A . Klute a n d D . B . Peters
University of Illinois a n d Agricultural Research Service, U . S . D . A . U r b a n a , Illinois, U . S . A .
A B S T R A C T : Sensitive, responsive tensiometers are highly useful in laboratory and field studies of water movement in unsaturated soil. Strain gauge pressure transducers of the diaphragm type have been incorporated into a tensiometer system that has a short response time, is capable of detecting tension changes as small as a few millimeters of water and has the advantage of an electrical output that can be recorded.
Construction details, precautions to be observed in use and operational procedures are given for direct reading and null m o d e s of measurement. A manifold for the use of a single transducer with a number of tensiometer cups and the possible use of the tensiometer in field measurements are described.
R É S U M É : Des tensiomètres sensitifs, à réponse rapide sont hautement utiles dans les études en laboratoire et en campagne d u mouvement de l'eau dans les sols non saturés. D e s jauges de contraintes du type diaphragme ont été incorporées dans u n système de tensiomètre qui avait un temps de réponse très court et était capable de détecter des changements de tensions aussi faibles que quelques millimètres d'eau et avait l'avantage de donner ses résultats électriquement ce qui permettait leur enregistrement.
Des détails de construction, les précautions à observer à l'usage et les procédés d'opérations sont donnés pour lecture directe. U n dispositif pour n'utiliser q u ' u n seul transducer avec u n certain nombre de tensiomètres et la possibilité d'utilisation du tensiomètre en campagne sont décrits.
The use of tensiometers to measure soil water tension is basic to a study of the m o v e m e n t and retention of water in unsaturated soils. Willard Gardner (1922) apparently first recognized the utility of porous ceramic cups in combination with a pressure measuring device to evaluate the capillary potential of soil water. The relationship between pressure head h, capillary potential \jj, tension T , suction S and the pressure P in the water in the cup of a tensiometer is:
9 pg
where: Pa is atmospheric pressure; g is the acceleration of gravity and S,x and h are expressed in terms of a length of fluid column of density p . In soil water studies the fluid is usually water.
Richards (1949) and others have m a d e extensive developments and improvements in tensiometers until at the present time these are widely used in the field and laboratory in soil water studies.
A tensiometer can be used to measure both pressure head and the hydraulic head of the soil water. Tensiometers m a y be regarded as piezometers with an added porous cup so that head measurements can be m a d e in unsaturated soil. A diagram of the relationships between these two devices and the components of head is shown in fig. 1 for the case of a tensiometer using a water manometer as a pressure measuring device.
1. This work was in part supported by Grant G-18897 of the National Science Foundation.
In soil water flow studies it is often desirable to be able to measure a rather rapidly varying pressure head. A n important characteristic of a tensiometer, in this regard, is its response time, defined by Richards (1949) to be XjKG where K is cup conductance and G is the gauge sensitivity. T h e gauge sensitivity is the pressure change per unit volume of fluid transferred to the tensiometer. T h e fact that a pressure measuring device such as a manometer, requires the transfer of a nonzero volume of water for its operation, dictates that a tensiometer will have a nonzero response time. Conventional tensiometers using Bourdon gauges or mercury manometers will have response times on the order of a minute or longer, which is far too long for measurements in m a n y dynamic systems.
S O I L - W A T E R S Y S T E M S
Saturated Unsaturated Piezometer
j— Tensiometer Porouscup
Reference level
F I G U R E 1. Diagram to show the relationship between hydraulic head H, pressure head h, and gravitational head Z as measured with piezometers and tensiometers
In addition to the response time problem there is also the fact that the required volume of transfer of water to or from the tensiometer is a disturbance of the flow system being observed. This m a y in some cases be quite significant.
There are at least two possible avenues by which improvement of the tensiometer can be effected; 1) m a k e the gauge sensitivity as large as possible by using a pressure measuring device which requires a very small volume of water for its operation, or 2) use a null balance technique.
M a n u a l null balance methods have been used by Miller (1951), Croney (1952), and Greacen (1960). Leonard and L o w (1962) describe a servo-null system. Most of these are either not well suited to measurements in rapidly changing systems or introduce an undesir-able degree of complexity in the instrumentation.
A more direct and simpler procedure is the use of diaphgram type pressure transducers using strain gauge resistance elements to sense the minute deflection of the diaphragm under an applied pressure (Klute and Peters, 1962). It is the purpose of this paper to describe a tensiometer system of this type and report some operational techniques that have been found useful.
