Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02405620 2005-02-28
BUBBLE WATER DEPTH MEASURING METHOD
AND SYSTEM THEREOF
Background of the Invention
'The invention is related to providing a bubble water depth measuring method
for
compensating fox a total error of a bubble Water depth or water level
measurement in a
reservoir that a water level shifts in a wider range to enable the measurement
of the water
depth or water level with a higher accuracy, using an industrial pressure
transducer, in which
the pressure transducer is manufactured in an environment that a
circumferential air
temperature is changed in the range of -40°C to +50°C, and a
system thereof.
Particularly, the invention is related to providing a bubble water depth
measuring
method for measuring a water column pressure to enable the remote-measurement
of a water
depth or water level in a reservoir, a lake or a river. Herein, it is noted
that only a water depth
measurement now will be explained below, because a bubble water level meter is
a device for
measuring a water depth and calculating it into a water level.
Prior Art
There has been much interest irr a bubble water level meter that can be used
for a
hydrology observatory, because the bubble water level meter can measure a
water depth under
an icy condition, if a water surface is frozen in a reservoir, a lake or a
river. The water level
meter for the hydrology observatory has characteristics as follows:
- In a reservoir where the changing depth of a water level is usually up to 1
Om.
- There are many areas where a circumferential air temperature of a water
level
observatory post is in the range of -40°C to +50°C in seasons.
- Most of the water level observatory posts are not equipped with warming and
cooling utilities but also lack a power source unit.
- The demand for a remote-water level measuring system is being increased
because
many water level observatory posts are established in uninhabited places.
In light of these facts, there is a problem in that a bubble type water level
meter has a
lower accuracy under the conditions of the severe weather change in seasons
and a larger
water level change depth.
The bubble type water level meter has advantages in that its installing,
maintenance
and operating costs are relatively lower and can measure a water level even
when a reservoir
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CA 02405620 2005-02-28
and a river are frozen in winter, but it is broadly not used as a hydrology
observatory because
its measuring error is larger.
Also, the bubble type can be operated with more stability compared with other
water
level meters in a river where the concentration of floating particles is
higher. A sand and earth
layer is swiftly changed and saves on the maintenance and operating costs but
its measuring
accuracy is low.
Referring to Fig. l, error factors that are caused upon measuring a water
depth
according to a bubble generating method will be explained below, and a unit of
a water
column pressure will be represented as cmH20 or mmH20 for the purpose of
consulting the
convenience in calling the term "error" as an abbreviation of "absolute
error". 1 is a water
column pressure tube, which , will be called "a water depth measuring tube",
10 is a
compressed gas generating device and 3 is a pressure transducer. A pressure
applied to the
lower end portion of the water depth measuring tube 1 is as follows:
Pc= yhx+Pa, (1)
Wherein, hx is an altitude difference of water filled in the water depth
measuring
tube l, which is considered as a water depth. 'y is a specific gravity
(gm/cm3) of water. yhx is a
water column pressure. Pa is an atmosphere pressure on a water surface.
The pressure transducer 3 measures a surplus pressure, not for an atmosphere
pressure (P~Pab-Pa; Pab-Absolute pressure). The water depth measuring tube 1
filled with
water generates bubbles at the lower end portion with compressed gas being
supplied to the
upper end portion thereof. Upon generating of the bubbles, the pressure
transducer 3 measures
the compressed gas pressure, and its result is as follows:
prax - ~x + ~px + lga -' pao ~- yg ~o '~ l~pb;
Wherein, ~px is an absolute error of the pressure transducer 3 at the time of
measuring Pmx. OPa=(Pa-Pao) is a difference between an atmosphere Pa on the
water surface
and an atmosphere Pao applied to the pressure transducer 3. Generally, Pao ~
Pa because a
water level observatory post is placed on a much higher position than a water
surface. Ho is
an altitude difference between the lower end portion of the water depth
measuring tube 1 and
the mounting position of the pressure transducer 3. yg is a density of
compressed gas to be
supplied to the water depth measuring tube 1. Opb is a pressure of a
supplementary
compressed gas changed according to the bubble pressure that is formed at the
lower end
portion of the water depth measuring tube 1. Opb will be ignored because its
reducing method
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CA 02405620 2005-02-28
is now developed. In expression (2), all items are a measuring error of a
water column
pressure yhx with the exception of the water column pressure yhx. The
measuring errors are
summed up is assumed as total absolute error ~~x of the water column pressure
yhx, and are
calculated as follows:
~f~x = L~~x -I- L~~a - ~'~~d ,
Wherein, spa - pa-pao = ya(Ho -hx) , ya is an air density, which can be seen
as
r$~ Pmx ~ Pa
. ygo is a density of a compressed gas to be used at an atmosphere. When the
water depth has changed over 10m in a reservoir, the altitude difference
between the lower
end portion of the water depth measuring tube 1 and the mounting position of
the pressure
transducer 3 usually becomes Ho>_20m.
Looking into ~Pa and ygHo, if Ho=20rn=2000cm, hx is changed in the range of
200
to 1 OOOcm, an air density ~a =1.2 ' 3.0-~ gr~ ~c'~sa 3 and a water depth is
measured using a
compressed gas, the change of ~Pa is as follows:
4Pa = 1.2° 10-3(2000-200) = 2. l6gmlcm2 = 2.16cmH20(if hz = 200cm)
OPa = 1.2M 0-3(2000-200) = 1.2gm/cm2=1.2cmH20(if hx= 1004cm)
ygHo = 1.2° 10-3° 1.2°2000 = 2.88gmlcm2~ 2.9cmH20(if hx=
200cm)
ygHo = 1.2°10-3°2°2000 = 4.8gmlcmz~ 4.8cmH20(if hx=
1000cm)
Herein, it is known that when hx=200~1000cm, the error changing range is 2.16 -
2.9 ~ -0.74cm to 1.2 - 4.8 ~ -3.6cm due to OPa-ygHo. If an allowance error of
the water depth,
water level is ~1 cm, the error component of ~Pa - ygHo cannot be ignored. Of
course, ya was
ignored though it is changed according to a temperature.
