Pressure measurements related to the fluid systems are the topic of this chapter. Absolute pressure refers to the absolute value of the force per unit area exerted on the containing wall by a fluid. Gage pressure represents the difference between the absolute pressure and the local atmospheric (atm) pressure. Vacuum represents the amount by which the atmospheric pressure exceeds the absolute pressure Pressure Measurements

Atmospheric pressure Negative gage pressure or vacuum Positive gage pressure P(absolute)

The standard SI unit for pressure is the (N/m ) or Pascal (Pa). 1 atm = x10 Pa = 760 mmHg Fluid pressure results from a momentum exchange between the molecules of the fluid and a containing wall. Pressure Measurements 2

For an ideal gas, the pressure is given by: P = (n)(k)(T) where: n: is the molecular density k=1.3803x10 J/molecule T: absolute temperature The mean path ( ) is the average distance a molecule travels between collisions = 2.27x10 T/P, T in K and P in Pa Pressure Measurements

Mechanical devices offer the simplest means for pressure measurements. The barometer is a device used to measure the atmospheric pressure Consider the U-tube manometer shown in figure 6.3. A pressure balance of the tube columns dictates that: P – P a = gh(  m -  f ) Mechanical Pressure- Measurements devices

Refer to figure 6.7 Bourdon-Tube Pressure Gage

Diaphragm and bellows gages measures pressure based on sensing the elastic deformation of materials as a result of pressure. The diaphragm deflection will be according to the pressure difference. The deflection is measured by appropriate displacement transducers or strain gages Diaphragm and Bellows Gages Diaphragm P2P2 P 1

The deflection generally follows a linear variation with  P when the deflection is less than 1/3 the diaphragm thickness. Consider figure 6.12 for a bellows gage. The pressure difference causes the bellows movements which may be converted into electrical or mechanical signal. LVDT can be used as a pressure gage…(figure 6.14) Diaphragm and Bellows Gages

The linear variable differential transducer (LVDT) assembled with a diaphragm can be used as a differential pressure gage. (see figure 6.14) The displacement of the core is connected with the diaphragm movement, which is in turn, indicates the pressure difference P 2 -P 1. The LVDT

It is known that the resistance of fine wires changes with the pressure according to: R = R 1 (b +  P) where: R 1 : is the resistance at 1 atm b: pressure coefficient of the resistance This gage can measure pressures as high as 100,000 atm The Bridgman Gage

It is known that, at low pressures, the effective thermal conductivity of gases decreases with pressure. The Pirani gage is a device that measures the pressure through the change in thermal conductance of the gas. The amount of heat loss-which depends on the gas conductance- from a heated filament wire, located in a vacuum space, indicates to the vacuum value. The Pirani Thermal-Conductivity Gage To vacuum space To bridge circuit

Another way that is used to sense the vacuum is through measuring the variation in resistance of the filament material. Pirani gages measure vacuums in a range of Pa since the thermal conductance changes very little above these pressures. The Pirani Thermal-Conductivity Gage

The Alphatron is a radioactive ionization gage, as shown in figure A small radium source emits alpha particles which ionize the gas inside the enclosure. The ionization degree is determined by measuring the output voltage E o. The E o is in fact linearly directed with the vacuum connected to the gage enclosure. The measuring range for this gage is 0.1 to 10 Pa. The Alphatron