T h e tensiometer (fig. 2) consists of a porous ' c u p ' connected by tubing and valves to a strain gauge pressure transducer. M o r e detailed specification of components is given in the appendix. Provision is m a d e for connection of the transducer to a k n o w n pressure source for calibration. T h e pressure transducer utilizes strain gauge resistance elements in a bridge circuit. Power for the bridge m a y be obtained from a well regulated d.c. supply operating from the a.c. mains, or from mercury cells. T h e latter are quite satisfactory. T h e
deflection of the diaphragm of the transducer in response to the changes in pressure in the water in the tensiometer causes a change in the resistance of the strain gauge elements in the arms of the bridge circuit, which in turn causes a change in the output voltage of the bridge. Within the range of unbalance of the bridge circuit encountered in this application the output voltage m a y be considered a linear function of the applied pressure. A two-point calibration of the tensiometer system is then sufficient. T h e calibration m a y conveniently be effected by using a water or mercury manometer which can be connected to the trans-ducer after first shutting the valve to the tensiometer cup. B y changing the elevation of the water in the open arm of the manometer by a k n o w n amount and hence changing the hydraulic head of the water in the tensiometer one can calibrate the entire transducer-readout system.
T r a n s d u c e r
P o r o u s "Cup1
I Electrical S y s t e m
y Hydraulic S y s t e m
F I G U R E 2. Diagram of the strain gauge pressure transducer-tensiometer system
Alternatively, a connection to a measured, controlled air pressure m a y be m a d e at point A (see fig. 2) for calibration of the system. Precautions must be taken to keep the tensiometer system filled with water w h e n this is done.
Transducers with bellows rather than flat diaphragms are not suitable because they have a larger volume change per unit pressure change. T h e transducer used in this w o r k has a gauge sensitivity of about 0.5 x 106 c m water per c m3. Measurements of gauge sensitivity on tensiometer systems (transducer plus connecting tubing and valves) have indicated gauge sensitivities of 1 x 105 c m water per c m3. This decrease in gauge sensitivity is believed to be due to the additional volume change introduced by the valves and tubing.
The readout system can be of two types, recording or non-recording. For non-recording use the output m a y be displayed on a meter. In either case the unbalance signal from the bridge must be detected. T h e particular transducer that w e have used has an output of about 4 m v per excitation volt for full scale deflection. W h e n the applied voltage is 6 volts, full scale output will be about 24 m v . For a transducer with a 30 p.s.i. range (e.g. about 15 p.s.i. or about 2000 c m of water) the change in the output will be about 12 |iV per c m of water. The amplification and sensitivity required in the readout device depends u p o n the sensitivity desired in the head measurement. For example, if it is desired to display a 100 c m range of hydraulic head or pressure head, the total range of output potential change will be about 1200 liV and the meter and amplifier used for readout must be selected accordingly. With the arrangement described herein w e have been able to detect pressure changes of one m m of water. Thermal drift of the tensiometer (see below) and
electrical noise in the amplifying system have prevented any further increase in sensitivity.
For recording the output, ad.c. amplifier capable of driving a recorder must be used. If the recorder is sufficiently sensitive one m a y be able to eliminate the amplifier and drive the recorder directly from the output of the transducer. W e have preferred d.c. rather than a.c. excitation because of the simpler equipment required for supplying a stable excitation voltage and obtaining the readout from the transducer.
It will usually be desired to adjust the response of the readout device, either a meter or recorder to a convenient value, e.g. 10 or 100 c m of water for full scale deflection. This m a y be done by: 1) adjustment of the excitation voltage o n the transducer, 2) adjustment of the gain of the amplifier used to drive the meter or recorder. W e have found that a voltage divider system (see fig. 3) between the amplifier and recorder is useful to aid in adjustment of the recorder deflection to the desired value.
T r a n s d u c e r
/ Z e r o S u p p r e s s V o l t a g e Divider
4 ' /
Amplifier R e c o r d e r
F I G U R E 3. Schematic drawing of the electrical system of the tensiometer. R\ should have a resistance equal to that of one arm of the bridge about 350 ohms, and Rz about 10 k to 100 k ohms. The value of Rs will depend on the amplifier-recorder combination
A zero suppression system, with which the majority of the signal from the transducer can be suppressed, will sometimes be useful in displaying and expanding to full scale a small part of a given pressure signal. F o r example, it m a y be desirable to display the upper 10 c m of a 100 c m pressure applied to the transducer so that small variations in the pressure can be detected. T h e particular amplifier listed above has this feature. A n external zero suppression can also be arranged as s h o w n in fig. 3.