The pressure transducer 3 includes a temperature compensation circuit for
correcting
the property that a pressure sensor mounted therein is changed according to a
temperature.
However, the temperature compensation circuit is lacking of compensating for
an error
changed according to a temperature t and a pressure P to be measured
perfectly. An error of a
curve ap = f(t;P) always happens.
For example, when the pressure transducer (Model PTX1000) that secures a
pressure
error 8p (_ +0.25% fs) at room temperature (t = 2024°C) measures a
pressure of P=1000cm
H20 while being cooled at -10°C, its measuring error ~p - -31 cm H20,
even though its use
temperature range is introduced as -40°C ~ +90°C. A more precise
pressure transducer
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CA 02405620 2005-02-28
(Model PDCR862) has a useable temperature range of -54°C~+125°C
and a measuring error
by of +0.1 % fs. Therefore, Op = 8gm/cm2, and an absolute error hx is ~8cm. Of
course, if
only a gas temperature is changed without cooling or heating the pressure
transducer on the
whole, the error is reduced. When a bubble water level meter is installed
outdoors, the
pressure transducer is cooled or heated on the whole. Under the condition that
a
circumferential air temperature is changed in the range of -
40°C~+50°C, there doesn't exist
any pressure transducer for securing Op < ~ 1 gm/cm3 in full range to be
measured.
Therefore, even though it is possible to compensate for the error ~~x caused
at the
time of measuring the water column pressure yhx, perfectly, when the water
depth hx is
~~x
calculated into ~~ - ~ ~, , knowing nothing about an average density y of
water causes a
corresponding error h'x as follows:
hX=~~; t~hX=~x-1- 'V-1~=~
fix _
Therefore, a total error of the measurement of the water depth hx is as
follows:
~r = l''°x -I- F~x .
x ~r ~
~h'x-~x-1-~r+~~x=~r+~~r.
x Y x (4)
Wherein, an error 8h'x is a parameter that varies according to a
circumferential
temperature and a measuring range, but it is not an integer. Due to this, it
cannot be simply
compensated. Therefore, a bubble type water depth measuring method is subject
to the error.
There are bubble type water depth and water level meters that exclude or
compensate for
8y and EBx. The bubble water measuring methods are disclosed in Publications
as
follows:
1) US Patent No. 5,791,187 issued on August 11, 1998, which is titled "Level
Measurement Method using Measurements of Water Column Pressure Thereof'
2) Canadian Patent No. 2,171,801 on January 23, 2000, which is titled "Level
Measurement Method using Measurements of Water Column Pressure Thereof'
3) Germany Patent DE19620656C2 issued on March 2, 2000
4) Japanese Patent No. 2855423 issued on February 10, 1999
5) South Korean Patent No. 185260 issued on December 28, 1998
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These known corresponding publications disclose a method of measuring a water
depth hx, which will be explained with reference to Fig. 2. 2 is a water
column pressure tube
that has a shorter length than a water depth measuring tube 1 by Oh. A water
pressure of the
water column pressure tube 2 filled with water is: yh2 = y(h2-~h). The water
depth measuring
tube 1 and the water column pressure measuring tube 2 are connected through
valves 51 and
52 to a buffer tank 4. Compressed gas is supplied through a valve So to the
buffer tank 4. 3 is a
pressure transducer.
As a part for enhancing the accuracy of the water depth measurement the
arrangement uses two measuring tubes 1 and 2 to measure a water specific
gravity y that is
changed according to the temperature and the components of water and then
divide a water
column pressure yhx by the water specific gravity y. It is interesting that
the separate
measurement of the water specific gravity y is not necessary. If only the
water depth hx is to
be determined, it can be calculated using a simple and effective expression as
follows:
_ L~Ja
~x 1- p~2 ~- _ Sao ~° ~~ '
Pmx
()
Wherein, Pm2 is a bubble pressure generated at the water column pressure
measuring
f
tube 2, yao is a specific gravity of air, and ~ °° ~' is ignored
because of a very small value.
Assuming that E~, ~a2=0, the expression (5) is as follows:
Pmx ~i~3 =, '~~x ~'a _ y~'ax8~ = h
x Prr~x -pmt ~x - ~~~x -'~~3~ ~d x
Herein, it is noted that the water specific gravity 'y is entirely excluded
from the
expression (S). It is because hx and h2 have a difference of ~h and it is
represented as yx=y2.
However, as EOx ~ 0, ~~2 ~ 0, a water depth h'x is as follows:
~x~1+ ~x~
x+~'~x \ x
~x - ~X 'f ~~x - ~2 - ~~2 - ~~ = l1 + ~~x - ~~2 ~
/1 + ~x
~x II\
~1 + F.1'~x _ ~.1'~2
y~ (6)
CA 02405620 2005-02-28
Lr~tx - ~r~a
!C 1.0
Herein, assuming that and it is a very small value, it may be ignored.
