Unit 6 Fluids And Pressure

Unit 6 Fluids and Pressure • • • • • • • •

What is a fluid? How is pressure defined? Pressure due to liquid and atmosphere What is gauge pressure 計示壓力 and absolute pressure 絕對壓力? How is pressure measured? What is blood pressure, systole 心臟收縮 and diastole 心臟舒張? How is the blood pressure measured? Bernoulli’s principle 伯努利原理 and its applications

1. Fluids and pressure in fluids Fluids include all liquids and gases. Both the human respiratory and circulatory system contain fluids. Atmospheric pressure, hydraulic pressure, and blood pressure are all examples of fluid pressure. 2. Definition of pressure Pressure is the force applied perpendicularly to a surface of area A, and is calculated by the following equation.

pressure =

force F = area A

Pressure is measured in pascals. 1 Pascal is equal to 1 newton per square meter (N/m2). One Pascal is a small pressure. An apple exerts about 1000 Pascals (Pa) on your hand. The greater the area a force is applied to, the smaller the pressure.

3. Liquid pressure 1. Pressure in a liquid increases with depth because of the greater amount of liquid pushing down. 2. Pressure at a given depth acts equally in all directions. 3. The pressure at a given depth does not depend on the shape of the vessel containing the liquid. It only depends on the depth. 4. Pressure depends on the density of the liquid. The denser the liquid, the greater the pressure at any given depth. .

Pressure due to the weight of a fluid P = hρg

h is the height of the liquid ρ is the density of the liquid g is the gravitational force (9.8 N/kg) The bottom of this container supports all of the weight of the liquid. The sides of the container do not exert any upward force because it is not possible for shear force to be applied on it. 4. Atmospheric pressure The atmosphere also exerts fluid pressure on the Earth. Patm is the static pressure exerted on Earth by the atmosphere at sea level. On a windless day, the column of air on 1.00 m 2 of Earth at sea level weighs about 1.013x 105 N. Patm = 1 atmospheric pressure (1 atm) = 1.013x 105 N/m2 = 1.013 x 105 Pa

Example: At what depth does water exert the same amount of pressure as the entire atmosphere? Calculate the depth at which water exerts pressure equal to 1 atmospheric pressure.  P = hρg

, so h x 1000 kg/m3 x 9.8 N/kg =1.013 x 105 N/m2 h= 10.1 m

5. Gauge Pressure, absolute pressure The pressure in the blood vessels include the pressure exerted by the blood, and the pressure exerted by the atmosphere. However, only the pressure exerted by the blood matters, since the atmospheric pressure is exerted on the blood going into the heart as well as the blood coming out of the heart. The pressure exerted only on the blood is the gauge pressure (Pg). This pressure is measured relative to the atmospheric pressure (1 atm). This is the pressure that is measured when taking your blood pressure or car tire pressure. The total pressure (pressure of the blood plus the pressure of the atmosphere) is the absolute pressure (Pabs). This pressure is measured relative to a vacuum (0 atm). The total or absolute pressure is equal to the gauge pressure plus the atmospheric pressure. The comparison of two gauge pressures is called relative pressure or differential pressure. Measurements of the pulmonary system 呼 吸 系 統 includes both gauge and relative pressures. The atmospheric pressure is exerted on everything except for things in a rigid air-tight container. This is because of Pascal’s principle. Absolute pressure is equal to gauge pressure plus atmospheric pressure.

Pabs = Pg + Patm • • •

absolute pressure in fluids cannot be negative. the smallest absolute pressure is zero. the smallest possible gauge pressure is Pg = -Patm (i. e. Pabs is zero)

When the absolute pressure of a fluid is less than the value of Patm, its gauge pressure is negative.

6. Measurement of gauge pressure Pascal’s principle 帕斯卡原理: A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. Pascal’s principle is used in remote pressure sensors. The sensor does not have to be contacting the liquid it is measuring because of the undiminished transmission of pressure throughout the fluid. This is useful in measuring blood pressure, since the sensor will not have to contact the blood. In mechanical pressure gauges such as an oil pressure gauge, the pressure of liquid creates a force, which is then converted into a pressure reading.

Open-tube manometer Manometers (壓力計 ) are used to measure gauge pressure. Manometers rely on the principle that the pressure of a fluid is P = hρ g (a) The liquid levels on both sides of the tube are the same. Both sides are open to atmosphere. Therefore atmospheric pressure pushes down on both sides equally. (b) The left side of the tube is open to the atmosphere. Pressure is applied on the right hand side. The positive gauge pressure Pg = hρ g is transmitted to the left hand side of the manometer, supporting liquid column of height h. (c) The pressure applied on the right is less than the atmospheric pressure by hρ g. This is a negative gauge pressure of - hρ g.

Mercury manometer This is a mercury manometer. It is very similar to what is used to measure blood pressure. The left side of the manometer is open to the atmosphere. The right side can be opened to the atmosphere by a valve to release pressure. • The gauge pressure can be represented as millimeters of mercury (mmHg). It may be above or below the atmospheric pressure • The reference point of gauge pressure is 1 atm. • Blood pressure measurement are commonly made by the mercury manometer, and values are usually given in mmHg. • When the valve is open, the mercury level on both sides will be the same since there is an equal amount of pressure on the left and right side • If the valve is closed, the pump can increase the pressure in the manometer. The height of the mercury in the left will show how much pressure has been added.

