Chapter 4 – Pressure and Sound Measurement

23/4/20 [email protected] 1

Chapter 4 – Pressure and Sound Measurement

Pressure:A force F perpendicular to an area A, the pressure

Unit of Pressure:Pa(N/m2)Used in Engineering: atm,at,mmH2O,mmHg,mbar 1 atm=1.013×105Pa ( 标准大气压 )

=760mmHg =1.033×104mmH2O =1.013×103mbar

P— 压力；F— 垂直作用力；S— 受力面积



Pressure Terms

Atmospheric pressure: the atmosphere surrounding the earth exerts a force on the unit earth surface, that is the pressure caused by the weight of the atmosphere. It varies with weather condition, the height above sea level , latitude.

Perfect Vacuum or pure vacuum ,which contains

no molecules, forms the primary standard for

absolute zero pressure.



Positive pressure( 正压 ): the gauge pressure when the absolute pressure is higher than the atmospheric pressure.

Gauge pressure( 表压力 )Pg: the pressure measured relative to the atmospheric pressure.

The differential pressure between the absolute pressure and the atmospheric pressure.

Absolute pressure( 绝对压力 )Pabs: used for the pressure measured relative to zero pressure.


Negative pressure( 负压 ): the gauge pressure when the absolute pressure is lower than the atmospheric pressure.

Vacuum( 真空度 ): the absolute pressure lower than atmosphere.


Where is the reference pressure.

Absolute pressure is a positive number. And Gauge pressure can be positive or negative.

Gauge pressure( 表压力 )Pg:

一般压力检测表所指的压力是表压力或真空度


There are two types of fluid systems; static systems and dynamic systems.A static system is one in which the fluid is at rest and a dynamic system is on in which the fluid is moving.

Static systems and dynamic systems


Static Pressure

The pressure measured in a static system is static pressure.


Static PressureThe absolute pressure at a depth H in a liquid is defined as: Pabs = P + (ρ x g x H) Where: Pabs is the absolute pressure at depth H. P is the external pressure at the top of the liquid. For most open systems this will be atmospheric pressure. ρ is the density of the fluid. g is the acceleration due to gravity (9.81 m/sec2)).H is the depth at which the pressure is desired.


DYNAMIC PRESSURE SYSTEMS

In a dynamic system, pressure typically is defined using three different terms. The first pressure we can measure is static pressure. This pressure is the same as the static pressure that is measured in a static system. Static pressure is independent of the fluid movement or flow. As with a static system the static pressure acts equally in all directions.


DYNAMIC PRESSURE SYSTEMS

The second type of pressure is what is referred to as the dynamic pressure. This pressure term is associated with the velocity or the flow of the fluid.

The third pressure is total pressure and is simply the static pressure plus the dynamic pressure.



Static and Dynamic PressureDynamic Pressure = Total Pressure - Static Pressure



1.Manometers （液体式压力计） U-tube manometer The cistern manometer （槽式压力计） The inclined tube manometer

2.Elastic Pressure transducerDiaphragms( 薄膜，弹性式压力计）

Diaphragms( 薄膜，弹性式压力计）

Reluctance diaphragm gauge （磁阻式） Capacitance diaphragm gauge

Bourdon tubes

Pressure Measurement Methods


3 、 Force-balance

Dead-weight tester( 活塞式压力计 )

Spring ( 弹性力平衡方法 )

4 、 Electrical pressure gauge

•Strain gauge

•Piezoelectric

•piezoresistance •Resonant


Uses the changes in resonant frequency in a sensing mechanism to measure stress, or changes in gas density, caused by applied pressure.

Resonant


P2

P1

1 2P P gh

The basic manometer consists of a U-tube containing a liquid.A pressure difference between the gases above the liquid in the two limbs produces a difference h in vertical heights of the liquid in the two limbs.

If one of the limbs is open to the atmosphere then the pressure difference is the gauge pressure.

Manometers


Water, alcohol and mercury are commonly used manometric liquids. U-tube manometers are simple and cheap and can be used for pressure differences in the range 20 Pa to 140KPa. The accuracy is typically about 1%.

•Temperature affect---------liquid expansion


Thus the pressure when measured by a U-tube manometer at a temperature , when the manometer liquid density at 0°C is known, is given by:

0

1

h gP gh


Manometer CorrectionsManometers can be very accurate and are frequently used as a calibration reference. It can therefore be important that you correct for changes in the parameters which lead to pressure--namely the fluid density and acceleration due to gravity.

According to Merriam (who makes the mercury manometer in the lab), the correction for these effects is

where the o subscripts denote standard values (sea level at 0ºC) and the t’s refer to the actual values. The standard values are

go = 980.665 cm/s2

o = 13.5951 g/cm3 (mercury)


The density of mercury varies with temperature like

The local acceleration due to gravity varies with latitude, altitude, and most interestingly, with the surrounding altitude. Sea level acceleration, gx, varies with latitude x (in degrees) like

Above sea level,

where H is elevation in feet and H’ is the average elevation of the general terrain within a radius of 100 miles


Cistern manometer( 贮液槽式液体压力计 )

An industrial form of the U-tube manometer is cistern manometer. It has one of the limbs with a much greater cross-sectional area than the other.A difference in pressure between the two limbs causes a difference in liquid level with liquid flowing from one limb to the other.

1 2

1 2

2 21 2

1 1

( )

( ) ( 1)

P P gH h d g

A h A d

A d AP P d g d g

A A

c d g

Hhd

P1

P2

A2

A1


This form of manometer thus only require the level of liquid in one limb to be measured from a fixed point.