The expression (6) is represented as follows:
~X = ytx ~l + ~ x ~~l - ~~'1x~- ~b2
x ,,JJ v ~ i
fis ~'t 1 + ~,,,~~x - ~~x 157
x~ ~x
(7)
Therefore, an absolute error ah'x that is resulted from the measurement of the
water
is as follows:
~n'x - ~L~x - ~~itex - ~62 ~~~~~
= dpx+ APax- y~Ho - ~apx -i- llP~x - y~Ho - ~a - ~iPrxz + y~aHo
= dpx + ~Pax- y~Ha - ~LSpx - L~pa + htp~ + ~~g - yg,.,~ia ~ ~h
Herein, considering that spa (= OPax-~Pa2) and (~yg2-ygx)Ho is a very small
value,
it is ignored. The resulting expression is as follows:
,,~,,~ _ h
~h'x~'~px-~~px ~p2~+~Pax-~gxHd
Therefore, Oh'x is as follows:
topx +(epz -~~? oh + (~a~ - y~Ho)l
~hx = r
The conventional method excludes the water specific gravity 'y, but it doesn't
compensate for errors ~px, ~p2 of the pressure transducers and an error
component due to an
altitude difference.
~~Pax - YgxHa ~' Yao tHa - ~x ~ - Yao ' ~oX Ho.= YaoHa ~1 _ Pm Pp Pa ~ - Yao
~s
For these reasons, the conventional method doesn't secure the higher accuracy
of the
water depth measurement. For example, if Ho=2000Cm, hx=1000Cm, Oh=100Cm, t = -
I O°C,
measuring the water depth hx (= I OOOcm) is as follows:
3lcraa,
Y,
°px =-34c»a,
y
pax YSXHa -3.6GT22
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.~.4N~= 34+31+3~ id-3.u=-7.6cn;
As a result, a water column pressure measuring error becomes larger, if a
water depth
in a reservoir, a lake, a river, etc. is measured by a water level meter,
because an error of a
pressure transducer that measures a bubble pressure is greatly changed
dependent upon a
circumferential air temperature t and a pressure P to be measured at an
unattended observation
post under the condition that an atmosphere temperature is in the range of -
40°C in Summer
to +40°C.
There often have occurred larger measuring errors of water depth or water
level, due
to the fact that the specific gravity of water changes with differences in
altitude between a
water surface and a position of the transducer to be mounted. An altitude
difference between
lower and upper ends of a water column pressure measuring tube and a
difference between a
pressure of a bubble generating compressed gas to be measured and a pressure
at a water
depth to be measured based on a compressed density upon the bubble generating
lies within a
larger range.
As described above, the conventional technology has a disadvantage in that its
water
level measurement in a reservoir cannot secure the accuracy of~1 cm contrary
to the fact that
the water level measurement of the reservoir requires the accuracy of less
than~1 cm.
For the purpose of explaining the invention in detail, firstly considering the
property
of a pressure transducer, the common characteristics of pressure transducers
known are as
follows:
The pressure transducer includes a temperature characteristic compensation
device
because the property of a pressure sensor is changed according to a
temperature. However, it
generally doesn't compensate for the temperature. If a circumferential
temperature is beside a
normal one, for example the temperature 20 ~ 25°C, the pressure
measuring error is increased.
For example, the pressure transducers Model PTX1000 and PDCR862 having a
relatively good performance have the following characteristics: when at room
temperature
t=24°C, the Model PTX1000 represents that b= ~0.25% fs, the Model
PDCR862 represents
that b= ~0.1%fs. The usable temperature ranges of each of Models PTX1000 and
PDCR862
are represented in Table 1 as -40°C~+9p°C and -
54°C~+125°C. Tables 1 and 2 represent
results that a pressure error ~p is calculated into a water column pressure
cmH2~, in which
the pressure error ~p is a difference between a reference pressure based on an
outputting
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signal, when the temperature t is 24°C, and a pressure based on an
outputting signal, when the
temperature t is changed in the range of -24°C~+50°C, the
pressure difference Op is equal to
an absolute error of a water depth measurement, if a water specific gravity y=
1Ø Relative
errors 8% are represented under the pressure error Bp. The calculated data is
rounded to two
decimals.
TABLE 1. PTX1000 ~p cmH20. 8%
fC P: kgnm
0 0.1 0.2 0.4 0.6 0.8 1
(+50) ~p 9 11 11.8 13.8 14.6 15.3 16
S% 11 5.9 3.45 2.43 1.9 1.6
(+40) ~p 8 8.2 8.5 8.84 9.9 10.24 1 D.9
b 8.2 4.25 2.2 1.65 1.28 1.09
(+30) ~p 3.5 5.1 5.43 6 4.26 3.8 3.4
5.1 2.7 1.5 0.7 0.47 0.3
(+10) ~p -9 -6.7 -7.9 -9.6 -10.3 -11 -11.8
b -6.7 -3.9 -2.4 -1.7 -1.4 -1.2
0 ~p -17 -12.8 -16.3 -18 -19.3 -20.4 -21.2
-1 -8.2 -4.5 -3.2 -2.55 -2.1
2.8
-10 4p -26 -19.4 -23.5 -26.7 -28.7 -30.3 -31.7
-19.4 -11.7 -6.7 -4.7 -3.7 -3.17
-20 Op -34.5 -32.7 -35.2 -38.4 -42.2 -43.5 -45.4
-32 -17.6 -9.6 -7 -5.4 -4.5
~nang~ng omy the temperature of compressed air, but not cooling or freeing the
pressure transducer on the whole, means that the pressure transducers are
represented as better
characteristics than those of Table 1. If the pressure transducer is used in a
bubble water level
meter, its whole temperature is changed according to a circumferential
temperature. Table 1
represents characteristics when a pressure is increased from 0 to lkg/cm2, in
which the
characteristics are better than when a pressure is reduced from 1 to Okg/cm2.
(It means
Histeresis error or characteristics.)
Table 2 represents the characteristics of the pressure transducer Model
PDCR826
that'are better than those of Model PTX1000. Seeing Table 2, the temperature
compensation
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CA 02405620 2005-02-28
error is little, when the temperature becomes +40, +30 or +IO°C. But,
the temperature
compensation error is relatively larger, when the temperature t becomes 0, -
10, -20 or +50°C.
