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A pressure transducer for determining atmospheric pressure and evapotranspiration with a hydraulic weighing lysimeter
Agricultural Meteorology, 26 (1982) 273--278 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
273
A PRESSURE TRANSDUCER FOR DETERMINING ATMOSPHERIC PRESSURE AND EVAPOTRANSPIRATION WITH A HYDRAULIC WEIGHING LYSIMETER* LEO J. FRITSCHEN and JAMES SIMPSON College o f Forest Resources, University o f Washington, Seattle, WA 98195 (U.S.A)
(Received December 17, 1981;accepted for publication February 5, 1982) ABSTRACT Fritschen, L.J. and Simpson, J., 1982. A pressure transducer for determining atmospheric pressure and evapotranspiration with a hydraulic weighing lysimeter. Agric. Meteorol., 26: 273--278. The construction and recording of pressure transducers for measuring atmospheric pressure and total pressure, i.e. a hydraulic weighing lysimeter, is described. The principle of operation consists of a variable concentric capacitor to control the frequency of oscillation of a free-running multivibrator. The sensitivity of the transducers was 84 Pa Hz -1 and 8 mm H20 Hz -l . Techniques which would increase the resolution of atmospheric pressure to 0.7 Pa and of a standpipe to 0.06 mm H20 are discussed. The temperature coefficient of the transducers is about 0.5 Hz°C -1 . INTRODUCTION A t m o s p h e r i c v a p o r p r e s s u r e , c a l c u l a t e d w i t h t h e p s y c h r o m e t r i c e q u a t i o n is p r o p o r t i o n a l t o a t m o s p h e r i c p r e s s u r e (P) e = e w - - 0 . 0 0 0 6 6 0 (1 + 0 . 0 0 1 15 T w ) ( T a -- T w ) P
w h e r e e is v a p o r p r e s s u r e ; e w is s a t u r a t i o n v a p o r p r e s s u r e at w e t b u l b t e m p e r a t u r e T w ; a n d Ta is air t e m p e r a t u r e . M e a s u r e m e n t o f a t m o s p h e r i c p r e s s u r e at r e s e a r c h sites ( f o r e x a m p l e w h e r e B o w e n R a t i o E n e r g y B a l a n c e d e t e r m i n a t i o n s are m a d e ) is o f t e n n e g l e c t e d b e c a u s e o f t h e e x p e n s e a n d d i f f i c u l t y o f a u t o m a t i o n . A t m o s p h e r i c p r e s s u r e is u s u a l l y o b t a i n e d f r o m t h e c l o s e s t w e a t h e r s t a t i o n a n d a d d e d t o t h e d a t a a t a l a t e r t i m e or c o n s i d e r e d t o be s o m e c o n s t a n t value. H o w e v e r , t h e use o f c o m p u t e r s at r e s e a r c h sites t o c o l l e c t a n d a n a l y z e d a t a on line suggest t h e n e e d f o r a t m o s p h e r i c p r e s s u r e measurement. M e a s u r e m e n t o f a t m o s p h e r i c p r e s s u r e , like o t h e r e n v i r o n m e n t a l v a r i a b l e s , r e q u i r e s t h e d e t e c t i o n o f a small c h a n g e in a large field. T h e s t a n d a r d a t m o s p h e r i c p r e s s u r e a t sea level is 1 0 1 . 3 kPa; it varies f r o m ca. 98 t o 105 k P a w i t h f r o n t a l s y s t e m s . F u r t h e r m o r e , a t m o s p h e r i c p r e s s u r e d e c r e a s e s b y ca. 10 Pa m -I in t h e l o w e r a t m o s p h e r e , T h u s an a l t i t u d e c h a n g e o f 3 0 0 m w o u l d cause * Research supported in part by USDA-SEA-AR Western Region No. 58-9AHZ-9-931.