The inclined tube manometer

The inclined tube manometer is a U-tube manometer with one limb having a larger cross-section than the other and the narrower limb being inclined at some angle to the horizontal. It is generally used for the measurement of small pressure differences and gives greater accuracy than the conventional U-tube manometer.


H d

h

2 21 2 ( 1) ( 1) sin

1 1

A AP P d g gx

A A

xP1

P2

Since A2 is much greater than A1, the equation approximates to:

1 2 sinP P gx

Initial zero level with no pressure difference



Example (p574_ 6.2)


Elastic element ( 弹性元件 )

( 单圈弹簧管 ) ( 波纹管 )

( 平薄膜 )

( 波纹膜 ) ( 膜盒 )


With diaphragm pressure gauges, a difference in pressure between two sides of a diaphragm results in it blowing out to one side or the other. If the fluid for which the pressure is required is admitted to one side of the diaphragm and the other side is open to the atmosphere, the diaphragm gauge gives the gauge pressure. If fluids at different pressures are admitted to the two sides of the diaphragm, the gauge gives the pressure difference.

Diaphragms


a, b : Bourdon tubesc, d : Diaphragmse: Bellow


1.Bourdon tubes


The bourdon tube may be in the form of a “C”, a flat spiral, a helical spiral. In all forms, an increase in the pressure in the tube causes the tube to straighten out to an extent which depends on the pressure. This displacement may be monitored in a variety of ways, for example, to directly move a pointer across a scale, to move a slider of a potentiometer, to move the core of an LVDT.


图 9-4 弹簧管压力计结构 1- 弹簧管； 2- 连杆； 3- 扇形齿轮；

4- 底座； 5- 中心齿轮； 6- 游丝； 7- 表盘； 8-

指针；9- 接头； 10- 横断面； 11- 灵敏度调整

槽

Bourdon 弹簧管压力计


通过调整螺钉可以改变拉杆与扇形齿轮的接合点位置，从而改变放大比，调整仪表的量程。转动轴上装有游丝，用以消除两个齿轮啮合的间隙，减小仪表的变差。直接改变指针套在转动轴上的角度，就可以调整仪表的机械零点。


弹簧管压力计结构简单 , 使用方便，价格低廉，测压范围宽，应用十分广泛。测压范围为 104 ～ 109Pa ；精确度一般为 ±0.5~2 ％ ( 最高可达±0.1 ％ ) 。


弹性元件常用的材料有铜合金、弹性合金、不锈钢等，各适用于不同的测压范围和被测介质。近来半导体硅材料得到了更多的应用。各种弹性元件组成了多种型式的弹性压力计，它们通过各种传动放大机构直接指示被测压力值。这类直读式测压仪表有弹簧管压力计、波纹管差压计、膜盒式压力计等。


2 Reluctance diaphragm gauge( 磁阻式弹性压力计）The displacement of the

central part of the diaphragm increases the reluctance of the coil on one side of the diaphragm and decreases it on the other.

With the two coils connected in opposite arms of an a.c. bridge, the out of balance voltage is related to the pressure difference causing the diaphragm displacement

20 0

2

N sL



Potentiometric Pressure Transducer


Elastic Diaphragms1) Must be able to withstand the load and the fluid type

2) Must be as flexible as sensitivity requires

3) Volume displacement should be minimal to achieve high frequency response

4) Natural frequency of diaphragm should be high

5) Output should be linear?


Flat vs CorrugatedFlat responds faster, but with perhaps with lower sensitivity


Strain Gauge Type

( 应变式压力传感器 )


Diaphragms (strain gage)


Capacitance pressure transducers were originally developed for use in low vacuum research. This capacitance change results from the movement of a diaphragm element. The diaphragm is usually metal or metal-coated quartz and is exposed to the process pressure on one side and to the reference pressure on the other. Depending on the type of pressure, the capacitive transducer can be either an absolute, gauge, or differential pressure transducer.


The capacitor can also form part of the tuning circuit of a frequency modulated oscillator and so give an electrical output related to the pressure difference across the diaphragm.


式中， E 为弹性膜片的弹性模量； u 为材料的泊松比


Piezoelectric Crystal ( 压电式压力传感器 )

压电式压力传感器体积小，结构简单，工作可靠；

测量范围宽，可测100MPa 以下的压力；

测量精度较高；频率响应高，可达 30kHz ，是动态压力检测中常用的传感器。

但由于压电元件存在电荷泄漏，故不适宜测量缓慢变化的压力和静态压力。


Dead-Weight Tester Schematic

Calibration of the pressure gauges in the region of 20Pa to 2000kPa is generally by means of the Dead-weight tester. Pressure is produced by winding in a piston. The pressure is determined by adding weights to the platform so that it remains at a constant height.

Force balance gauge



At static equilibrium the piston will float and the chamber pressure can be deduced as:

A number of elemental errors contribute, including air buoyancy effects,variations in local gravity, uncertainty in the known mass of the piston and added masses,shear effects,thermal expansions of the piston area,and elastic deformation of the piston.


An indicated pressure , Pi can be corrected for gravity effects, e1 and air buoyancy effects, e2 ,by:

p=pi(1+e1+e2)


and for the air buoyancy effects by:

A gravity correction for elevation, ,and latitude, ,can be applied to correct for gravity error effects using the dimensionless correction:

Chapter 4 – Pressure and Sound Measurement

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