The concept of pressure can be used to explain the behavior of liquids.
The plaque floats downstream until it reaches another narrow opening, where it may become lodged and applyNewton's second law completely stop blood flow.
If this happens in an arteries.
In this chapter, we will learn how plaque can cause blood to flow faster through an arteries and how plaque can be removed from the wall of the arteries.
The fluid's pressure increases when the ball is deeper in the air.
The fluid was at rest in all of them.
We will explain phenomena involving fluid dynamics in this chapter.
To answer questions like this, we must compare the forces that stationary air exerts on a surface to the forces on the sur face by moving air.
We know the directions of the forces that external objects exert on these systems and can deduce the direction of the net force due to air pressure on different sides of these objects.
The right bulb is the system.
The bulb is being moved.
The pressure of air is E on B.
Something is pushing up from below.
The air pressure on the side of moving air is less than on the side of stationary air.
The floating balloon is the system.
The Earth is moving downward.
The analysis of each experiment using the force diagrams shows that moving air exerts a smaller force on the system than stationary air.
The air exerts a net force on the object in the direction of the side past which the air was moving in each of the three experiments.
The stationary air exerts more pressure on the object than the moving air.
There are two explanations for the pattern.
The pressure on one side of an object decreases because a moving fluid is warmer than a stationary fluid, and the warm fluid has a lower density than the cold fluid.
As the speed with which the fluid moves across the surface increases, the pressure that a fluid exerts on a surface increases.
An experiment that can disprove one or both of these explana tions is what we're going to do.
The paper rises when a piece of moving air comes from your body.
The paper will rise.
There is less pressure on the top surface when the air is moving compared to the stationary air below the paper.
The paper will rise when the pressure from below is greater.
The card is not straight.
The warm air from if you vigorously breath is less dense than surrounding blow air and tends to rise.
Both explanations predicted the outcome.
Both explanations can be rejected based on this experiment.
The outcome matches the prediction based on Explanation 2 and is different from the prediction based on Explanation 1.
We can reject Explanation 1 based on the experiment's outcome.
Experiments did not reject Explanation 2.
The difference in the pressure of stationary and moving air increases when air speed increases.
We can assume that as a fluid's speed increases, the pressure that the moving fluid exerts on the surface de crease.
Explanation 2 is a qualitative version of a rule formulated in 1738 by Daniel Bernoul.
The greater the speed of the fluid, the lower the pressure.
Bernoul i's principle has important fluid-flow implications in biological systems, for example, in the flow of blood through blood vessels.
When the blood is moving fast, the pressure against the wall is lower.
Bernoulli's principle has two other applications.
A clarinet is a musical instrument.
The air pressure across the top of the reed decreases relative to the air pressure below it.
The pressure above and below the reed equalizes once the mouth is closed.
The air flows across the top of the reed to the bottom.
The is not moving and the pressure above the reed drops.
The opening and closing of the reed are rhythmic.
There is a snoring sound when air moves through a narrow opening above the process.
The soft palate is closed when the air is not moving.
When the starting air flow stops, the pressures equalize and the passage reopens.
The first 1 had lightbulbs.
Air not moving below the palate is at a higher flow rate.
The pressure of a fluid against a surface is closed.
We need to quantify the rate 3 in order to apply this idea later.
The soft palate reopens when the pressures equalize.
Maybe you took a shower in which a small amount of water flowed from the shower head.
The water flow rate was low.
The snoring sound is caused by the vibrating palate and air flow.
A larger flow rate will get you cleaner.
The flow rate should be related to the speed of the fluid.
Figure 11.4a can be used to explore the relationship.
The aorta has a diameter of 1.5 cm and an average flow rate of 80 cm3>s.
The average speed of the aorta is determined.
The flow rate can be rearranged.
The unit is correct.
The magnitude is about half a meter per second.
If the diameter is reduced from 1.5 cm to 1.0 cm, you can determine the average speed of blood flow.
Blood speed goes up when the aorta diameter goes down.
The flow rate of fluid through a vessel is influenced by the diameter of the vessel.
The faster the blood flows, the greater the risk of dislodging plaque.
The narrower the airway from the nose to the mouth, the faster the air moves and the more likely you are to snore.
The effects are dependent on the speed of the fluid, like blood or air in different parts of a vessel or pipe in which the diameter changes from one section to another.
Let's see if we can tell the difference between one part of a vessel and another.
There is a pipe carrying fluid.
If the fluid was compressed, it would take up a wide opening.
In order to keep the flow rate constant, the speed will be increased.
The figure below shows the speed of the blood as it passes through the constriction.
10 cm/s is the measurement.
One of the arteries has its normal value reduced.
The cross-sectional areas should be 90 cm/s.
As fluid speed increases, the fluid pressure against a surface decreases.
The flow rate of a fluid through a pipe depends on the speed of the fluid and the cross-sectional area of the pipe.
There are differences in pressure that cause fluid flow.
The blood flow from the arterial side to the ve nous side has a gauge pressure of about 100mm Hg.