0002-1571/82/0000--0000/$02.75 © 1982 Elsevier Scientific Publishing Company
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a 3% change in pressure. This would result in a vapor pressure change of 20.4 Pa, given atmospheric pressure of 100 kPa, dry bulb t e m p e r a t u r e of 33°C and wet bulb temp er at ur e of 23°C. The 20.4 Pa is equivalent to a 1% error in vapor pressure if the 300 m height correction were n o t applied or 0.7% error in the saturation deficit or vapor pressure deficit. Thus the flux of water vapor would contain a similar percentage error. Similarly, the d et er m i nat i on of evapotranspiration with a hydraulic weighing lysimeter requires the detection of a water column height change of a fraction o f a mm in a total height of 4 m. Typically, a differential pressure transducer is used to d e t e c t the small change in height between a live and a d u m m y standpipe (Fritschen et al., 1973), however, measurement of total pressure with a sensitive device would be more desirable. This paper describes a variable capacitance circuit for use with a mercury barometer. The same principle is used to measure atmospheric pressure or water level o f a hydraulic weighing lysimeter. MATERIALS AND METHODS
Enfield and Gillaspy (1980) described a pressure transducer for r e m o t e data acquisition from tensiometers. The principle t hey used was adapted to the m e rc ur y b ar o meter (Fig. 1) and to a hydraulic weighing lysimeter (Fig. 2). These pressure transducers are simply variable concentric capacitors in which the capacitance (C) varies with the height of a m ercury column according to
C(pF)
= 24.1 KL/log
(D/d)
I ~121-~OuT3 Fig. 1. M e r c u r y b a r o m e t e r w h e r e c o m p o n e n t s are: 1. stainless steel t u b e s ; 2. glass t u b e filled w i t h m e r c u r y ; 3. electrical c o n n e c t i o n s ; 4. v e n t e d cap; 5. m u l t i v i b r a t o r circuit; 6. c o n s t a n t a n e l e c t r o d e ; 7. m e t a l can electrically c o n n e c t e d to 5; 8. glass c o n t a i n e r for m e r c u r y ; a n d 9. m e r c u r y .
275
~2 7
*OUT ~5
\ \\\\"1
.
/9
t
Fig. 2. Pressure t r a n s d u c e r w h e r e t h e c o m p o n e n t s are: 1. stainless steel t u b e ; 2. t e f l o n t u b e ; 3. electrical c o n n e c t i o n s ; 4. m e t a l case; 5. m u l t i v i b r a t o r circuit; 6. c o n s t a n t a n elect r o d e ; 7. w a t e r filled t u b e c o n n e c t i n g t h e h y d r a u l i c weighing l y s i m e t e r ; 8. n o n - c o n d u c t i n g c o n t a i n e r ; a n d 9. m e r c u r y .
where K is the dielectric constant of the insulator; L is the length of the capacitor (m); D is the inside diameter of the outer electrode; and d is the outside diameter of the inner electrode. A free-running multivibrator, LM 555CN, is used to convert the capacitance to frequency. The frequency of oscillation (f) of the capacitor is given by f = 1.44/(R1 + 2R2) C where R1 and R2 are resistors shown in Fig. 3.
+ 5-15V
OUT--l-. 31
I
[ UA555HC.Oluf T
1""
Fig. 3. Diagram of t h e m u l t i v i b r a t o r circuit. T h e n u m b e r s refer t o chip c o n n e c t i o n s . R1 and R2 were 1 M o h m for t h e b a r o m e t e r and 3 M o h m for t h e pressure t r a n s d u c e r .