T h e selection of the tensiometer ' c u p ' or porous plate will be dictated by: a) the geometry required in the flow system to be studied a n d b ) the required bubbling pressure.
T h e bubbling pressure is the pressure required to force air through the wetted porous plate. There are n u m e r o u s possible porous materials a n d shapes that m a y be used.
Porous fired clay plates and filter candles and fritted glass filter sticks and plates in graded pore sizes are available from laboratory supply houses. Porous sintered bronze plates appear promising for application in low tension w o r k (less than 200 c m water).
They m a y be soldered to a suitable metal support and thus a tensiometer can be fabricated entirely from metal parts. Fritted glass filter sticks a n d candles can be obtained with a connecting glass tubing as an integral part of the item. T h e major disadvantage of fritted glass is its fragility, but they are useful. Regardless of the choice of cup a rigid mechanical joint a n d hydraulic seal must be m a d e between the cup and the rest of the tensiometer.
This m a y be a cemented joint (.e.g an E p o x y resin cement) or an O-ring seal, or in the case of sintered bronze, a soldered joint. Ceramic to metal, and glass to metal cemented joints m a y give difficulty. T h e cement used m a y not bond properly and differential thermal expansion of the dissimilar materials m a y cause stresses that the cement cannot overcome.
T h e shape of the porous material is usually a tube, a cup, or a flat plate, depending on
whether the tensiometer is to be inserted into the flow system or merely placed in contact with the boundary of the flow system.
T h e bubbling pressure of the selected cup material should not be excessively higher than is required for the particular flow system to be studied. For example, if it is k n o w n that the pressure head will not fall below —100 c m of water, the porous material selected need not have a bubbling pressure greater than approximately 135 c m of water. In this way the conductance of the tensiometer cup will kept as large as possible, which will help to shorten the response time.
The tubing and valves used to connect the transducer to the porous cup must provide a leak free, rigid hydraulic connection. Copper tubing, or brass pipe and tubing fittings have been found satisfactory. Soldered joints m a y also be used. W e have had greater freedom from leaks with flare type fittings rather than the compression type of tubing fitting. Care must be exercised in the assembly of the tubing and valve assembly to obtain joints that will not leak under suctions approaching one atmosphere.
The valves used for selection of the tensiometer cup or the standard source of calibrating pressure must be of a type that have zero volume change w h e n they are operated, in order to prevent hydraulic pressure transients in the water filled tensiometer, which m a y d a m a g e the transducer or cause disturbance of the flow system. Plug type brass valves have been found useful. Glass stopcocks m a y also be used but of course are relatively fragile and introduce the problem of glass to metal seals that was mentioned above.
U P A T R A N S D U C E R
"Masking T a p e D a m
^^
4V-><v, >:v„
*viT e n s i o m e t e r C u p s
F I G U R E 4. Manifold arrangement to permit use of one transducer with a number of tensiometer cups. The valve Vs leads to a source of deaerated water, V\, V<i, ..., Vn are valves for selecting a given tensiometer cup. Valve Vc leads to the calibrating system
A n u m b e r of tensiometer cups m a y be operated, one at a time, with a single transducer by using a manifold arrangement such as that diagrammed in fig. 4 . Only one of the selector valves should be open at a time, i.e. the valve to a given tensiometer cup must first be closed, before the valve to the next cup to be selected is opened. A manifold arrange-ment such as this has the disadvantage that it increases the volume of water in the tensio-meter, increases the probability of leaks and increases the volume change per unit pressure change for the entire tensiometer setup. In addition there will generally be a hydraulic transient observed w h e n the valves are operated. This transient m a y be negli-gible but occasionally is rather troublesome. In spite of all these disadvantages, the mani-fold system does permit readout from a n u m b e r of tensiometers without the added expense of a transducer for each cup. If a sufficient number of transducers is available, one m a y use a transducer on each tensiometer cup and use electrical switching to select a trans-ducer for connection to the readout system.
The tensiometer system must be completely filled with water, preferably deaerated.
There are m a n y interstices, nooks and corners in which air bubbles m a y become lodged.
