Harwood
Engineering Company, Inc.
Harwood
Engineering Company, Inc.
There are many research laboratories in industry engaged in getting fundamental engineering data with an accuracy of 0.1 percent or better. Phenomena which are sensitive to pressure may require instrumentation accurate to 0.03 or even 0.01 percent.
The National Bureau of Standards should have primary standards which are somewhat more accurate than any instrument portable enough to be brought in for calibration. There are pressure-measuring instruments which are capable of an accuracy of 0.01 percent at pressures up to a few thousand pounds per square inch. The primary pressure standards against which these are calibrated should be definitely better, with an accuracy of 0.003 percent. The possible accuracy drops off as the pressures increase, and considerable effort is required to develop primary standards adequate to the present requirements in the high-pressure field.
The first extensive use of the free-piston gage was by Amagat (1).³ The basic form and two modifications are in current use. They are illustrated in Figure 1, Figure 2, and Figure 3.
When its output is piped to the upper side of the second piston (B), the force developed is additive to the dead-weight load. The second piston makes the unit suitable to 10,000 kg/cm² (142,000 psi). Leakage is controlled by an interface fit between piston and cylinder. At high pressure the piston becomes free to rotate. The use of similar pistons of various sizes permits measurements over a wide range.
The literature abounds with descriptions of instruments which are variations of the basic concept of the simple piston gage. Mostly, they are clever arrangements to allow the operator to handle small weights. It is probably fair to say that uncertainties are built into the devices in proportion to the departure from the simply loaded piston.
The controlled clearance piston gage, Figure 4, permits a size adjustment of the cylinder bore to the desired clearance. The measuring piston (a) is contained in a jacketed cylinder (b). An independent pressure is used between the jacketed and jacketing cylinder (c) to deform the jacketing cylinder to the desired clearance. The pressure in the jacketing cylinder is sealed off by Bridgman unsupported area rings (d) whose initial seal is accomplished by a mechanical load from nut (e).
The relation between the pressure PJ required in the jacketing cylinder and the pressure PM being measured is expressed approximately by
The free-falling time is controlled readily by minor adjustments of jacket pressure. If the close clearance is maintained, the effect of the distortion of the cylinder is eliminated. It will be shown later that this is a notable improvement since in other designs the elastic distortion of the cylinder is one order greater than the distortion of the piston. A still further improvement probably will result from the use of carboloy pistons. Otherwise the apparatus is more elaborate than unique. The elaborations take advantage of well-known design points with a view to maintaining accuracy and precision, and to securing ease in manipulation.
The dead-weight system, Figure 5, is patterned after the 10,100-lb. dead-weight system in the Engineering Mechanics Section at the National Bureau of Standards (4). The dead weights themselves (f) are made of austenitic stainless steel for long-time stability and freedom from oxidation, corrosion, and magnetism. The loading system has 1000 lb. of dead weight, consisting of nine 100-lb. platters held in a chain suspension attached to the yoke (g). The weights are lifted on and off the suspension by the power cylinder (h) on the base. Smaller 10- and 5-lb. weights (i) are provided for hand-loading on the yoke. The piston is rotated either clockwise or counterclockwise by means of a pulley (j) and motor arrangement to eliminate the corkscrew effect. It is patterned after that described by Meyers and Jessup (5). The yoke suspension rods (k) are insulated electrically from the upper cross rail (l). Thus, by electrical sensing, there is assurance that the weights supported by the piston are free of other parts.
The measuring piston and cylinder are so arranged that they may be removed readily and interchanged with similar components for other ranges. The cost of the piston assemblies is on the order of 3 percent of the total cost of the instrument, while the piston itself represents only a fraction of 1 percent of the total cost of the instrument. The change-over from one piston size to another is done readily with hand tools.
To obtain the pressures as so defined, the indications of a practical dead-weight piston gage are subject to a number of corrections. The more important of these, which will be of concern to those who hope to measure a pressure to a part in a thousand, will be discussed in some detail. Some of these errors can be evaluated and corrections applied, but in every case there will remain some residual uncertainty which may or may not be important.