276
Mercury barometer A glass t u b e ( 3 . 7 8 m m inner diam., 6.0 m m o u t e r diam., 800 m m long) w i t h o n e end sealed was filled w i t h m e r c u r y (Fig. 1) and was inverted into a glass m e r c u r y reservoir. A stainless steel t u b e (6.07 m m inner diam., 9.52 m m o u t e r diam., 8 0 0 m m long) w h i c h h a d b e e n soldered to the cap o f the m e t a l can was placed over t h e glass t u b e . An e l e c t r o d e was inserted into t h e m e r c u r y reservoir a n d t h e electrical g r o u n d was c o n n e c t e d t o the m e t a l lid. In t h e field, t h e f r e q u e n c y o f oscillation was to be d e t e r m i n e d f o r one m i n u t e periods with a d a t a s y s t e m t h a t c o n t a i n e d several 99 9 9 9 pulse c o u n t e r s . A value o f o n e M o h m was used f o r R I and R2 to o b t a i n t h e desired f r e q u e n c y . A t 100 kPa, the f r e q u e n c y was a b o u t 1 3 0 0 Hz. T h e b a r o m e t e r was calibrated b y inserting an unsealed glass t u b e t h r o u g h t h e stainless steel t u b e into the m e r c u r y . A v a c u u m p u m p and gauge w e r e a t t a c h e d t o t h e u p p e r end o f t h e glass t u b e . T h e r e l a t i o n o b t a i n e d was P = 1 5 5 . 0 5 E 6 ( 1 / f ) - - 13 107, R 2 = 0 . 9 9 4 T h e m a x i m u m value o f v a c u u m tested was 95 kPa. T h e slope o f t h e a b o v e r e l a t i o n was a s s u m e d to e x t e n d linearly t h r o u g h o n e a t m o s p h e r e . T h e interc e p t was a d j u s t e d b y c o m p a r i n g t h e o p e r a t i n g b a r o m e t e r w i t h a F o r t i n - t y p e b a r o m e t e r . T h e t e m p e r a t u r e c o e f f i c i e n t was d e t e r m i n e d to be 0 . 5 3 8 H z ° C -1 . T h e r e f o r e t h e usable r e l a t i o n b e c a m e P = 1 5 5 . 0 5 E 6 { 1 / [ f + 0 . 5 3 8 ( T - - 20)] } - - 13 107 T h e sensitivity o f t h e b a r o m e t e r is a b o u t 84 Pa Hz -1 . By c o u n t i n g f r e q u e n c y for o n e m i n u t e , t h e r e s o l u t i o n was 1.4 Pa.
Pressure transducer T h e pressure t r a n s d u c e r was a s s e m b l e d as s h o w n in Fig. 2. T h e w a t e r - m e r c u r y i n t e r f a c e reservoir consisted o f t w o 28.6 m m PVC caps c e m e n t e d on a s h o r t piece o f PVC pipe. A t e f l o n fitting was t h r e a d e d i n t o t h e b o t t o m of t h e reservoir. A t e f l o n t u b e (1.59 m m inner diam., 3.18 m m o u t e r diam.) was a t t a c h e d to t h e fitting and inserted t h r o u g h t h e stainless steel t u b e . T h e stainless steel t u b e was 3.52 m m inner diam., 4.88 m m o u t e r diam., and 6 0 0 m m long. T u b e fittings w e r e t h r e a d e d into t h e t o p o f t h e reservoir for t h e w a t e r c o n n e c t i o n and f o r the electrical g r o u n d . F o r this a p p l i c a t i o n t h e electrical g r o u n d was inserted into the m e r c u r y b e c a u s e t h e w a t e r pressure line ran t h r o u g h brass fittings which were g r o u n d e d . T h e e l e c t r o d e was a t t a c h e d to t h e stainless steel t u b e w h i c h was m o u n t e d on plastic insulators. T o o b t a i n a f r e q u e n c y c o m p a t i b l e with t h e d a t a s y s t e m c o u n t e r s , t h r e e M o h m resistors w e r e used f o r R1 a n d R2. T h e pressure t r a n s d u c e r was c a l i b r a t e d against a w a t e r c o l u m n ranging f r o m 1 t o 3 m a b o v e t h e t r a n s d u c e r . T h e r e l a t i o n o f height o f w a t e r c o l u m n (H) to f r e q u e n c y was