The Histeresis characteristics of the Model PDCR826 are inferior to that of
Model PTX1000.
The pressure error Op is up to two times over Table 2, if the pressure is
shifted from a high
state to a low state. If the Histeresis characteristics are bad, the pressure
error becomes greater,
when the water depth is small.
TABLE 2 PDCR826
tC P:kg/cm
0 0.1 0.2 0.4 0.6 0.8 1
(+50) ~p 1 1.08 1.15 1.32 1.59 1.83 1.98
1.08 0.57 0.33 0.26 0.23 0.19
(+40) ~p 1 0.3 0.31 0.43 1.11 1.01 0.78
0.3 0.155 0.108 0.186 0.127 0.08
~ ~p -1.5 0.017 0.097 0.044 0.035 0.06 0.34
0.017 0.048 0.011 0.006 0.0075 0.034
(+10) ~p -0.8 -0.92 -0.88 -0.0035 -0.085 -0.68 -0.94
-0.92 -0.44 ~0 -0.014 -0.085 -0.094
0 ~p 1.5 7.5 8.5 11.5 14.37 17.2 19.5
7.5 4.25 2.87 2.4 2.15 1.95
-10 Op 1 1.5 1.03 1.56 1.9 2.2 2.6
1.5 0.52 0.4 0.32 0.275 0.26
-20 ~p 0,5 -1.84 -1.35 -0.5 ~0 1.04 2.07
b -1.84 -0.67 -0.13 "'~ 0.13 0.2
aeemg the temperature compensation characteristics, when a maximum pressure is
applied, the pressure transducer is adjustable near to an error S%fs at a
normal temperature
with a relative error being less. The less a measuring pressure, the greater
an error S is.
Fig. 3 shows a changing curve of a pressure error Op when t = 0°C and -
10°C, from
which the following characteristics is known. When P = 0, the output of Model
PTX1000
becomes zero. The reason is because a temperature compensation circuit itself
mounted in the
pressure transducer represents a zero deviation according to the temperature
change. If only
the temperature of the compressed air is changed, but the temperature
compensation circuit is
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not heated or cooled, the curve of Op = f(t,P) is raised to about 26cmH20, and
the pressure
error ~p becomes significantly less.
The bubble type water level meter is exposed to changes in temperature, if it
is
mounted in a water level observatory post that is not equipped with cooling
and heating
devices. Therefore, a water column pressure measuring error is changed due to
the pressure
error characteristics Op = f(t;P) changed according to the temperature t and
measuring
pressure P in Tables 1 and 2. The curve of Op = f(t;P) is divided into several
sections to be
represented as an approximate straight line in each section.
An object of the invention is to measure a water depth in an accuracy using
water
column pressure measuring tubes of n>_2 under the condition that a
circumferential
temperature t is changed in the range of -40°C~+50°C, even
though the property of a pressure
transducer is severely changed.
SUMMARY OF THE INVENTION
According to the invention, a water depth measuring method comprises steps of
making a bundle of reference water column pressure measuring tubes of a U
shape of the
number of n>_2 at a same length with a water depth measuring tube in order to
compensate for
a total error ~t1x of a water depth measurement; filling an amount of water
into the reference
water column pressure measuring tubes to form water columns hol, hoe, ...hon
therein;
measuring the water pressure in the reference water column pressure measuring
tube by a
pressure transducer before measuring a water depth; subtracting previously
known water
column pressure yhoi and yhoj derived from the measured water pressure values
Pmi, and Pmj
to calculate total errors ~ai and ~~j; calculating a total error ~~ac based on
the total errors ~Di
and ~~j, in which the total error ~Ox was generated upon measuring of the
bubble generating
pressure Pmx in the water column pressure measuring tubes; subtracting the
total error ~~x
from the bubble generating pressure Pmx, dividing the calculated water column
pressures by
the water column pressure ~yhoi(j) in the reference water column pressure
measuring tube
having most approximate value thereto and multiplying the re-calculated value
by the water
column pressure hoi(j) thereby to measure a water depth in a higher accuracy.
A bubble water depth measuring system comprises a compressed gas generator, a
pressure transducer, a reference water column pressure measuring tube, a water
depth
CA 02405620 2005-02-28
measuring tube, an arithmetic logical transducer for calculating a water depth
and a drive
controller for supplying/interrupting compressed gas.
The water depth measuring tube has a length corresponding to a water depth.
The
reference water column pressure measuring tubes of n>_2 of a U shape has the
same inner
diameter as that of the water depth measuring tube coupled therewith. A
diaphragm is
connected through an electromagnetic valve to one tube of the reference water
column
pressure measuring tube to adjust the speed of the compressed gas from a
buffer tank to be
supplied to the reference water column pressure measuring tubes. A transparent
container is
connected to the other tube of the reference water column pressure measuring
tubes to
measure an amount of water therein and check it, periodically, and includes a
nipper for
supplementing water reduced due to the evaporation. A tube is directly mounted
above the
transparent container and has the same inner diameter as that of the reference
water column
pressure measuring tubes and a length portion, on the surface of which scales
are formed. A
thin film tube is made of rubber and directed to the upper portion of the tube
to be expanded
by a gas pressure, and a manual valve connected to the upper end of the thin
film tube.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention now will be described in detail with reference to the
accompanying, in
which:
Fig. 1 is a view illustrating an error measured according to a bubble type
water depth
measuring method;
Fig. 2. is a view illustrating an apparatus for performing a conventional
water depth
measuring method;
Fig. 3 is a view illustrating error-changing curves dependent upon the change
of a
temperature and a measuring pressure of a pressure transducer;
Fig. 4 is a view illustrating a bubble type water depth measuring method
according to
the invention;
Fig. 5 is a view illustrating the transformation of a curve of an error Op of
a pressure
transducer into a straight line;
Fig. 6 is a view illustrating a configuration of an apparatus for performing a
bubble
type water depth, water level measuring method according to the invention;
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Fig. 7 is a view illustrating the closure of a reference water depth measuring
tube
according to the invention; and,
Fig. 8a and Fig. 8b axe views illustrating an angle error of mounting a
reference
water depth measuring tube according to the invention.