Equation
1The change in Da in the bore radius a of a hollow cylinder of outside radius b = wa, where Po is the pressure on the outside, Pa is the pressure inside, and Pe is the pressure on the end face, is:
Equation
2Small variations in dimensions may have a great effect on the position of the pressure drop. (It is even possible that the position may be a function of pressure.) The variations may occur because of the design, because of irregularities in machining, or because of distortions in use. For example, when a piezoelectric gage is calibrated by a sudden release of pressure, the piston of a gage connected to the system will drop violently. If it is stopped at the blind end of a cylinder it may mushroom slightly, Figure 6a. If it is stopped by contact with the open end of the cylinder, the latter may develop a burr, Figure 6b. Therefore it can be said with certainty, only that the effective pressure in the crevice is less than the pressure measured. The distortions of the piston and cylinder may be calculated on the basis of an effective pressure in the crevice which is the mean between that at the two ends, provided that the fall of pressure takes place in a region remote from the ends of the piston, and of the bore of the cylinder. "Remote" can be taken as one diameter in the case of the piston, and three bore diameters for the cylinder.
Equation
3
Equation
4
Equation
5
Equation
6The change in the effective area of the gage will be the mean of the changes in the cylinder and piston (Case 1) or
Equation
7If the piston is expanded at the lower tip (Case 3), in a blind cylinder, Figure 6a, the distortion at 200,000 psi might vary from +0.19 percent at the bottom of the stroke, to +0.70 percent when the tip of the piston has risen several bore diameters away from the end of the cylinder, Figure 6c.
Equation
8The change in the effective area of the piston gage (piston Case 1) is
Equation
9
Equation
10For carboloy, with v=0.22 and E=88 x 106 psi
Equation
11| Nominal Area, square inch | Approximate Diameter, inch | Error in Area, percent |
| 1/200 | 0.0798 | 0.025 |
| 1/100 | 0.1128 | 0.018 |
| 1/50 | 0.1596 | 0.012 |
| 1/20 | 0.2523 | 0.008 |
| 1/10 | 0.3568 | 0.006 |
| 1/5 | 0.5046 | 0.004 |
| 1/2 | 0.7979 | 0.0025 |
In the southern part of the United States, the value of gravity will be more than 0.1 percent smaller than the standard value. In Canada and the northern part of the United States the local value will be higher.
If the latitude f and the elevation h in feet above sea level are known, the gravity correction Cg will be given approximately by:
This correction usually will compensate for gravitational variation with an error of less than 0.005 percent in any part of the United States.
For example: at Boulder, Colorado, the reading on a piston gage, before gravity correction, was 101,200 psi. The latitude was 40°01' (sin 80°02' = +0.1730) the elevation 5350 ft.
In this case had the value observed at this location by the U.S. Coast and Geodetic Survey been used, the corrected pressure would have been 101,091 psi. This difference of 6 psi is reasonable since the errors in the formula are largest in mountainous country.
The density of air at room temperature and sea-level pressure is about 0.0012 gram per cc; and the mass under these conditions will be reduced by 1 part in 7000.
The temperature of the piston is somewhat higher than that of the surroundings because of the dissipation of energy in the fluid escaping between the piston and cylinder. The temperature rise in the piston is difficult to estimate because of the uncertainty in the thermal transfer between the piston and the exterior. Since the dissipated energy is proportional to the rate of leak, measurements can be made at various rates, and an extrapolation made to zero leak.
When the submerged part of the piston is of uniform cross section, the pressure measured is that at the level of the lower end of the piston. In some designs the piston is enlarged to provide a stop for its upward motion or to give increased strength. If these enlargements are submerged in liquid, the weight of the fluid displaced by the enlargement should be subtracted from the dead-weight load.
With some designs it is not possible to observe the liquid level, and therefore not possible to determine the submerged volume. In such a case it is necessary to determine the buoyancy correction by test. It will usually be less than a pound per square inch.
In an intercomparison by cross floating, two piston gages are connected together and to a common pressure generator, such as the intensifier, of suitable range and capacity. Either piston gage can be isolated by means of valves in the connecting tubing. A telescope with an eyepiece scale or the equivalent, is set up to observe the position of one of the pistons in its range of motion. At the selected pressure, the rate of fall of each piston is observed with the gage isolated. The two gages are connected together and one of the loads is adjusted by adding small weights until both pistons fall at approximately the same rate as when isolated. An exact balance is usually not obtained, but by observing rates of fall at various loads, an interpolation can be made to the load for which the rates of fall would be the same with the gages connected as when they are isolated.