277 H = -- 7.336 + 15.073E3 ( l / f ) , R 2 = 0.9997 The t e m p e r a t u r e coefficient was determined at full scale (6.65 m H 2 0 equivalent) to be 0.555 Hz°C -1 . Therefore, the useable relation became H = - - 7 . 3 3 6 + 15.073E3 { 1 / I f + 0.555 ( T - - 2 4 ) ] } The sensitivity of the pressure transducer at 4 m water column height is 8 mm H 2 0 Hz -1. Summing the frequency for one minute increases the sensitivity to 0.13 mm H20. This is equivalent to transpiration for a 10 minute period. This sensitivity may be increased by a factor of 2 by inclining the mercury column at a 63 ° angle from vertical. The t em perat ure coefficient is equivalent to 4.4 mm°C -I for the vertical column. However, if the pressure transducer is located in a manhole adjacent to the lysimeter where the temperature varies by only a few tenths of a degree during the day, the readings can be corrected for the t em p erat ure variations. RESULTS AND DISCUSSION The barometer and pressure transducer were installed at a field research site during the spring o f 1981. T hey operated w i t h o u t difficulty t h r o u g h o u t the summer and fall of 1981. One of the big advantages of the oscillator circuit is its lack of dependence upon stabilized input voltage. The circuit will operate with an input voltage from 5 to 15 volts. Since the o u t p u t is varying f r eq u en cy which is counted, signal lines may be very long but they should be shielded to avoid undesired pickup. Only three wires are required to operate either system. The sensitivity of the transducers may be improved by increasing the frequency o f oscillation. With the cases described, the frequency was adjusted so that a 99 999 pulse counter would n o t overflow during one minute of counting. The sensitivity could be doubled by increasing the frequency to ensure that the counter would overflow once but n o t twice during one minute. Although the accuracy of these pressure transducers is n o t voltagedependent, it is highly d e p e n d e n t upon precise timing. At 1300 Hz, a timing error of 0.01 s during one minute c o u n t period would result in an error of 18.2 Pa atmospheric pressure and 0.03 mm H 2 0 equivalent of the lysimeter standpipe. Th e error in atmospheric pressure would be a b o u t 0.02% but the error could be 200% of one minute values of evapotranspiration rates at midday. The latter error would be pr opor t i onat el y smaller if half-hourly or hourly values were used. With the computer-controlled data system used for this study, a timing precision of 100 ps is achievable which would be equivalent to 0.00028 m m H20. F or lysimetric purposes, the measurement of total pressure rather than differential pressure is more desirable. The total pressure measurement negates the need to maintain a very stable d u m m y standpipe, maintain a record o f the d u m m y standpipe, and minimize t e m p e r a t u r e gradients along the standpipes.
278 REFERENCES Enfield, C.G. and Gillaspy, C.V., 1980. Pressure transducer for remote data acquisition. Trans. ASAE, 1195--1200. Fritschen, L.J., Cox, L. and Kinerson, R., 1973. A 28-meter Douglas-fir in a weighing lysimeter. For. Sci., 19: 256--261.
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A PRESSURE TRANSDUCER FOR DETERMINING ATMOSPHERIC PRESSURE AND EVAPOTRANSPIRATION WITH A HYDRAULIC WEIGHING LYSIMETER* LEO J. FRITSCHEN and JAMES SIMPSON College o f Forest Resources, University o f Washington, Seattle, WA 98195 (U.S.A)
(Received December 17, 1981;accepted for publication February 5, 1982) ABSTRACT Fritschen, L.J. and Simpson, J., 1982. A pressure transducer for determining atmospheric pressure and evapotranspiration with a hydraulic weighing lysimeter. Agric. Meteorol., 26: 273--278. The construction and recording of pressure transducers for measuring atmospheric pressure and total pressure, i.e. a hydraulic weighing lysimeter, is described. The principle of operation consists of a variable concentric capacitor to control the frequency of oscillation of a free-running multivibrator. The sensitivity of the transducers was 84 Pa Hz -1 and 8 mm H20 Hz -l . Techniques which would increase the resolution of atmospheric pressure to 0.7 Pa and of a standpipe to 0.06 mm H20 are discussed. The temperature coefficient of the transducers is about 0.5 Hz°C -1 . INTRODUCTION A t m o s p h e r i c v a p o r p r e s s u r e , c a l c u l a t e d w i t h t h e p s y c h r o m e t r i c e q u a t i o n is p r o p o r t i o n a l t o a t m o s p h e r i c p r e s s u r e (P) e = e w - - 0 . 0 0 0 6 6 0 (1 + 0 . 0 0 1 15 T w ) ( T a -- T w ) P