Different types of fluid flow are familiar to us.
There is a smooth flow in a wide river and a more tur bulent flow in a narrow chan nel.
There are two types of fluid flow in wind tunnels.
Turbulent flow occurs when a fluid moves quickly.
If you design a car so that air moves over it with streamline flow, you can reduce the drag force that the air exerts on the car and improve gasoline mileage.
The qualitative version of Bernoul i's prin ciple was developed earlier in the chapter.
We assume that the fluid is incompressible, that the fluid flows without friction, and that the flow is streamlined.
The work-energy equation can be used to describe the behavior of the fluid as it moves.
The initial state of the system is shown in Figure 11.10a.
The left side of the volume has a cross-sectional area.
The right side of the volume has a cross-sectional area.
The equation is applied to fluid flow.
The fluid in front is negative.
The volume of fluid moved from position 1 to position 2 as a result of the work done on the system.
Since we assume the fluid is incompressible, the volume of fluid stays constant.
The fluid is moving faster through the narrow tube at position 2 than it was earlier when moving through the wider tube at position 1.
The fluid at position 2 is at a higher elevation than the fluid at position 1.
The work done by the fluid behind and ahead of the shaded volume changed the energies.
The generalized work-energy equation can be used to represent this.
We should write expressions for each of the terms in the equation.
The system is being worked on by two forces.
Positive work can be done if it points in the direction of the system.
Negative work is done when it points in the opposite direction of the system.
The fluid is incompressible.
The above three expressions can be replaced with Eq.
The right side of the equation shows energy density as the same as energy per unit of volume of fluid.
The amount of work done on the fluid per unit volume is shown on the left hand side.
Bernoulli's equation describes the flow of a pressible fluid.
The equivalent of Bernoul i's prin ciple is the equation.
Bernoulli's equation is difficult to use for visualization of fluid dynamics processes.
Since Bernoulli's equation is based on the work-energy principle, we can use bar charts similar to the ones used in Chapter 6 to represent such processes.
A fluid dynamics bar chart is described in the Reasoning Skill box.
There is a fire in the building.
Just after leaving the pump to the pressure at the exit of the smal hose, compare the pressure in the hose.
Take a picture of the situation.
A fluid dynamics bar chart can be created.
Draw a sketch of the process.
Pick positions 1 and 2 at appropriate locations in order to answer the question.
One of the positions could be a place where you want to know the pressure in the fluid and the other one could be a place where the pressure is known.
The exit of the pump and the exit of the water from the smal hose are the locations of the unknown pressure.
Place bars of relative lengths on the chart to represent this process.
The easiest way to start is by analyzing the potential energy density.
The origin of the vertical coordinate system should be chosen for the fire hose process.
The energy density at position 1 is zero.
The exit of the water from the smal hose is at a higher elevation and there is a positive potential energy density bar for position 2.
Consider the energy that comes from it.
The water flows from a wider hose to a narrower one.
The longer bar at position 2 is due to the greater energy density at 2.
The bar for position 1 is one unit and the bar for position 2 is three units.
The bars on the right side of the chart are longer than the bars on the left side.
We need to account for the change in pressure.
There is a shaded box in the center of the bar chart.
The total difference in energy densities should be accounted for by the difference in the pressure heights.
The bar chart is complete.
We can use it to write a mathematical description for the process.
Work-energy bar charts and Bernoul i bar charts are very different.
We adapt our problem-solving strategy in this section.
We show a strategy for finding the speed of water as it leaves a bottle.
The general strategy is on the left side of the table while the specific process is on the right.
The hole is 10 cm deep.
Take a picture of the situation.
The fluid where the pressure, elevation, and speed are known is where you know the points 1 and 2 at positions in water leaves the hole.
Assume that the fluid flows without ing.
Is it possible to assume flow friction.
A bar chart is a representation of the process.
The sketch and bar chart show the speed of the fluid at Bernoulli's equation.
Bernoul's pressure is atmospheric at 1 and 2.
The answer changes in limiting cases and so forth.
The correct unit for speed is the unit m/s.
If we got 120 m/s it would be too high, but the magnitude seems rea sonable.
There is a horizontal distance away from the bottle from where the water streams onto the floor.
The floor is close to the hole.
Predict this horizontal distance using your knowledge.
If we were to perform the experiment with a small hole, the water would land short of our prediction.
We need to increase the diameter of the hole to 3mm in order to land the water.
In the chapter, we discuss the effect of friction on fluid flow.
The shaded water is the Earth.
After a rainstorm, the basement is filled with water to a depth of 0.10 m. A water pump with a short 1.2- cm-radius outlet pipe connects to a 0.90- cm-radius hose that goes out the basement window to the ground outside.
Water can be removed from the basement at a rate of 6.8 m3>hour.
Determine the time interval needed to remove the water and the water pressure at the pump outlet pipe.
A sketch of the situation is shown.
The water is in the basement, in the pump, and in the hose.
The pump isn't part of the system.