By having one of the pistons fall repeatedly over the same interval, while the other falls through various parts of its range it is possible to observe small variations in diameter. By this method a commercial piston gage with a simple cylinder was ascertained to have an effective area constant over its length to within 1 part in 50,000. Since the diameter of this piston was about 0.16 inch, it must have been uniform to 1.6 microinch or better.
This particular observation happened to have been made at a pressure of about 1000 psi. When the same kind of comparison was attempted at 5000 psi, the rate of fall was so much greater that the comparison was quite unsatisfactory. The enormous change in sensitivity was caused by an increase in the bore of the cylinder estimated to be only about 8 microinches.
While this method is quite satisfactory at low pressures, the accuracy falls off rapidly at higher pressures. For example, suppose that a 150-psi mercury column is used to calibrate a pair of 30,000 psi piston gages, which have a sensitivity of 1 ppm of their range or 0.03 psi. Then each 150-psi step in this comparison can be done to 0.03 psi, or 1 part in 5000. But the area of a piston good enough to attain this sensitivity probably can be measured to better than 1 part in 10,000.
The small distortion of the cylinder or piston in the 150-psi step of pressure gives rise to just as large a correction, in relation to the 150 psi, as the larger distortion under 30,000 psi is with respect to the 30,000 psi range of the instrument.
A satisfactory comparison with a mercury column will give the user of the piston gage the valuable assurance that he has not overlooked some large systemic error in the latter. But a calibration of a piston gage against a mercury column cannot be regarded as inherently better than a standardization by direct measurement on piston and weights.
One solution to this problem is a set of experiments which can be repeated at any laboratory and will reproduce definite pressures. In some cases a suitable transfer instrument and a set of fixed-pressure points would replace the primary standard. The analogous situation exists in the field of temperature measurement. The platinum-resistance thermometer and four fixed-temperature points define the temperature scale over a range of 600°C to the satisfaction of most users.
The fixed-pressure points may be based on changes of state or polymorphic transformations which should satisfy the following conditions:
Bridgman's value of the freezing pressure of mercury at 0°C, 7640 kg/cm² (108,660 psi), has been used by a number of observers. Occasionally a higher temperature has been used when a higher pressure was required. The temperature coefficient of the melting pressure is about 3000 psi per degree C, so that accurate temperature measurements and precise control are required. These are much easier at 0°C, where an ice bath can be used.
In his work at the high pressures Bridgman has used the bismuth I-II transition at about 360,000 psi; L-III-V near 50,000 psi; L-V-VI near 90,000 psi, L-VI-VII near 320,000 psi. Between these points the melting-point pressure measurements on the basis of a value of 9630 bars (139,670 psi) for the freezing pressure of water at 30°C, with the expectation of adjustment if a better determination should change that value.
Professor Bridgman measured pressures at the phase changes of water and of mercury in 1912. Since then, in so far as is known, there has not been an independent determination. Rather, the value reported by him has been used without question. While the Bridgman values were sufficiently accurate for his pioneering work, a vast amount of data reported with greater accuracy than that claimed by Bridgman are still dependent on his value. This is not as serious as it might seem at first glance. Bridgman's value should stand until an independent determination has been made with the improved tools of the present day. Quantitative work reported prior to the publication of the new value will have to be corrected when correlated to subsequent work—should a correction for Bridgman's value be indicated.
The mercury bomb was a simple high-pressure vessel with a cavity 1 inch diameter and approximately 3 inches long. Freshly distilled mercury was sealed in a polyethylene sack and placed in the bomb cavity.
A gold-chromium resistance element, subjected to the high pressure, was used as a transfer device. The gold-chromium resistance was part of a 120-ohm equal-arm bridge. The other arms were in a bath at room temperature, close to the pressure cell. The bridge was driven by alternating current at 1000 cps, 50 milliamp total current. One arm of the bridge was shunted by an adjustable resistance box. An a-c null indicator was used to detect balance. The sensitivity of the indicator was adequate to detect changes in the resistance of the gold-chromium wire of 1 part in 107. A duplicate bridge in a temperature-controlled bath was used to correct for drift in the null indicator. The drift during a run was not more than 1 part in 106.
The system was charged to about 10,000 psi by a hand pump. This pressure was held in the system by a check valve when the hand pump was removed. The piston of intensifier (B) was then advanced to the end of its stroke raising the pressure to about 90,000 psi. Another check valve held the pressure in the rest of the system after the pressure in intensifier (B) was released. During the rest of the experiment the pressure was raised by advancing the piston of intensifier (A). The movement of the piston of this intensifier was followed in the sight glasses.