The exact technique to be followed to attain complete filling will vary from one experi-mental arrangement to another. W e have found the following procedures, either singly or in combination, to be useful:
1. Assemble the tubing system under water. T h e valves m a y be taken apart and reassem-bled under water thereby insuring complete filling of the annular space in and around the O-ring seals in the valves;
2. Saturate the tensiometer cups before insertion in the flow system and then keep them wet until the tensiometer is assembled ;
3. Flow deaerated water through the tubing to dissolve trapped and lodged air bubbles;
4. Flush the tensiometer system with carbon dioxide followed by a flushing with deaerated water.
In a given flow system it m a y not be feasible to use some of these techniques. For example, 1) m a y not be practical and as an alternative 4) m a y be used. In most cases it should be possible to arrange the tensiometer system so that the portion from the tensio-meter mounting block to the tensiotensio-meter selection valves can be filled with water before connection to the tensiometer cups. T h e transducer can best be inserted with the mounting block pointing upward in the position shown in fig. 4 . T o aid in elimination of air from this part of the system a temporary masking tape d a m can be constructed around the block as shown. Air bubbles on the threads o n the inside of the block should be dislodged using a small wire. T h e transducer is fastened in place while the water level in the d a m is kept above the gasket which seals the transducer. Caution: w h e n the transducer is inserted be sure that a pressure relief channel is provided to prevent damage to the transducer. A very high hydrostatic pressure can be developed in the water in a closed system w h e n inserting a transducer into the mounting block. This precaution also applies w h e n removing the transducer. A pressure relief system can be provided by connecting a water-filled leveling bulb to valve Vs and by leaving the valve open while the transducer is inserted.
That portion of the tubing and valve system between the selection valves and the trans-ducer mounting block can be tested for leaks and/or the presence of air bubbles by connect-ing a capillary tube to valve Vc in place of the standard manometer. Adjust the volume of water in the system so that a meniscus is located at s o m e place in the capillary tube with valves Vs, V1, V2, ... Vn closed, and Vc open. Apply air pressure within the range of the transducer to the capillary tube and observe the meniscus. It should deflect a small amount, if at all, and then remain stationary. Continued motion of the meniscus suggests that a leak is present. A n excessive movement of the meniscus as the pressure is applied indicates entrapped air. This test should also be performed with a partial vacuum (not more than 1/2 to 3/4 of an atmosphere to avoid cavitation) applied to the capillary tube.
S o m e systems that do not leak under pressure will leak under vacuum. Application of a pressure less than atmospheric m a y cause air to c o m e out of solution in the water in the tensiometer and confuse the test observations.
The response time of the tensiometer system as described in this paper and as measured in the conventional manner (Richards, 1949) is one second or less. In m a n y cases the speed of response of the readout system is limiting. W h e n the tensiometer is used in soil that is relatively dry or in soil with a very low conductivity, e.g. a drained sand, the speed of response of the instrument will sometimes be quite low. T h e high impedance of the soil to flow of even the very small volume of water that must be transferred is sufficient to cause a lengthened response time. A procedure that can be used to overcome this problem is the null m o d e of operation using a differential type of transducer. A diagram of the experimental arrangement for this is shown in fig. 5. In flow systems where this problem is likely to be encountered the pressure changes involved in the flow in the soil will probably be slow. A manual null balance technique is thus feasible. T h e change in
back pressure required to cause the output of the transducer to remain constant and hence to keep the diaphragm stationary is a measure of the change in pressure in the water in the tensiometer.
Variations of r o o m temperature m a y cause the temperature of the water in the tensio-meter to change and thereby cause a change in pressure due to the difference in thermal expansion of the tubing and the water. If the tensiometer is in contact with rather wet soil at a high hydraulic conductivity there m a y be little or n o discernible pressure change.
d. c.
P o w e r S u p p I y
1 1
R e a d out S y s t e m
To Tensiometer C u p
To Regulated Back-pressure
Differential Pressure Transducer
F I G U R E 5. Diagram to show the use of a differential pressure transducer as a null device However, if the tensiometer is in soil which happens to possess a low conductivity, the flow necessary to dissipate the pressure buildup is impeded, and thermal drift of the tensio-meter will be observed. Another effect of temperature changes is the direct effect o n the
F I G U R E 5. Diagram to show the use of a differential pressure transducer as a null device However, if the tensiometer is in soil which happens to possess a low conductivity, the flow necessary to dissipate the pressure buildup is impeded, and thermal drift of the tensio-meter will be observed. Another effect of temperature changes is the direct effect o n the