DETAILED DESCRIPTION OF THE INVENTION
Referring to Fig. 4, only two water pressure transducers (n=2) are shown for
simply
explaining the invention. 1 is a water depth measuring tube, 2~ and 22 are
reference water
pressure measuring tubes that are connected through valves SI, SZ and S3 to a
buffer tank 4.
The buffer tank 4 is connected to a pressure transducer 3. Pressure gas Pg is
supplied through
a valve So to the buffer tank 4. The reference water depth measuring tubes 21
and 22 are made
as a U shape, each of one portion of which is connected to the valves S~ and
S3 and other
portion of which are connected in turn to the buffer tank 4 and the pressure
transducer 3
with the other end being opened. The water pressure measuring tube, 2~ and 22
are filled with
river water. As compressed gas is supplied to the water pressure measuring
tubes for a
predetermined short time, the water previously filled is pushed in a direction
contrary to the
gas supply. At this time, the reference water pressure measuring tubes each is
kept at water
column hol and hoe (hol < ho2)- The water column hol and hoe are selected
according to a
measuring range of a water depth hx and the property of a pressure transducer.
An algorithm of measuring the water depth hx is as follows:
When a bubble is generated at the water depth measuring tube 1 with the
valves 52 and S3 being closed and the compressed gas being supplied to the
buffer tank 4, the valve So is closed. At this time, the gas pressure Pmx is
measured by the pressure transducer 3 and then recorded in the memory of
the system.
Pmx = yhx + g~x (9)
As the valve S1 is closed and then the valve S3 is opened and closed for a
short time, water filled in the reference water pressure tubes is pushed up
along the other tube thereof. At that time, the water column hoe is
maintained, and the pressure P",~ is measured and then recorded.
Pm2 = yho2 + E~2 ( 10)
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Herein, the water column hoe is previously known. From the expression (10),
EB'2 is
recorded with y'ho2 being subtracted from P",2.
ED'2 = Pm2 - 'y~ho2 ( 11 )
EO'2 may not be equal to X02, because an average specific gravity ~ is used
with the
specific gravity y of the water column hog being unknown.
With the valve 53 being closed and the valve 52 being opened for a short time
and
closed, the water column pressure yhol is measured.
Pml = yhol + E~1 (I2)
A result that y'hol is subtracted from Pml is recorded.
EO'1 = Pml - ~hol (13)
The measuring turn of P",, and P,nz is changeable.
In the expression (9), E~x is calculated as follows:
'l.Ox = ~l~l + ~~ ~~1 ~P,nx - Pml
Pm? - Pml
( 14)
The water depth hx is calculated as follows:
_ Pmx _ Fix . _ :7lax +~6x _ ~:Llx
~x Pm2 -~11~ ~~2 ~ gaol +~b2 -~~ ~°2
~ + Eax - ~11X
~gx
x ~ + ~~z _ ~~2
:~2 (15)
or
1+ ~~x _ ~~x
hr - Pmx - ~~x - ~ ~~x
x Pml _ F~1 ~1 x 1 + .~.L~1 - ~..~1
r~ol ( 16)
The expression (15) or (16) is selected as follows: if Pmx is close to Pm2,
the
expression (15) is selected, and if Pmx is closer to Pml, the expression (16)
is selected.
2 CC 1.0
Assuming that X02 , the expression (1) is as follows:
h' =h 1+ ~,,y,x1 1 ~,~,~Z ~h ~1+ dx ~2
~x ~~ ~2 ~ x ~ ~x ~~2 ~ 17
r'~ x . L;12
Herein, ~~ ' ~oz ' ~x is ignored because it is of very small value.
13
CA 02405620 2005-02-28
A relative error $hx of h'x resulted from the water depth measurement is as
follows:
rS hx _ 1= ~x _ X12
hx = ~x y~ax . boa 7 (l g)
An absolute error Ohx is as follows:
_ _~ _~~h
x x
L~hx _ C~hx . ~'dx -
Y .~02 ( 19)
Ox and OZ are as follows: ~x = E~ - ~~'x, in which ~~x is a measuring absolute
error. The error is an approximate one that a curve of Op = f(t;P) is
converted into a straight
line. Therefore, the larger the number of sections that the curve ~p = f(t;P)
is formed into the
~z - s~2 _ ~~2 - ~pmz - Yhoz ~- ~pmz - Y~oz ~- Y~oz ~~' -1
straight line, the less ~x is %' II. Therefore, if
y'=y, 02=0.
Assuming that the water specific gravity y = 0.0998gm/cm3, but y = 1.Ogm/cm3
in
the section of hoe and hoe = SOOm,
1~2 _ ~.~998 v'1~~~ 1 -l~ _ x.099 PYYd~C~Yd2
1.~0.99~8
At that time, the water depth error is about 0.1 cm ( 1 mm). When the
expression ( 19)
is derived, the water columns hol and hoe were assumed to be not changed at
the reference
water column pressure measuring tubes 21 and 22. As over time water is escaped
as vapor. If
the water columns hol and hoe each becomes hoi-Bho~ and hoe-~lhoz, Oh°x
is increased more, to
which will be explained below. Also, an evaporation-preventing device will be
explained
below.