If the volume is plotted against pressure, at constant temperature, there is obtained a nearly straight line A-B, Figure 8, representing the compression of the liquid, a horizontal straight line B-C, representing the change in volume at constant pressure of the mixture of liquid and solid, and the nearly straight line C-D representing the compression of the solid. This is under isothermal conditions, which are never realized by the experimenter. When the specimen is compressed, it is heated, and is therefore at a pressure which is a little high. If only one phase is present, either liquid or solid, the approach to equilibrium is nearly completed after 5 minutes. With both phases present, the latent heat of the phase change is large, and relatively long time is required for the system to come to equilibrium as this heat is transferred to the bath.
In these measurements the pressure is increased in steps of about 5000 psi, and the piston is held stationary at each step for 5 minutes. As long as only liquid mercury is present, the pressure drops back slightly and stabilizes during each hold period, A to B, Figure 8. When solid mercury makes its appearance, the pressure drops back farther in the 5-minute period and the curve drops off, as at E. When all-solid line C-D is reached, there is an abrupt transition to the quick equilibrium condition, and on further compression, the curve resembles A-B.
On expansion, a zig-zag line D-C-F-A would be described. If at the point G, the volume were held constant the pressure would settle out toward the equilibrium point. The time of several hours required for a close approach to equilibrium may exceed the experimenter's patience. A quicker way is to juggle pressures so as to start close to the expected asymptote, as at H or I. Then the equilibrium pressure can be approached from both sides, the decay being followed only long enough to predict the position of the asymptote. This should be repeated at several points along the line B-C, including one point close to C. If the mercury is impure, the corner at C will not be sharp, as in the dotted line.
In addition to the plot of pressure (or what is more convenient, readings on the transfer gage) against volume, it is also desirable to plot pressure against time. In Figure 9 are such curves. In (a) only liquid is present, and the decay is rapid. This is a leak check showing a loss of about 3 psi per minute after disappearance of the initial transient following an expansion; (b) was taken near (F) with both phases present; (c) and (d) were taken at (H) and (I) and define the melting pressure as their common asymptote.
It is desirable that the system be absolutely tight. If the leak in, say, 30 minutes cannot be detected by the pressure-measuring means when only one phase is present, its effect may be neglected. If it is perceptible but small, its effect can be estimated and a correction applied.
From a curve such as (a), Figure 9, with only one phase present, the leak in psi per minute may be estimated. The flow through the leak is supplied by the expansion of the fluids, mostly gasoline, and the contraction of the pressure vessel under this pressure change. The fall of pressure with both phases present, as (c) in Figure 9, can be divided into two parts, the pressure drop associated with the expansion of the fluid under the leak, and that associated with the change in volume due to the phase change. When the pressure is falling rapidly, as at the beginning of curve (c), the mercury is freezing, the sample is warmer than its surroundings and is giving up heat to the pressure vessel. When the pressure is falling very slowly, the fluids are expanding very slowly, and most of the leak is supplied by the expansion which results from melting of the sample. The sample then will be absorbing heat from the pressure vessel and will be a little cooler. At the point of (c) where the slope is the same as that of the leak curve, the sample is neither melting nor freezing and its temperature is the same as that of its surroundings. The difference between the pressure at this point and that at the asymptote is approximately the leak correction.
An alternative and equivalent estimate of the effect of leak is obtained by multiplying the rate of the leak from curve (a) by the time constant of the decay of pressure in curve (c) or (d).
A dead-weight load was set up on the piston gage, the pressure raised until the piston was at the top of its travel. While the piston fell through its range (1/8 inch) observations were made on the pressure under the piston with the gold-chromium cell, on the jacketing pressure with the manganin cell, and on the time of fall. The jacketing pressure was adjusted until the rate of fall was about 30 seconds. Readings were made at the top and the bottom of the travel. The dead-weight load on the piston was increased in 20-lb. steps until the pressure used in the mercury-poing measurements had been exceeded. The load corresponding to the mercury point was obtained by interpolation between calibration points on the basis of the resistance change in the gold-chromium cell.
