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J. M. SAVINO' and W. L. SIBBITT2 Purdue University, West Lafayette, Ind.
Capillary Viscometer for Inert Gases and Vapors at High Temperatures and Pressures
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R E C E N T YEARS, the trend has been to increase the operating pressures and temperatures in applications such as jet engines, rocket motors, and nuclear reactors. In many cases gas viscosity data are not available for these new operating conditions; hence the motivation for making viscosity measurements. Reliable viscosity values not only fill the wants of researchers and engineers but also guide the physical chemist in improving existing theories and developing more advanced ones. A program was initiated at Purdue University to develop a viscometer for measuring the viscosity of water vapor at pressures and temperatures up to 510
A coiled capillary viscometer for testing nonreacting gases, vapors, and mixtures to 81 5' C. and 51 0 atm. was successfully calibrated and tested with nitrogen gas and carbon dioxide gas a t 2 5 " C. and pressures to 270 and 48 atm., respectively
C A P I L L A RY 116 C O I L S )
P I E Z O M E T E R RING
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1 Present address, National Aeronautics and Space Agency, Lewis Research Center, Cleveland, Ohio. Present address, Los Alamos Scientific Laboratory, Los Alamos, N. M.
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Available for Sixty Cents The complete manuscript containing the derivation of Poiseuille's equation and its corrections, table of nomenclature, detailed calibration data, and tabulation of viscosities o f nitrogen and carbon dioxide from which the curves in this article were plotted. Address: Editor, I/EC, 1 155 Sixteenth St., N.W., Washington, D. C., sending cash, money order, or check payable to American Chemical Society.
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The equipment consisted primarily of a capillary, electric furnace, gas flowmeter, pressure-stabilizing system, and manometer VOL. 51, NO. 4
APRIL 1959
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SUMMARY C U R V E , 70: F 553 F POINTS CALCULATEC USING WHITE'S ( 2 1 )
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Figure 1.
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Calibration curve for coiled capillary, K
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The curve of the CaDillarY constant as a function o f Reynolds number was determined a t
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atm. and 1500' F. (815' C.). Many methods are available for measuring fluid viscosity ; their suitability depends on the type of fluid and the testing range. Barr ( 7 ) and Merrington ( 8 ) present excellent surveys of viscometer types. For this work a steady-flow coiled capillary-type viscometer was chosen, to which Poiseuille's equation with appropriate correction factors applies. The plan was to calibrate the apparatus with nitrogen gas at pressures close to 1 atm. and a t various temperatures where the viscosity is already well established. Before the water vapor measurements, tests were made separately with nitrogen and carbon dioxide gases at room temperature and pressures to 270 and 48 atm., respectively. The results established the validity of the calibration tests and the reliability of the apparatus as an accurate viscometer. Apparatus
The apparatus consisted primarily of a capillary, an electric furnace to house the capillary and control its temperature, a gas flowmeter, a pressure-stabilizing system, a stainless steel U-type mercury manometer, and auxiliary equipment such as thermocouples, pressure gages. and valves. Savino (76) gives a detailed description of apparatus, fabrication, measuring techniques, analysis, and corrections. The capillary test section with its preheater, hydrodynamic entrance length, exit line, and gas cooler was made of No. 347 SS thick-walled tubing with a ',14-inch outside diameter and an inside diameter ranging from 0.082 to 0.085 inch. The diameter was chosen large enough to avoid the possibility of plugging by small foreign particles Lvhich might get into the capillary. The inlet and outlet of the test section were fitted with piezometer ring-type pressure taps. T h e distance between the inlet and exit tap holes was 498 feet 103,'4 inches.
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The length was dictated by the necessity to produce a measurable pressure drop. The test section was coiled into a compact bundle having a mean diameter of 10 feet. When the test section was fabricated from random lengths of tubing, great care was exercised to ensure the continuity of the inner surface. The furnace had a toroid shape. The capillary bundle was surrounded with commercially built electric resistance heaters, covered by high temperature insulation. The power was supplied to the heaters by variable transformers (Powerstats) which were manually controlled. The capillary temperature was measured by 42 No. 28 gage Chromel-Alumel thermocouples. Thirtytwo couples were equally spaced approximately 1 foot apart and fixed permanently in place. The other 10, also equally spaced around the capillary, could be withdrawn at any time to check on the stability of their calibration. All the thermocouples were calibrated a t the boiling point of water and the freezing point of zinc and aluminum. The manometer used to measure the pressure difference between the inlet and outlet piezometer ring taps was made of thick-walled stainless steel tubes to permit high pressure operation. A chrome-plated iron float was madc to float on top of each mercury column. That the float would always be in the same position relative to the mercury was assured by its shape and its close fit in the manometer tube. Thus. the pressure difference was found directly by measuring the float position relative to a known horizontal reference plane. established for a zero pressure drop condition. The floats were detected with differential transformers to within =t0.00025inch. The manometer and the transformers with their drive mechanisms were totallv enclosed in a housing to reduce the effect of ambient air temperature variations. I t was possible to measure any pressure difference
