are held a few inches apart. Which direction to the papers move if you blow in-between them? What principle explains this? If two cars pass each other going in opposite directions, would they be pushed apart of pulled together?

Quiz 13.2 Answers Summarize Pascal’s principle. A change in pressure at any point in a fluid is transmitted equally & unchanged in all directions throughout the fluid. Describe how a hydraulic system is able to increase force. The increased output force is produced b/c the fluid pressure is exerted on the larger output area of the output piston. Describe the relationship between fluid speed and fluid pressure. As the fluid speed increases the fluid pressure decreases. How does a plane wing produce lift? Using Bernoulli’s principle, the faster moving air on the top of the wing produces a low pressure area. The higher pressure below the wing drives the wing upward to equalize the pressure. What would happen to a balloon that is pulled to the bottom of a pool? The balloon would be compressed the further down you pull it. The area of an output piston is 25x greater than the input piston. If the input force is 40N, what is the output force? It ultimately is 25x the input force (40N) = 1000N How does the output distance compare to the input distance? The output distance is 25X smaller than the input force to balance out the work. Two pieces of paper are held a few inches apart. Which direction to the papers move if you blow in-between them? They move together. What principle explains this? Bernoulli’s principle. If two cars pass each other going in opposite directions, would they be pushed apart of pulled together? Pulled together because of Bernoulli’s principle.