First, according to a method of the invention, when the water depth hx was
measured
using a pressure transducer Model PTX1000, a water depth measuring absolute
error ~h'x
(cm) is represented in Table 3. The measuring conditions are as follows:
When t = -10°C in a water depth of 200~600crn, the curve of ~p =
f(t;P) is
represented as a straight line converted. The water depth is selected so that
hol = 200cm and
hoe = 600cm. The measuring range of the water depth hx is 200 ~600cm. Assuming
that the
water specific gravity y = 0.0998gm/cm3, but ~ = l .Ogm/cm3, Ho = 20m
(2000cm), in which
the compressed gas is a compressed air.
_ _ TABLE 3. _
hx cm 200 300 -( 400 500 600 800 1000
h'x cm 199,999 299.65 399.28 499.79599.94 800.8 1002.48
14
CA 02405620 2005-02-28
dhx cm ~0 -0.35 - ~ -0.72 - ~ -x.204 I _0.06 ~ +0.8 I +2.48
When Table 3 is written, ~hx is calculated as follows: if the water depth hx
of SOOcm
is measured, as shown in Table I, hol = 200 and hoe = 600, when t = -
10°C. When hx = SOOcm,
the errors of the pressure transducer Model PTX1000 are as follows: dpi _ -
23.5, dp2 = -28.7,
~px = -27.6 cm H20. Under these conditions, according to the algorithm of the
invention, h'x
and the measuring result of yhx are as follows:
Pmx - !' °x + ~'d x - l'' ° x + d~7 x -i- ~pCa - ,'~'~Ha
= 0.9598 ~ 500 - 27.6 + 1.2 ~ 10 -~ ~'20D0 - 500 ~ -1.2 ~ 10 -3 ° 1:~ -
2000
_ ~r'T~:~G'Yt2~2~
The measuring results of yhol and yho2 are as follows:
Pmt = Y~1 + ~~t _ D.9998 ~ 2DD - 23.5 + 1.2 ~ 1D3 ~20DD - 2DD ~ -1.2 ~ 1D-3 ~
1.2 - 24D0
=17~ .74err F~2 G~
Pm2 -yho~ +Ed2 =0.9998 ~ 6DD -28.r +1.2 ~10-3~2ilDD -6D0~-i.2 ~iD-3 ~1.5-2DDD
= 569.D2cm H2 0
t"'.d j = P,n1 - Y~Ot = l~$ ~~4 -1.0 ~ 200 = -24.26
~d2 = Pm2 - Y~o~ _ $69.02 -1.0 ~ 600 _ -30.98
Ed X = ~dj + ~'d2 - QCs i , ~p"ix - pmt ~ _ -2r~.26 + - 30:98 + 24.26470;5 -
175 .54
P,n2 -Prat 569.02 -17$.54
_29.296
P - ~d' 470.5 + 29.296
.'. hx = mX a J~o2 = ~ 600 = 499.796CYYt
P",2 - Ed2 569.02 + 30.98
dhX = 499:796 - 50a = -0.204crn
Herein, it is known that when hx = 500cm, a measuring error dh'x = -2mm.
In Table 3, the absolute error dh°x is represented as a negative "-"
sign. When
hx>600cm, Oh°x becomes larger, which is represented as a positive "+"
sign. When h =
1 OOOcm, dh°x = +2.48cm. The cause is follows:
Referring to Fig. 5, when t = -10°C, a changing curve of dpi is
exaggeratedly shown.
It is represented in a straight line as follows:
~dx _ Edi + ~a"~ - ~di ~Pmx ' Pm1
Pm? _ Pmt
If the curve of Op is approximated into a straight line II (Dotted line) in a
section of
hx that is a range of 600 ~ 1000cm, the error Oh'x may be significantly
reduced. Unlike Fig. 4,
the reference water column pressure measuring tubes of three (n = 3) are
selected to have
CA 02405620 2005-02-28
water column pressures hol, hoe and ho3, respectively. If Pmx > 600, E~'x is
calculated as
follows:
t t ~d~ - ~~2 _
~.6 x = ~~' 2 + Pmt - pmt ~Pn'x Pn.2
If n >_ 3, the expressions (14) and (15) are represented as follows:
~e' - ~~t
~~ X = ~ei + J r (PmX _ Pmz ~
Pmj - Pm li
(20)
~t = Pmx ~~x
X Pmt - ~~a tjJ (21 )
or
L.t = PmX --X
Jdx Pmi - E~;. ~~ (22)
Like this, it is noted that the invention can secure a higher accuracy because
the total
error of the water column pressure is compensated at once.
The error Oh'x represented in Table 3 is a result of assuming that hol = const
and hoe
= const. However, if water filled in a reference water column pressure
measuring tube 2i has
escaped as time passed, hoi is reduced and becomes hoi - ~h. In other words,
h'oi = hoi-~h.
If hoi is substituted into the measurement expressions of E~i and h'x, an
error Oh'x is
increased. In this case, an error 4h"x caused due to ~h will be obtained by
the reference of the
expressions (20) and (21 ).
All reference water column pressure-measuring tubes are in water, which means
the
temperature conditions are the same. Therefore, water columns Oh reduced in
all the reference
measuring tubes are the same to one another. ~~"i, E~"j, E~'°x and ~h"x
are as follows:
Ee= p~,. - y~o~ _ r(~o~ - ~ )+ ~a, - r~o~
~4-y~
~J.=PYYdj -~doj.=.~t..lJ _.~N~'r
'L~LiJ.-~b~r y
~ x = ~~t + ~pmx - Pmi ~
PmJ - Pmi
- ~dE _ ~h~+ Ee . _ yer~ _ Ee. + yeh
t f' _(,~., 1
l'"oj. + ~~ J - of 7oi. - ~.~~ ~P"u. lI"oi + ~~i
~~, ?'~ + h 12 j + Edgy. ~d ~P"ex ?hot + EAR ~~
a (23)
a"x is changed only by -yah.