INDUSTRIAL AND ENGINEERING CHEMISTRY
greater than 0.025 inch of mercury with an error of less than 1yo. The mass flow rate of gas passing through the capillary was measured at the capillary exit with a Precision wet test meter (Precision Scientific Co., Chicago, Ill.). For rates encountered in this experiment the normal error as given by the manufacturer was 0.5, a check showed it to be less than lY0. T o maintain a constant water level in the meter, the gas was saturated with water vapor prior to entering the meter, by bubbling the gas through water. The meter was equipped with a circuit which started and stopped a timer at the beginning and end of any single revolution (0.1 cubic foot) of the meter dial. The gas temperature in the meter was measured with a mercury-in-glass thermometer whose smallest subdivision was 0.5' F. The flow rate through the meter was so low that the absolute pressure in the meter was essentially atmospheric. The pressure at the capillary inlet piezometer was measured with Heise gages having ranges of 0 to 2000 and 0 to 10,000 p.s.i.g. with subdivisions of 2 and 10 p.s.i., respectively. Both gages were calibrated with a dead-weight tester. For pressures less than 25 p.s.i.g. a Meriam mercury manometer directly readable to 0.10 inch was used. The pressure-stabilizing system consisted of a high-pressure gas source and a pressure regulator. A filter to remove foreign particles and a cold trap for taking out moisture were located between the source and the regulator. For the carbon dioxide tests, the cold trap was bypassed. h-itrogen gas from commercial cylinders was used as a source for pressures below 2300 p.s.i.g. Above 2300 p.s.i.g. the nitrogen was charged into a source tank, where it was compressed to 10,000 p.s.i.g. by pumping water into the tank. The commercial cylinder of liquid carbon dioxide was the source for the gas viscosity measurements. Experimental Procedure
The test runs for calibrating the capillary and measuring viscosity values were very similar. With the exit and throttle valves closed, the capillary was pressurized to a desired capillary inlet pressure. The equalizer valve connecting the manometer legs a t the top was opened and the reference plane established for the zero pressure difference condition. The water level in the flowmeter was checked, and the flow was started by opening the exit valve and adjusting the throttle valve. S l o ~ l ythe equalizer valve was closed and the mercury level positions in the manometer were noted. If it appeared that the range of the manometer was going to be exceeded, the flow was reduced. Steady-state conditions were assumed to
CAPILLARY VISCOMETER exist when pressure difference and the time for three or more revolutions of the flowmeter dial remained constant. Readings were then recorded for the mercury level position ; the manometer, capillary, flowmeter, and barometer temperatures ; the capillary inlet, barometric, and flowmeter pressures; and the time, T , for one revolution (0.1 cubic foot) of the meter dial. For the calibration tests one arbitrary fixed flow rate was chosen for each run and four, five, or six sets of readings were recorded. This check for reproducibility aided in detecting effects due to possible unknown irregularities such as leaks, impurities, and foreign particles in the capillary and the manometer, which would cause a scattering in the value for the capillary constant for a given Reynolds number greater than the maximum estimated scatter. Calibration tests were made at ambient room temperature and 553" F. At 553' F., the test procedure was the same as for room temperature, but the capillary temperature was established prior to testing. For the viscosity measuring tests all conditions for a given run were held constant except the Reynolds number. A set of data was recorded for each flow condition, thus giving a measure of reproducibility.
Results Calibration Tests. The curve of the capillary constant, K , as a function of Reynolds number, N R e , was determined at two temperatures, 70' and 553' F., by using nitrogen gas as a calibrating fluid (Figure 1). The average deviation of the test data from the summary curves was less than 0.570 with a 1.370 maximum for several sets of points. The maximum estimated error ( 7 6 ) was 12.37,. From the Kso =0.2734 X 10-8 ~p.-ft.5:lb.~-sec. (straight capillary) was calculated the effective capillary diameter, D = 0.0829 inch, which agrees well with the estimated average diameter of 0.083 inch. The calibration curve calculated with White's (37) curvature correction for laminar flow in a curved pipe is very close to the experimental curve (maximum difference is 0.6%). Hence, White's correction could have been applied to Poiseuille's equation with little sacrifice in accuracy. It would have been desirable to run all calibrating tests close to atmospheric pressure, where the nitrogen viscosity values are more accurately known. This was not possible because the pressure drops would have exceeded the manometer range for some flow conditions. Hence, to extend the 70' E'. calibration = 838 the operating curve beyond A17~Re pressure level was raised (313 p.s.i.a.
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Figure 2.
Viscosity of nitrogen at
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Viscosity values for nitrogen agree with those of other investigators
viscosity gives a Ks at 5.53' F. equal to in this instance). The 553' F. curve the calculated value. Hence, neither could not be extended in this way source of data is to be preferred, because no high-pressure viscosity data except possibly because Keyes' correlaexist a t that temperature. The 70' F. curve was not extended beyond - 1=~ ~tion is more recent. Because of thc: small difference (1Yo) between Ks, and 1600 because the data were too widely either Ks, the 70" F. calibration curve scattered. The scattering may have could be used for temperatures up to been due to early transition to turbulent 1000' F., with a n additional error not flow. exceeding 2 or 3y0. The shape of the 70' F. calibration Viscosity Measurements. The viscurve in Figure 1 reveals some characteristics of laminar flow in a curved cosity of nitrogen and of carbon dioxide capillary. In the region ~ V R