The piston was measured by the Gage Section of the National Bureau of Standards with an accuracy of about ±0.00002 inch.
| Weights: 268.73 lb. | ||
| Area: 0.0024446 square inches | ||
| Pressure, uncorrected: 109,930 psi | ||
|
|
|
|
| Zero shifts, in mercury-point runs |
...
|
±65
|
| Zero shifts, in piston-gage runs |
...
|
±215
|
| Correction for leakage |
+20
|
±10
|
| Piston measurement, ±0.00002 inch |
...
|
±80
|
| Piston taper, 0.00003 inch |
...
|
±120
|
| Residual clearance, 0.000010 to 0.000020 inch |
-30
|
±10
|
| Elastic distortion |
+65
|
±10
|
| Temperature of piston |
-25
|
±15
|
| Weight measurement |
...
|
±10
|
| Buoyant effect of air on weights |
-15
|
|
| Gravity at Foxboro, Massachusetts, USA |
-35
|
±5
|
| Temperature of ice bath, ±0.02°C |
...
|
±60
|
| Conduction down tubing |
-150
|
±150
|
| Total Correction |
-170
|
|
| Corrected Pressure |
109760
|
±750
|
There were differences in zero before and after the mercury-point and the piston-gage runs. The two zero readings were averaged, on the assumption of equal changes during increase and decrease.
The system was found to be losing pressure at a rate of about 2 psi per minute when only liquid was present. This rate was multiplied by the 10 second time constant of the approach to equilibrium conditions when both phases were present.
The residual clearance between piston and cylinder was estimated from the leakage rate, including the effect of the expansion of the fluid under the pressure change during the fall of the piston, and assuming that the drop in pressure occurred in 1/10 inch of length in the piston.
The elastic distortion of the steel piston was calculated from Equation 10.
The value of gravity was interpolated from Coast and Geodetic Survey data at points within 10 miles of Foxboro, Massachusetts, where the experiment was conducted.
The temperature of an ice bath, using good commercial ice, usually can be expected to be 0.00 ± 0.02°C. Several measurements of samples during these tests fell within this range. The conduction of heat down the pipe to the mercury cell would raise the temperature of the latter by an amount estimated not to exceed 0.1°C.
A difference between pressures at the upper and lower limits of travel of the piston was observed. This was found to be caused by a taper in the piston which developed when the piston had been scored in previous tests. (This taper of 0.00012 inch in ½ inch of length was 10 to 100 times that which would be tolerated in a new piston.) The ratio of 0.7 between change of jacket pressure and change of measured pressure indicated that the line of contact between piston and cylinder was near the top. The area of the piston and cylinder was near the top. The area of the piston was computed on the diameter of 0.05579 ± 0.00002 inch measured 1/8 inch from the top. An additional uncertainty in area was taken as that corresponding to the taper in 1/8 inch of length.
Additional possible errors, not evaluated, include those resulting from possible changes in the resistance in the gold-chromium wire which were not reflected in the zero shift. This alloy is a new one for pressure measurement, and very little experience has been accumulated. In particular, little or nothing is known as to the proper pressure-seasoning treatment. (This particular element had been subjected to two applications of pressure to 140,000 psi.)
In the manganin and gold-chromium cells the packing used for the insulated electrical lead included a plastic which softened in contact with kerosene or gasoline, and was responsible for a progressively increasing electrical leakage. This was serious since one corner of the Wheatstone bridge is grounded, and a leakage through 100 megaohms will produce a significant error. Other packing materials are being tried.
The controlled-clearance piston gage was used at pressures as high as 120,000 psi, with no indication that the limit of its range was being approached. (The pressures to which this instrument was used were limited by fittings rated at 100,000 psi.) Adequate floating times for the measurements were obtained. Indications were that clearances could be held to a few microinches, provided the surfaces of the piston and cylinder were that good. The small clearances make necessary precautions to eliminate abrasive particles in the working fluid. The use of carboloy pistons may be indicated from considerations of wear.
The gold-chromium pressure cell seemed promising. The time required to reach constant reading seemed somewhat shorter than for manganin. The very small temperature coefficient should be valuable. The elastic defects of hysteresis, drift, and after-effect, required further study since they were obscured by the electrical leakages in other parts of the bridge.
These measurements give a value 1 percent higher than obtained by Bridgman for the melting pressure of mercury. This difference is not serious in view of the rather large experimental error of ±0.7 percent due to identifiable sources.
The largest errors can be reduced substantially in future work. A better choice of the insulating material in the electrical leads should reduce the troubles with zero shift. An unworn piston would have variations in diameter less than a tenth as great as those in the one used. The temperature of the mercury sample can be measured directly.
