Vacuum systems Calculations

In Chapter 2, essential terms in vacuum technology (e.g. pV-throughput, pumping speed, conductance, etc.) were defined. These are required for the quantification of gas loads in vacuum systems. Calculations based on relevant relationships were demonstrated (Examples... 

Metallization layers are generally deposited either by CVD or by physical vapor deposition methods such as evaporation (qv) or sputtering. In recent years sputter deposition has become the predominant technique for aluminum metallization. Energetic ions are used to bombard a target such as soHd aluminum to release atoms that subsequentiy condense on the desired substrate surface. The quaUty of the deposited layers depends on the cleanliness and efficiency of the vacuum systems used in the process. The mass deposited per unit area can be calculated using the cosine law of deposition ... 

When you write on a blackboard with chalk, you are not unduly inconvenienced if 3 pieces in 10 break while you are using it but if 1 in 2 broke, you might seek an alternative supplier. So the failure probability, Pf, of 0.3 is acceptable (just barely). If the component were a ceramic cutting tool, a failure probability of 1 in 100 (Pf= 10 ) might be acceptable, because a tool is easily replaced. But if it were the window of a vacuum system, the failure of which can cause injury, one might aim for a Pf of lO and for a ceramic protective tile on the re-entry vehicle of a space shuttle, when one failure in any one of 10,000 tiles could be fatal, you might calculate that a Pf of 10 was needed. 

The material properties of window glass are summarised in Table 18.1. To use these data to calculate a safe design load, we must assign an acceptable failure probability to the window, and decide on its design life. Failure could cause injury, so the window is a critical component we choose a failure probability of 10The vacuum system is designed for intermittent use and is seldom under vacuum for more than 1 hour, so the design life under load is 1000 hours. 

Another design approach for calculating saturated gas loads for vacuum systems is given in Reference [28]. 

Pressure/vacuum, 435, 466 Vacuum systems, 343 Absolute pressure conversions, 363 Air inleakage, 366 Calculations, 366-375 Dissolved gases release, 368 Estimated air inleakage, table, 366 Evacuation time, 371 Maximum air leakage, chart, 367 Specific air inleakage rates, 368 Temperature approach, 375 Classifications, 343 Diagrams, 380 Pressure drop, 353 Pressure levels, 343, 352 Pressure terminology, 348 Pump down example, 381 Pump down time, 380 Thermal efficiency, 384 Valve codes, 26... 

The importance of the first three of these factors has already been discussed. The temperature factor would include the cost of insulation plus the increase in metal thickness necessary to counteract the poorer structural properties of metals at high temperatures. Zevnik and Buchanan17 have developed curves to obtain the average cost of a unit operation for a given fluid process. They base their method on the production capacity and the calculation of a complexify factor. The complexity factor is based on the maximum temperature (or minimum temperature if the process is a cryogenic one), the maximum pressure (or minimum pressure for vacuum systems) and the material of construction. It is calculated from Equation 2 ... 

The Sieverts-type apparatus consists of a calibrated volume determined physically, a reactor whose temperature is controlled by the temperature control system and the cooling system, a vacuum system, a pressure monitoring system, valves, and source of hydrogen and argon delivery. The quantity of desorbed hydrogen (number of molls) is calculated using ideal gas flow ... 

When simultaneously pumping permanent gases and condensable vapors from a vacuum system, the quantity of permanent gas will often suffice to prevent any condensation of the vapors inside the pump. The quantity of vapor which may be pumped without condensation in the pump can be calculated as follows ... 

For dehydration, place the platinum (nickel) crucible with the prepared salt ( 5 g) into a test tube with a standard ground-glass joint (Fig. 63). Preliminarily weigh the crucible and the salt with an accuracy up to 0.01 g. Connect the test tube to a vacuum system. Evacuate it (10- mmHg) first at room temperature during 10-20 min, and then at 150 °C on an oil bath or a bath with Wood s alloy. Dehydrate the substance up to a constant mass. Calculate the composition of the product according to the change in its mass. 

Sufficient data are given for finding the heat balance and the liquor circulation rate, and for sizing the auxiliaries such as lines, pump, heat exchanger and vacuum system, but those calculations will not be made. 

The clean, dry, calibrated bulb is attached to a vacuum system, such as site A on the line illustrated in Fig. 5.2, and evacuated to 10-3 torr or lower. Gas may be admitted to the calibrated bulb by isolating the working manifold from vacuum and opening the stopcocks and valves leading to one of the upper gas storage bulbs, C, while the pressure is monitored by manometer D. When the desired pressure is reached, the valve on the storage bulb is turned off, pressure and temperature measurements are made, and then the stopcock on the calibrated bulb is turned off. At this stage we know the pressure, temperature, and volume of the gas in the calibrated bulb, which permits the calculation of the number of moles via the ideal gas equation. 

Fig. 7.2. A versatile bubbler manometer. The bubbler manometer Is securely mounted by the reservoir and attached to the vacuum system. It is then easily filled by the following process. The level of the bottom end of the vertical tube dipping into the reservoir is marked on the outside of the reservoir. Next, a calculated amount of mercury is filtered into the reservoir. With the valve between the two arms open, a vacuum is slowly drawn on the manometer. The mercury level must not drop below the mark on the reservoir, or else bubbles will enter the vertical tube and shoot mercury through the vacuum system. If the mercury level in the reservoir comes close to the mark, the manometer is brought up to atmospheric pressure and more mercury is added. When the proper amount of mercury is present in the fully evacuated manometer, the mercury level should be about 10 mm above the mark on the reservoir, and the upper meniscus should be in a region of the manometer suitable for measurement, as illustrated. Once the manometer is properly filled and evacuated, the valve is closed to isolate the reference arm at high vacuum.

In Chapter 1, the types of gas flow that could be established in vacuum systems were defined. This chapter deals with the quantification of viscous and molecular flow for simple, model systems (pipelines of constant, circular cross-section, orifices and apertures, etc.). These are nevertheless useful, and worked examples are presented to encourage users to quantify existing or proposed systems and to provide reassurance that calculations are not only relatively straightforward but very useful indeed. 

A stainless steel high vacuum system (V = 15L) has been pumped for 36 h and the pressure is 1 x 10 7 mbar. A pressure-rise test, starting at 10 5 mbar, shows a pressure of 1.5 x 10"3 mbar after 20 min. Calculate the amount of gas entering the chamber and comment on the source of the gas. 

The walls of a vacuum system have a surface area of 4 m2. The specific outgassing rate ( lh) is 4 x lO PanPs-1 m-2 and a = 1. If it is assumed that there are no other significant gas sources, calculate the pumping speed necessary to achieve lO mbar after 55 min. 

From values of / and c, the diffusion coefficient (D) and dynamic viscosity (q) can be calculated (Examples 1.16-1.19). Estimation of the Knudsen (H d) and Reynold s numbers defines the nature of gas flow (viscous, molecular, intermediate) in vacuum systems (Examples 1.20-1.22). 

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