Barometer Mercury barometers ( 氣 壓 計 ) are used to measure atmospheric pressure. As shown in the diagram, the atmospheric pressure is exerted on the mercury open to the atmosphere, causing the mercury in the closed tube to rise. There is no pressure in the tube because it is a vacuum. The height of the mercury in the closed tube can be used to find the atmospheric pressure which equals hρ g. 1 atm = 760 mm Hg = 760 Torr = 1.013 x 105 N/m2 (Pa) (density of mercury: 13.6 x 103 kg/m3)

7. Blood pressure The left ventricle pumps blood to the arteries (動脈), and causes the pressure in the blood vessels to rise and fall. The blood pressure can be felt on the neck or the inside of the wrist (腕), according to Pascal's principle. Systolic and diastolic blood pressures Systole When the left ventricle contracts, blood pressure in the arteries increases. The aortic valve ( 主動 脈瓣 ) closes when the pressure in the aorta (主動脈) is larger than the pressure in the heart. This is called systole. The corresponding peak pressure is systolic pressure 收縮壓. Diastole The pressure in the aorta then decreases as the blood in it flows to the body. This causes a pressure wave to travel through the arteries that slowly fades. When the pressure in the aorta is less than the pressure in the left ventricle, the aortic valve is forced open. This is diastole. The pressure of the blood when the aortic valve opens is called the diastolic pressure 舒張壓.

8. Measuring blood pressure A common way to measure arterial blood pressure is the auscultatory ( 聽 診 ) method. This method requires a sphygmomanometer (血壓計), which includes of a blood pressure cuff, a hand pump, a mercury manometer, and a stethoscope (聽診器). The cuff used to measure the blood pressure should not be too narrow, or it will falsely raise the blood pressure. The inflatable bladder inside the cuff should have a width that is 40% of the arm circumference, and a length that is 80% of the arm circumference. The stethoscope consists of 4 basic parts: a bell, a diaphragm, tubing, and earpieces. The bell can detect a broad spectrum of sounds and is used to listen to low-pitched heart and lung sounds.

The diaphragm is used to listen to high pitched heart and lung sounds. The tubing should be thick enough so that external noise cannot be heard. Fluid flow in a pipe When a fluid is flowing slowly along a pipe, the flow is said to be steady (laminar flow 層 流 ). Streamlines, which are lines representing the direction of fluid flow, are drawn parallel to the pipe walls. When the liquid flows faster than a certain speed, the friction between the pipe walls and the liquid increases. This creates turbulence, and the streamlines are no longer straight. This is called turbulent flow (湍流). How to determine systolic and diastolic pressures In normal blood arteries, blood travels in a smooth, laminar flow. Nothing special can be heard by the stethoscope in these cases. When measuring blood pressure using the auscultatory method, the pressure of the cuff around the arm increases until the pressure blocks the arterial blood flow. The pressure is slowly released until it falls below the systolic pressure. The pressure of the cuff is now slightly below the systolic pressure, but above the diastolic pressure. The blood will flow in spurts when the blood pressure is above the cuff pressure, and will stop when it is below the cuff pressure. During this time, the blood flow is turbulent, resulting in audible sound. The Korotkoff sounds ( 柯 氏 音 ) can be heard during blood flow.

There are five types o Korotkoff sound.1 The first Korotkoff sound can be heard when the cuff pressure falls just below the systolic pressure. As the pressure in the cuff is allowed to fall further, thumping sounds continue to be heard as long as the pressure in the cuff is between the systolic and diastolic pressures, as the arterial pressure keeps on rising above and dropping back below the pressure in the cuff. The fifth Korotkoff sound is the silence when the cuff pressure falls below the diastolic pressure. The blood flow has returned to normal and is laminar. Blood pressure is measured in millimetres of mercury (mm Hg), and is shown as systolic pressure over diastolic pressure. For example, 120/80.

9. Bernoulli’s Principle (Optional) The following equations apply to an incompressible, frictionless, steady flow fluid.

P + 12 ρ v 2 + ρ g hor= c o n s ta n t P1 + 12 ρ v12 + ρ g h1 = P2 + 12 ρ v22 + ρ g h2 For h1=h2

1

P1 + 12 ρ v12 = P2 + 12 ρ v22

http://en.wikipedia.org/wiki/Korotkoff_sounds

We can conclude from the equation that a higher fluid velocity equals lower fluid pressure.

When air flows between two vehicles, it increases in velocity because of the narrower passageway. This creates a low pressure between the vehicles. The higher pressure on the outside of the vehicles pushes them together.

(a) This Bunsen burner has an adjustable nozzle used to control the amount of air entering to cause combustion (b) This atomizer uses a squeeze bulb to propel air over perfume so that the perfume can be changed into vapour form (c) This aspirator uses high velocity water to create negative pressure to suck air into a tube. It is used by dentists and surgeons. It is also used to drain flooded basements (d) This water heater uses the movement of hot air to suck cool air into its chimney

Check list After studying this unit you should be able to • recall fluids and examples of pressure in fluids • define pressure and recall its unit • recall liquid pressure, connect the pressure in a fluid with its depth and density, P = hρg . • recall atmospheric pressure Patm and the following relation for Patm at sea level: Patm = 1 atmospheric pressure (1 atm) = 1.013x 105 N/m2 = 1.013 x 105 Pa • recall definition of gauge pressure, absolute pressure, and how they are related, the type of pressure in human systems. • Recall pascal ‘s principle, • describe how a open-tube manometer may be used to measure gauge pressure. • describe the principle of mercury manometer and gauge pressure in mmHg • describe the principle of barometer and define the atmospheric pressure in terms of mm Hg height. • Explain what is blood pressure, explain systolic pressure and diastolic pressure • describe parts of sphygmomanometer • describe parts of a stethoscope • explain the difference between steady (laminar) and turbulent flow. • Explain the measurement of systolic pressure and diastolic pressure • Explain the record of a blood pressure measurement: the meaning of the figures. • Recall Bernoulli’s principle and its applications