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 and absolute pressure? •How is pressure measured? •What is blood pressure, systole and diastole? •How is the blood pressure measured? •Bernoulli’s principle and its applications

Fluids and Pressure in fluids Fluids: all liquids and gases Human circulation system and respiration system contain fluids examples of pressures in fluids : – blood pressure – atmospheric pressure – Hydraulic pressure

Pressure F P= A

F is the force applied perpendicularly to area A SI unit for pressure: N/m2 (Pascal) 1 Pa = 1 N/m2 other common unit for pressure: mm Hg (1 atmospheric pressure = 760 mmHg)

The greater the area a force is applied, the smaller the pressure.

Static 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

The bottom of this container supports all the weight of the fluid. The sides of the container do not exert any upward force because it is not possible for shear force to be applied on it.

Atmospheric pressure an example of pressure due to the weight of a fluid standard atmospheric pressure Patm is the average value at sea level (static pressure) 1 atm = 1.013x 105 N/m2 = 1.013 x 105 Pa i.e. on a windless average day at sea level, the column of air on 1.00 m2 of the earth’s surface has a weight of 1.01 3x 105 N

Atmospheric pressure

Question: At what depth does water exert the same amount of pressure as the entire atmosphere? Calculate the depth in water at which water exerts pressure equal to 1.00 atm. 1000 kg/m3 x 10 m/s2 x h=1.013 x 105 N/m2 h= 10.1 m

Gauge Pressure and Absolute Pressure If a pressure is measured relative to 1 atm, then it is called gauge pressure. (Pg 表压 ) Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below it. Comparison of two gauge pressure is called relative pressure or differential pressure. Blood pressure is a gauge pressure. The difference of blood pressure between two points in the pulmonary system is a relative pressure..

If a pressure is measured with respect to vacuum (0 atm), then it is called an absolute pressure. (Pabs 绝对压力 )

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),

Measurement of gauge pressure Pascal’s principle: 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. 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 ) is a device to measure gauge pressure: Pg=ghρ ,

Open-tube manometer (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) A 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. A manometer with one side open to the atmosphere can be used for measuring gauges pressures Pg = hρ g by just measuring h.

Mercury manometer • Gauges pressures can be represented as millimeters of mercury (mmHg) above or below Patm • The reference point of a gauge pressure is 1 atm • Blood pressure measurement are commonly made by the mercury manometer, and values are usually given in mmHg • If the valve is open, then equal pressure on both sides, mercury have same heights; • If the valve is closed, the pump can increase the pressure in the manometer. The height of mercury column on the left will show the pressure added by the pump.

Barometer Mercury barometers ( 氣壓 計 ) are used to measure atmospheric pressure. 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 is atmospheric pressure which equals hρ g . 1 atm = 760 mm Hg = 760 Torr 1 atm = 1.013 x 105 N/m2 (Pa) (density of mercury: 13.6 x 103 kg/m3)

Blood pressures

Systolic and diastolic blood pressures 收缩 壓

舒張 壓

Measuring blood pressure

A Sphygmomanometer

Sphygmomanometer

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 ), and a stethoscope ( 聽診器 ). The main parts of a sphygmomanometer contain a pressure cuff, a hand pump with a valve, a pressure dial or a mercury manometer. 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.

Measuring blood pressure A stethoscope possesses 4 basic parts: a bell, diaphragm, tubing, and earpieces. The bell detects 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 the external noise cannot be heard

Fluid flow in a pipe When a fluid flows 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 walls of the pipe. 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 ).

Fluid flow in a pipe

Laminar flow occurs in layers without mixing.

Turbulent flow mixes the fluid. There is more interaction, greater heating, and more resistance than in laminar flow.

How to determine systolic and diastolic pressures

Below optional

Bernoulli’s Principle For an incompressible, frictionless steady flow fluid, the following sum is constant:

P + 12 ρv 2 + ρgh = constant 2 1 or P1 + ρv + ρgh1 = P2 + 2 ρv2 + ρgh2 1 2

For h1=h2

2 1

P1 + ρv = P2 + ρv 1 2

2 1

1 2

2 2

the greater the fluid velocity, the smaller the fluid pressure

Bernoulli’s Equation

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 .

Applications of Bernoulli’s Principle

(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

Applications of Bernoulli’s Principle (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

Nebulizers (atomizers) are aerosol therapy units in which suspended fine particles or droplets appear in the administered gas. This is accomplished by the Bernoulli principle. Nebulizers of this type are allpurpose and rely on the restriction to convert liquid to vapor.