w h e r e e is v a p o r p r e s s u r e ; e w is s a t u r a t i o n v a p o r p r e s s u r e at w e t b u l b t e m p e r a t u r e T w ; a n d Ta is air t e m p e r a t u r e . M e a s u r e m e n t o f a t m o s p h e r i c p r e s s u r e at r e s e a r c h sites ( f o r e x a m p l e w h e r e B o w e n R a t i o E n e r g y B a l a n c e d e t e r m i n a t i o n s are m a d e ) is o f t e n n e g l e c t e d b e c a u s e o f t h e e x p e n s e a n d d i f f i c u l t y o f a u t o m a t i o n . A t m o s p h e r i c p r e s s u r e is u s u a l l y o b t a i n e d f r o m t h e c l o s e s t w e a t h e r s t a t i o n a n d a d d e d t o t h e d a t a a t a l a t e r t i m e or c o n s i d e r e d t o be s o m e c o n s t a n t value. H o w e v e r , t h e use o f c o m p u t e r s at r e s e a r c h sites t o c o l l e c t a n d a n a l y z e d a t a on line suggest t h e n e e d f o r a t m o s p h e r i c p r e s s u r e measurement. M e a s u r e m e n t o f a t m o s p h e r i c p r e s s u r e , like o t h e r e n v i r o n m e n t a l v a r i a b l e s , r e q u i r e s t h e d e t e c t i o n o f a small c h a n g e in a large field. T h e s t a n d a r d a t m o s p h e r i c p r e s s u r e a t sea level is 1 0 1 . 3 kPa; it varies f r o m ca. 98 t o 105 k P a w i t h f r o n t a l s y s t e m s . F u r t h e r m o r e , a t m o s p h e r i c p r e s s u r e d e c r e a s e s b y ca. 10 Pa m -I in t h e l o w e r a t m o s p h e r e , T h u s an a l t i t u d e c h a n g e o f 3 0 0 m w o u l d cause * Research supported in part by USDA-SEA-AR Western Region No. 58-9AHZ-9-931.
0002-1571/82/0000--0000/$02.75 © 1982 Elsevier Scientific Publishing Company
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a 3% change in pressure. This would result in a vapor pressure change of 20.4 Pa, given atmospheric pressure of 100 kPa, dry bulb t e m p e r a t u r e of 33°C and wet bulb temp er at ur e of 23°C. The 20.4 Pa is equivalent to a 1% error in vapor pressure if the 300 m height correction were n o t applied or 0.7% error in the saturation deficit or vapor pressure deficit. Thus the flux of water vapor would contain a similar percentage error. Similarly, the d et er m i nat i on of evapotranspiration with a hydraulic weighing lysimeter requires the detection of a water column height change of a fraction o f a mm in a total height of 4 m. Typically, a differential pressure transducer is used to d e t e c t the small change in height between a live and a d u m m y standpipe (Fritschen et al., 1973), however, measurement of total pressure with a sensitive device would be more desirable. This paper describes a variable capacitance circuit for use with a mercury barometer. The same principle is used to measure atmospheric pressure or water level o f a hydraulic weighing lysimeter. MATERIALS AND METHODS
Enfield and Gillaspy (1980) described a pressure transducer for r e m o t e data acquisition from tensiometers. The principle t hey used was adapted to the m e rc ur y b ar o meter (Fig. 1) and to a hydraulic weighing lysimeter (Fig. 2). These pressure transducers are simply variable concentric capacitors in which the capacitance (C) varies with the height of a m ercury column according to
C(pF)
= 24.1 KL/log
(D/d)
I ~121-~OuT3 Fig. 1. M e r c u r y b a r o m e t e r w h e r e c o m p o n e n t s are: 1. stainless steel t u b e s ; 2. glass t u b e filled w i t h m e r c u r y ; 3. electrical c o n n e c t i o n s ; 4. v e n t e d cap; 5. m u l t i v i b r a t o r circuit; 6. c o n s t a n t a n e l e c t r o d e ; 7. m e t a l can electrically c o n n e c t e d to 5; 8. glass c o n t a i n e r for m e r c u r y ; a n d 9. m e r c u r y .
275
~2 7
*OUT ~5
\ \\\\"1
.