16
CA 02405620 2005-02-28
J2" - Pmr - ~dX h . -_ Y~x + ~dx - Edx
x Pmj -~~,j °J ~°J -}dh~dJ -~~"- °t
_ !''°x 't ~dx - ~rdx - ~2~h~.
- h°7
°j -~ t ~t~J - ~.~J -r2lh~
[I,1 + dh
-~x~ ~x~.h°.=hx 1+LSh
~' ~' d ~ hx ~ (24)
~h
~x - -
~x
(25)
dx dh
Comparing the expression (25) with the expression (18), only axis replaced
by~x,
the absolute error as follows:
~hx = ~ld~
(26)
If the water column hoi in the reference water column pressure measuring tube
is
reduced by ~h=Smm due to water evaporation, Oh'x increases upto +Smm before
evaporation.
If Oh'x is positive "+", the error will be increased more +Smm. On the
contrary, if ~h'x is
negative "-", the error will be reduced less +Smm. For these reasons, there
needs to be
countermeasures for preventing the evaporation of water filled in the
reference water column
pressure-measuring tubes, checking its water column hoi and supplementing the
evaporated
water. The invention is designed to comply with the countermeasures.
Another problem is that upon the calculation of E~I and Eaj ~y'hoi and ~hoj
are
subtracted from Pmi and Pmj using an average value ~ because the water
specific gravity y is
unknown. The water depth measuring error 8hx(~y) happens because of the error
of
~Y - ~r~ -Y~~y resulting from the water specific gravity y.
~~'xt,~3 ~-a~~°'~~7
hx (27)
A water temperature of reservoir is usually 3~4°C after the water
surface is frozen in
winter. An average temperature of a water depth doesn't exceed 22°C.
The temperature of the
water surface is raised up to 24°C. If the water is clean, its density
is changed in the range of
0.999992 to 0.997802gm/cm3. The concentration of floating materials is usually
O.Sgm/ ~ (_
5°10-4gm/cm3). When the water temperature reaches around 22°C,
the water specific gravity
y= 0.997802 + 5°10-4 = 0.998302gm/cm3. In winter, the concentration of
floating particles is
reduced, significantly. If the average density is used irrelevant to seasons,
8y is changed in the
range of -8.4° 10-4 to +8.5 ° 10-4.
17
CA 02405620 2005-02-28
-4
If hoi = 200cm and hx = 3 OOcm in the expression (27), ~'~~'~ - ~'~suo , and
~hx
0.169 ~ 0.17cm. If hx = 600cm, 6hx = 0.11 cm. Therefore, the influence of y'
is very small.
For it, it is most important to take a measure to prevent the evaporation of
water filled in the
water column pressure measuring tube 2i.
An effective and simple method of the evaporation prevention is to store water
in a
closed space. The closed space is maintained at a relative humidity of 100%.
Only, the
relative humidity is changed by an absolute amount until reaching 100%.
Another liquid can
be filled in the water column pressure measuring tube instead of water.
Herein, it is noted that
the specific gravity change according to a temperature of the liquid is
exactly confirmed.
Referring to Figs. 6 and 7, an apparatus of performing a water depth, water
level
measuring method is shown according to the invention.
As shown in Fig. 6, 1 is a water depth measuring tube, 21, 22 and 23 are
reference-
measuring tubes of U shape that forms water columns of h~l < h«2 < ho3. 3 is a
pressure
transducer, and 4 is a buffer tank which supplies compressed gas to a
plurality of measuring
tubes. 10 is a compressed gas generator, for which a micro compressor or a
compressed
nitrogen tank can be used. 50, 5I, 52, 53 and 54 is a diaphragm for adjusting
an amount of
compressed gas to be introduced into the reference measuring tubes. Instead of
a diaphragm,
a valve having a small inner diameter can be used. 71, 72 and 73 are
transparent containers for
measuring an amount of water filled in the reference measuring tubes 21, 22
and 23. 81, 82 and
83 are a corrugated tube made of a thin rubber film or another soft material.
91, 92 and 93 are
manual valves. The detailed configuration of the transparent container 7i and
the corrugated
tube 8i is shown in Fig. 7. 11 is a digital converter for converting an
outputting signal from
the pressure transducer 3 into a unit of mmII2O. 12 is an arithmetic logical
controller or
microprocessor to calculate a water depth according to the invention, which
includes devices
for forming outputting signals such as code, analog signals, etc. 13 is a
drive controller for
controlling the operating of the valves 5i and the compressed gas generators
10 and 11. Of
course, the digital converter 1 l, the arithmetic logical controller 12 and
the drive controller 13
can be integrated with each another as one integrated circuit chip.
2i is closed to prevent the evaporation of water filled therein. The valves 5o
and 51
are opened in turn based on the outputting signal from the drive controller
13, and the other
valves 52, 53 and 54 are closed. Then, as the compressed gas is supplied to
the water depth
measuring tube 1, the water filled in the water depth measuring tube 1 is
gotten out downward
18
CA 02405620 2005-02-28
and bubbles are generated. At this time; the valve So is closed. When the
outputting signal
from the pressure transducer 3 is stabilized, the water column Pmx is
measured, which is
stored in the arithmetic logical controller I2, and the valve 51 is closed.