Bernoul's equation is used to determine the pres upward with its origin at the pump outlet pipe.
There is a pump outlet pipe.
We want to determine the pressure.
The time interval needed to remove the water is mine.
The flow rate is 6.9 m3/h.
Since the fluid flow rate must be the same at both intervals, the time hose is necessary.
The unit for time interval is correct, and the magnitude is normal for pumping water from the basement or turbulence.
Take hours, not minutes or years.
We are at the pump outlet.
The energy density changes should be included in the expression for flow rate.
The fluid moves quickly.
The narrower hose at position 2 is larger than the wider one.
The final energy density is determined using Eq.
15 m3 equals 1150 m2210.10 m2.
Bernoulli's equation can be applied to a pump from most hardware stores.
Each nonzero bar in the chart has a nonzero term in it.
Assume that the hose from the pump to the outside has a diameter of 0.90 cm.
We assumed in our previous discussions and examples that fluids flow.
We assumed there was no interaction between the fluid and the walls of the pipes they flow in.
For many processes, such as the transport of blood in the small vessels in our bodies, fluid friction is very important.
Take a look at the following situation.
You have an object that can slide on a horizontal surface.
You let go when you push the puck.
Even if nothing else pushes the puck, it will continue to slide at a constant speed with respect to the ice.
If there is a little sand in the ice, the puck slows down and someone or something has to push it forward to balance the opposing force.
If a fluid flows through a horizontal tube with no forward pressure, we would expect it to continue to flow at a constant rate.
There must be more pressure at the back of the fluid than at the front of it.
The force on the fluid due to the forward pressure is greater than the force on the fluid due to the opposite pressure.
The flow rate can be affected by the physical properties of the fluid and the vessel.
The quantities are important.
It is more difficult to push fluid through a small tube than it is through a large tube.
A long tube has more resistance to flow than a shorter tube.
The water flows more quickly than molasses.
The flow should be affected by thethickness orstickiness of the fluid.
The data is reported in units.
The flow rate increases rapidly as the radius increases.
The flow rate increases by a factor of 16 1242.
The flow rate increases by a factor of 81 1342.
As the length of the tube increases, we can see that the flow rate dewrinkles.
The type of fluid was not investigated in this experiment.
Water flows faster than oil under the same conditions.
The fluids have different flow rates if we push them through the same tube with the same pressure difference.
Jean Louis Marie Poiseuille established a relationship between physical quantities using an experiment similar to that described above.
He wrote an expression for the pressure that was needed to cause a particular flow rate, instead of writing the flow rate in terms of the other four quantities.
The net force pushing the fluid is similar to the pres.
This idea of the pressure difference needed is related to the circulatory system and can be used to cause the same flow rate.
Poiseuille's law can be used to determine the unit for viscosity.
To do this, we need 16 times the pressure to be different.
The latter equation is used to find the units.
The units for flow rate are m3>s.
The last combination of units can be changed to N # s>m2.
We rearranged Poiseuil e's law person's heart rate.
The New Rolin Graphics jr vessel is reduced to 0.10 times its original value.
The person's blood pressure will increase as a result of the reduced flow rate.
Concepts from fluid dynamics can be used to explain phenomena.
A roof being ripped off a house during a high-speed wind and the dislodging of plaque in an arteries is analyzed in this section.
You've seen pictures of roofs being blown from houses during hurricanes.
On a windy day, the air inside the house is not moving, whereas outside the air is moving very quickly.
Net pressure against the roof and windows is created when the air pressure inside the house is greater than the air pressure outside.
The roof and win dows will blow off the house if the net pressure is great.
A quantitative estimate of the net force exerted by the inside and outside air on a roof is done in the following example.
Bernoul i's equation is used to find the pressure difference.
The situation is shown.
We can now determine the net force of the air on the roof.
The net force is enough to lift the roof.
The air at the Rolin Graphics is incompressible and flows without pressure.
One ends up in the house under its roof because the roof is thin and the air is barely moving.
The other passes just above the roof with the air moving fast.
The energy density would be the same at both oints 1 and 2.
A trailer is covered by a 2.0 m canvas.
The trailer is moving at 29 m/s.
The net force on the canvas is determined by the air above and below it.
Take a look at the houses.
The plaque may block a large portion of the roof.
If the house is the location of the vessel opening, then it is from there.
The normal value is about one-ninth that.
The air pressure in the narrowed portion of the arteries is 9 times greater than the liquid in the glass, which is in the unblocked part of the vessel.
It is 81 times greater in the air in the straw.
In Bernoulli's equation, the sum of the three terms should be the same at some other location along a streamline.
As blood speeds by the plaque, its energy density is 81 times greater, and consequently its pressure is less than the pressure in the open vessel just before and just after the plaque.
A blood clot can be caused by a pressure differential that causes the plaque to pul ed off the wal and tumble down stream.
The net force that the blood exerts on the plaque is estimated.
Blood flows through the unobstructed part of a blood at a speed of 0.50 m/s using Bernoulli's equation.