[276]6._Pressure_measurements_UPD

[276]6._Pressure_measurements_UPD - Languages for...

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Languages for engineering communication - 6 Pressure measurement 6.1 Introduction Pressure is represented as a force per unit area and has the same units as parameter discussed previously in lecture No.4 as stress, F A σ = The new aspect of the same parameter which will be discussed in this lecture is the force exerted by a fluid per unit area on a containing wall. The pressure measurement devices for fluid are usually measure pressure in three different forms: absolute pressure, vacuum and gage pressure. Absolute pressure is the absolute value of the force per unit area exerted on the containing wall by a fluid. Gage pressure is the positive difference between the absolute pressure and the local atmospheric pressure. Vacuum is the negative difference between the local atmospheric pressure and the absolute pressure. Fig. 1 Relationship between pressure terms From these definitions in Fig. 1 we see that: 1. The absolute pressure is usually positive. 2. The gage pressure may be positive or negative (vacuum) 3. The vacuum is usually smaller than the local atmospheric pressure. 1
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Some common units of pressure Because a fluid pressure is result of a momentum exchange between the molecules of the fluid and containing wall, it depends on the total number of molecules striking the wall per unit time and on the average velocity v of the molecules. For an ideal gas the pressure is: 2 2 3 2 2 1 1 [ ] [ ] 3 sec m N p nmv kg Pascal m m = = = (1) where n is molecular density, molecules/unit volume; m is molecular mass and velocity v is root mean square velocity: 2 2 2 2 1 2 3 ....... 3 n rms v v v v kT v v n m + + + = = = (2) where T 0 K is the absolute temperature of the gas, k =1.3803 23 10 / J K - × is Boltzmann’s constant, molecular mass, velocity is: 2 2 2 [ /sec] sec sec J K J Nm kgmm m m K kg kg kg kg = = = = = Since the pressure depends on collisions between the molecules, it should be dependent on the average distance passed by a molecule of radius r between collisions. The mean free path λ in an ideal gas is 2
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2 2 8 r n λ π = [ 3 2 m m m = ] (3) More n smaller is the mean free path. For air the Eq. (3) reduced to 5 2.27 10 [ ] T m p - = × (4) Where 0 T K and pressure p must be in Pascal [ 2 / N m ].The mean free path decreases with increase in the gas pressure p (or the density n ) and with decrease in temperature T. The typical examples of mean free path in air at 20 C were calculated using Eq.(4): 1atm = 1.0132x 5 10 Pa - ( 29 8 1 6.564 10 atm m - = × 1torr = 133.32 Pa ( 29 5 1 4.989 10 torr m - = × 1 m μ = 0.13332 Pa ( 29 1 0.04989 m m = 0.01 m = 1.332 3 10 Pa - × ( 29 0.01 4.989 m m = At a standard conditions (p=1 atm) is quit small (about 0.1A), while in vacuum it reaches several meters length. 6.2 Vacuum devices with electrical output
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This note was uploaded on 11/15/2010 for the course CHEE 638 taught by Professor Hampton during the Spring '10 term at MO Southern.

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[276]6._Pressure_measurements_UPD - Languages for...

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