/9
t
Fig. 2. Pressure t r a n s d u c e r w h e r e t h e c o m p o n e n t s are: 1. stainless steel t u b e ; 2. t e f l o n t u b e ; 3. electrical c o n n e c t i o n s ; 4. m e t a l case; 5. m u l t i v i b r a t o r circuit; 6. c o n s t a n t a n elect r o d e ; 7. w a t e r filled t u b e c o n n e c t i n g t h e h y d r a u l i c weighing l y s i m e t e r ; 8. n o n - c o n d u c t i n g c o n t a i n e r ; a n d 9. m e r c u r y .
where K is the dielectric constant of the insulator; L is the length of the capacitor (m); D is the inside diameter of the outer electrode; and d is the outside diameter of the inner electrode. A free-running multivibrator, LM 555CN, is used to convert the capacitance to frequency. The frequency of oscillation (f) of the capacitor is given by f = 1.44/(R1 + 2R2) C where R1 and R2 are resistors shown in Fig. 3.
+ 5-15V
OUT--l-. 31
I
[ UA555HC.Oluf T
1""
Fig. 3. Diagram of t h e m u l t i v i b r a t o r circuit. T h e n u m b e r s refer t o chip c o n n e c t i o n s . R1 and R2 were 1 M o h m for t h e b a r o m e t e r and 3 M o h m for t h e pressure t r a n s d u c e r .
276
Mercury barometer A glass t u b e ( 3 . 7 8 m m inner diam., 6.0 m m o u t e r diam., 800 m m long) w i t h o n e end sealed was filled w i t h m e r c u r y (Fig. 1) and was inverted into a glass m e r c u r y reservoir. A stainless steel t u b e (6.07 m m inner diam., 9.52 m m o u t e r diam., 8 0 0 m m long) w h i c h h a d b e e n soldered to the cap o f the m e t a l can was placed over t h e glass t u b e . An e l e c t r o d e was inserted into t h e m e r c u r y reservoir a n d t h e electrical g r o u n d was c o n n e c t e d t o the m e t a l lid. In t h e field, t h e f r e q u e n c y o f oscillation was to be d e t e r m i n e d f o r one m i n u t e periods with a d a t a s y s t e m t h a t c o n t a i n e d several 99 9 9 9 pulse c o u n t e r s . A value o f o n e M o h m was used f o r R I and R2 to o b t a i n t h e desired f r e q u e n c y . A t 100 kPa, the f r e q u e n c y was a b o u t 1 3 0 0 Hz. T h e b a r o m e t e r was calibrated b y inserting an unsealed glass t u b e t h r o u g h t h e stainless steel t u b e into the m e r c u r y . A v a c u u m p u m p and gauge w e r e a t t a c h e d t o t h e u p p e r end o f t h e glass t u b e . T h e r e l a t i o n o b t a i n e d was P = 1 5 5 . 0 5 E 6 ( 1 / f ) - - 13 107, R 2 = 0 . 9 9 4 T h e m a x i m u m value o f v a c u u m tested was 95 kPa. T h e slope o f t h e a b o v e r e l a t i o n was a s s u m e d to e x t e n d linearly t h r o u g h o n e a t m o s p h e r e . T h e interc e p t was a d j u s t e d b y c o m p a r i n g t h e o p e r a t i n g b a r o m e t e r w i t h a F o r t i n - t y p e b a r o m e t e r . T h e t e m p e r a t u r e c o e f f i c i e n t was d e t e r m i n e d to be 0 . 5 3 8 H z ° C -1 . T h e r e f o r e t h e usable r e l a t i o n b e c a m e P = 1 5 5 . 0 5 E 6 { 1 / [ f + 0 . 5 3 8 ( T - - 20)] } - - 13 107 T h e sensitivity o f t h e b a r o m e t e r is a b o u t 84 Pa Hz -1 . By c o u n t i n g f r e q u e n c y for o n e m i n u t e , t h e r e s o l u t i o n was 1.4 Pa.
