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Hydrostatic Leveling Systems 19 © 1965 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. 1965 PELISSIER: HYDROSTATIC LEVELING SYSTEMS 19 HYDROSTATIC LEVELING SYSTEMS” Pierre F. Pellissier Lawrence Radiation Laboratory University of California Berkeley, California March 5, 1965 Summarv is accurate to *0.002 in. in 50 ft when used with care. (It is worthy of note that “level” at the The 200-BeV proton synchrotron being pro- earth’s surface is in practice a fairly smooth posed by the Lawrence Radiation Laboratory is curve which deviates from a tangent by 0.003 in. about 1 mile in diameter. The tolerance for ac- in 100 ft. When leveling by any method one at- curacy in vertical placement of magnets is tempts to precisely locate this curved surface. ) *0.002 inches. Because conventional high-pre- cision optical leveling to this accuracy is very De sign time consuming, an alternative method using an extended mercury-filled system has been deve- The design of an extended hydrostatic level is loped at LRL. This permanently installed quite straightforward. The fundamental princi- reference system is expected to be accurate ple of hydrostatics which applies must be stated within +O.OOl in. across the l-mile diameter quite carefully at the outset: the free surface of machine, a liquid-or surfaces, if interconnected by liquid- filled tubes-will lie on a gravitational equipoten- Review of Commercial Devices tial if all forces and gradients except gravity are excluded from the system. The forces and gra- There are two fundamental types of hydro- dients that may disturb an extended well-and- static leveling systems in use today. The first tube system are: most common type is based on the bubble level. 1. Air-pressure gradients In this type of level, a small tube is partially 2. Surface tension filled with liquid and sealed, so that a bubble is 3. Temperature gradients included. 4. Flow gradients 5. Vapor pressure When care is taken to suppress thermal gra- 6. Tides. dients in the liquid with a massive metal housing, the surface of the liquid is accurately level. The While the effect of these forces can be calcu- bubble-in conjunction with an accurately curved lated, inspection disposes of some of them. Air- ground-glass cover- serves as a precise indicator pressure gradients in air conditioned spaces are of the location of the liquid surface. This ref- measured in inches of water with a manometer; erence-level surface can be extended mechani- clearly the system must be hermetically sealed cally (as in the carpenter’s level) with string (as and provided with sealed air-return lines. The in a line level) or optically, using optical systems forces of surface tension cause errors in capil- of modest or highly refined types, depending on laries and small tubes; if measuring wells 2 in. the requirements. The highest precision in the in diameter or larger are used, these errors art of optical leveling has probably been attained will be negligible. The vapor pressure of water at BNL and CERN where careful work in solitude, at room temperature can be quite troublesome if in air conditioned tunnels, yields closures of thermal gradients exist, because a distilling about 0.010 in. /mile. Two weeks or more would system results. A difference of O.l”C between be required for a single optical leveling traverse two parts of the system yields a vapor-pressure of the 200-Be’\; machine. During the survey, no difference of approximately 0.004 in. to act as other work could be done in the portions of the the driving force for a still. The gradients due tunnel occupied by the leveling party. The time to mass flow will cause an error. Thus it seems required for optical leveling makes it unattrac- safest to exclude water or other liquids with high tive for the 200-BeV machine. vapor pressure. The second basic type of hydrostatic leveling The thermal effects in a practical system are system is available commercially in two forms. of two types. The first occurs when the system, The first of these is the garden-hose type of in equilibrium, is uniformly warmed or cooled. water-filled, extended hydrostatic level. In this The difference in the coefficients of thermal ex- type of level two or more surfaces are connected pansion of the liquid and its enclosure, the tubes, by tubing or hose. In practice, this simple causes a change in the apparent volume of liquid level, visually read, is accurate to ii/32 in. in in the system (analogous to the change in bubble 100 it, when used with moderate care. The size with temperature in bubble levels). No er- second commercial type of water-tube level uses ror results from this effect, only an equal change a micrometer dipper for measuring the level and in level in all measuring wells. This effect can ::: Work done under the auspices of the be eliminated by choosing tubing with a volume U. S. Atomic Energy Commission. thermal expansion coefficient equal to that of the 20 IEEE TRANSACl’IONS ON NUCLEAR SCIENCE June liquid. (Lexan is a very close match for mer- To detect precisely the location of a mercury cury. ) surface, a micrometer head with a hardened steel or tungsten ball tip approximately 0.040 in. The second type of thermal effect is due to the in diameter is fitted to the top of the measuring existence of a thermal gradient across the sys- well. An ohmmeter on the high-resistance range tem. This thermal gradient causes a density (12 V or more and a fraction of a milliampere) is gradient in the liquid. used to measure contact with the surface. This contact is repeatably accurate within *O.OOOi in. Since the level in each well is determined by a or less. hydrostatic or mass balance among all wells, an increased temperature in one well causes a de- For remote reading of the mercury surface a creased density of liquid and thus a higher liquid photoelectric device has been developed with an level with no corresponding flow. This error, accuracy and repeatability of 0.0001 in. or less, with mercury as the liquid, is 7 X 10-5 in. per in. but for the AGS a capacitance, inductance, or of depth per degree centigrade. This error, for eddy current device that is not sensitive to radia- oils and other low-vapor-pressure liquids is tion must be used. Many commercial devices are about five times higher than for mercury. It is available. Experience over nearly a year with obvious that the thermal errors can be acceptably floats indicates an uncertainty in readings due to low if the liquid depth is small and vertical tubing sticking, and to condensation of mercury on the runs are avoided. In practice, the overall depth float, which changes its floating level by several can be held to i/2 in. or less without difficulty. thousandths of an inch. Due to these uncertainties, This would ensure a residual system error of no floats will be used in future work. = 0.00035 in. even with 10°C gradients across the system. In precise work the thermal coefficient Tubes of various plastics, about i/8 in. in of the measuring well must be determined in an diameter have been used in most work. This oven and used to correct readings. With care in tube is easily filled, because the mercury me- design, the measuring-well error can be made niscus pushes air out ahead of it. Larger tubes negligible. are more difficult to fill because air is trapped in the line. The time constant of a system with two The probable maximum effect of tides on the 2-in. measuring wells connected by a O.iOO-in. system can be easily calculated. The daily earth tube 100 ft long is 5 min. This system is slightly tide has an amplitude of about 1 ft. The slope of over -damped. A number of systems using dif- this tide wave will be about 0.004 in./mile. The ferent materials, tube sizes, and lengths have leveling system lies on an equipotential of gravity. been built, all of which behave normally. This equipotential moves with the earth and thus the system may not actually respond to the earth tide. Other tidal effects in coastal regions are due to two primary causes. In the first, the ocean tides deform the continental shelf. In the second, Conclusion the lens of ocean water exerts a gravitational force on the liquid-filled system. In our experi- Hydrostatic leveling systems can be quite ments with a 90-ft-long system in Berkeley, no easily designed and built. Manually read systems tidal effects as large as 0.0001 in. in 90 ft are of various types in lengths to iO0 ft have been apparent. The system for the proposed AGS will built that are stable and dependable. A recording be subdivided into 600-ft lengths, partly to de- system 90 ft long installed in Berkeley has shown crease the response time and partly as insurance no tidal disturbances as large as 0.0001 inch. A against tidal effects that might appear in a large similar hydrostatic system 1000 ft long will be system. In any event none of the tidal effects constructed in the Bay Area this year, and ex- a’oove are significant as far as machine operation perience gained will be applied to the final design is concerned.
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