Pressure transducer T h e pressure t r a n s d u c e r was a s s e m b l e d as s h o w n in Fig. 2. T h e w a t e r - m e r c u r y i n t e r f a c e reservoir consisted o f t w o 28.6 m m PVC caps c e m e n t e d on a s h o r t piece o f PVC pipe. A t e f l o n fitting was t h r e a d e d i n t o t h e b o t t o m of t h e reservoir. A t e f l o n t u b e (1.59 m m inner diam., 3.18 m m o u t e r diam.) was a t t a c h e d to t h e fitting and inserted t h r o u g h t h e stainless steel t u b e . T h e stainless steel t u b e was 3.52 m m inner diam., 4.88 m m o u t e r diam., and 6 0 0 m m long. T u b e fittings w e r e t h r e a d e d into t h e t o p o f t h e reservoir for t h e w a t e r c o n n e c t i o n and f o r the electrical g r o u n d . F o r this a p p l i c a t i o n t h e electrical g r o u n d was inserted into the m e r c u r y b e c a u s e t h e w a t e r pressure line ran t h r o u g h brass fittings which were g r o u n d e d . T h e e l e c t r o d e was a t t a c h e d to t h e stainless steel t u b e w h i c h was m o u n t e d on plastic insulators. T o o b t a i n a f r e q u e n c y c o m p a t i b l e with t h e d a t a s y s t e m c o u n t e r s , t h r e e M o h m resistors w e r e used f o r R1 a n d R2. T h e pressure t r a n s d u c e r was c a l i b r a t e d against a w a t e r c o l u m n ranging f r o m 1 t o 3 m a b o v e t h e t r a n s d u c e r . T h e r e l a t i o n o f height o f w a t e r c o l u m n (H) to f r e q u e n c y was
277 H = -- 7.336 + 15.073E3 ( l / f ) , R 2 = 0.9997 The t e m p e r a t u r e coefficient was determined at full scale (6.65 m H 2 0 equivalent) to be 0.555 Hz°C -1 . Therefore, the useable relation became H = - - 7 . 3 3 6 + 15.073E3 { 1 / I f + 0.555 ( T - - 2 4 ) ] } The sensitivity of the pressure transducer at 4 m water column height is 8 mm H 2 0 Hz -1. Summing the frequency for one minute increases the sensitivity to 0.13 mm H20. This is equivalent to transpiration for a 10 minute period. This sensitivity may be increased by a factor of 2 by inclining the mercury column at a 63 ° angle from vertical. The t em perat ure coefficient is equivalent to 4.4 mm°C -I for the vertical column. However, if the pressure transducer is located in a manhole adjacent to the lysimeter where the temperature varies by only a few tenths of a degree during the day, the readings can be corrected for the t em p erat ure variations. RESULTS AND DISCUSSION The barometer and pressure transducer were installed at a field research site during the spring o f 1981. T hey operated w i t h o u t difficulty t h r o u g h o u t the summer and fall of 1981. One of the big advantages of the oscillator circuit is its lack of dependence upon stabilized input voltage. The circuit will operate with an input voltage from 5 to 15 volts. Since the o u t p u t is varying f r eq u en cy which is counted, signal lines may be very long but they should be shielded to avoid undesired pickup. Only three wires are required to operate either system. The sensitivity of the transducers may be improved by increasing the frequency o f oscillation. With the cases described, the frequency was adjusted so that a 99 999 pulse counter would n o t overflow during one minute of counting. The sensitivity could be doubled by increasing the frequency to ensure that the counter would overflow once but n o t twice during one minute. Although the accuracy of these pressure transducers is n o t voltagedependent, it is highly d e p e n d e n t upon precise timing. At 1300 Hz, a timing error of 0.01 s during one minute c o u n t period would result in an error of 18.2 Pa atmospheric pressure and 0.03 mm H 2 0 equivalent of the lysimeter standpipe. Th e error in atmospheric pressure would be a b o u t 0.02% but the error could be 200% of one minute values of evapotranspiration rates at midday. The latter error would be pr opor t i onat el y smaller if half-hourly or hourly values were used. With the computer-controlled data system used for this study, a timing precision of 100 ps is achievable which would be equivalent to 0.00028 m m H20. F or lysimetric purposes, the measurement of total pressure rather than differential pressure is more desirable. The total pressure measurement negates the need to maintain a very stable d u m m y standpipe, maintain a record o f the d u m m y standpipe, and minimize t e m p e r a t u r e gradients along the standpipes.
278 REFERENCES Enfield, C.G. and Gillaspy, C.V., 1980. Pressure transducer for remote data acquisition. Trans. ASAE, 1195--1200. Fritschen, L.J., Cox, L. and Kinerson, R., 1973. A 28-meter Douglas-fir in a weighing lysimeter. For. Sci., 19: 256--261.