The arithmetic logical controller 12 judges on which section of yhoi ~ yho2
and Yho2
'yho3 the water column pressure Pmx is corresponded to and outputs its control
signal to the
drive controller 13. For example, if the water column pressure Pmx is
corresponded to the
section of yho2 ~ yho3, the valve 53 is opened for a predetermined short time,
the compressed
gas is supplied to the reference measuring tube 22 to push up the water
therein along its left
tube and form the water column hoe. At this time, the water column pressure
Pmx is measured.
The arithmetic logical controller 12 calculates a water depth hx according to
a water depth-
measuring algorithm of the invention.
The characterized portion of the system is a configuration of the reference
measuring
tube 2i. Referring to Fig. 7, the transparent container 7i, the corrugated
tube 8i and the manual
valve 9i are enlarged. The transparent container 7i measures an amount of
water to be injected
into the reference measuring tube 2i and also is used in checking an amount of
water
evaporated and supplementing corresponding amount of water in the reference
measuring
tube 2i. 14i is a tube having the same inner diameter as that of the reference
measuring tube 2i,
on the outer wall of which scales are formed in a unit of mm. 15i is a nipper
such as an
injector which is used to inject water into the transparent container 7i or
supplementing water
upon evaporating. The tube 14i has a length of .~ that ~ l Ocm. The
transparent container 7i
has an inner volume v1 as follows:
vr= ~2 ~hor W
2 (28)
If the water column hoi is subject to being formed in the reference measuring
tube 2i,
the water volume v~ ~ ~'°' . ~ is an inner diameter of the tube. When
such like an amount of
water is filled in the transparent container 7i, the water is fully filled in
the transparent
container 7i, and the remaining water is raised up to a middle position ('~
~~~' ) of the tube 14i.
Therefore, an exact water volume v~ can be confirmed through the scales of the
tube 14i.
After a certain time period passed, the water column hoi is reduced due to the
evaporation. At this time, the water column error ~lhoi is checked as follows;
the compressed
gas continues to be supplied through the valve Si to the reference measuring
tube 2i; the water
in the reference measuring tube 2i is filled in the transparent container 7i,
and the scale of the
19
CA 02405620 2005-02-28
tube 14i is confirmed to check ~lhoi; additional water is supplemented using
the nipper 15i. In
this case, the manual valve 9i may be opened.
The tube 8i is expanded upon the air injection thereinto, the volume of which
is sufficient.
Even if air of SOOcm3 is injected, the tube 8i is easily inflated.
The tube 2i for a time period 't, the water is raised up along the left
portion of the
reference measuring tube 2i to form the water column hoi. The diaphragm 6i
acts to adjust the
amount of compressed gas to be injected or the injecting speed. The diameter
of the
diaphragm's hole is smaller that the inner diameter of the reference measuring
tube 2i. The
diaphragm 6i is not necessary to be separately made, but instead of it a
manual adjustable
valve is available.
At this time, air filled in the left portion of the reference measuring tube
2i is injected
into the transparent container 7i and the tube 8i. The air volume is about
vio. If the transparent
container 7i is closed, the air pressure is increased. But, as the tube 8i is
expanded, the air
pressure becomes smaller. The water column pressure P'mi of ~yhoi is as
follows:
Pmi = !'"oi + '1L~~ + ~~~ = Poi + ~pc >
Wherein, ~pc is a pressure required for expanding the tube 8i. The ~pc becomes
smaller, if its material is soft and its size is larger. The ~pc is previously
measured and stored
in the arithmetic logical controller 12.
Next, the valve 9i is opened to measure the water column pressure Pmi, and
then the
valve 9i is closed to measure a water column pressure P'mi. The ~pc is as
follows:
~p~ Pmi pm~ (30)
Of course, the tube expanding pressure Opc is changed according to the
temperature
of air in the tube 8i and the position where the water column hoi is raised
upward or dropped
downward in an appointed position. In order to prevent the increasing of the
water depth
measuring error, the change of the tube expanding pressure ~pc must be secured
so that
~pc«E~. To it, the tube 8i is made of a very thin film and has a sufficient
volume. For
example, a balloon can be preferably used. Herein, most important condition is
as follows:
~pe - ~pel - ~pc2 - ~pc3 - v- pan (3 1 )
If the condition is secured, the errors of the tube expanding pressure Opc are
offset to
one another. The condition of the expression (31) is secured by adjusting the
size of the tube
8i. For example, the position where the valve 9i is mounted on the tube 8i is
adjustable. Under
CA 02405620 2005-02-28
the condition that the tube expanding pressure ~pc is measured and recorded,
the water depth
is measured according to the algorithms of the invention.
~~ =P~ -LYia +~c~
i ma a;
~~X=~tl; +d~c+ Ft"~~,J +dt~c ~ -~~c~pmx-P.:~i
Pmi _ Pmi
_ ~L~~ + r'~~7c + F~~1 - ~~~ ~Pmx - pmx
Pn- ~'m~ (32)
Wherein, B~pc is a difference between Opc previously recorded and ~'pc caused
upon measuring; ~pc=~'pc-apc. Therefore, ~~'x has the difference by 6pc
compared with
~~, but if 40pc is smaller than the error of ~Bx, ~Opc may be ignored.
As described above, the reference measuring tubes 21, 22 and 23 are almost
closed not
to evaporate the water filled therefrom. Especially, an amount of evaporated
water is much
more reduced in winter because the water temperature is lower. If the
circumferential
temperature is below -5°C, an amount of water can be checked without
using the transparent
tube 7i, because the possibility of freezing water is very high. Therefore, if
an amount of
water is checked and supplemented before the winter starts, it is enough. In
summer, it is
enough that an amount of water v~ filled in the reference measuring tube 2i is
checked.
The water depth measuring tube 1 and the reference measuring tube 2i are made
of
materials to which water is not adhesive. The cheapest thing is a polyurethane
tube, and the
more preferable thing is a TeflonTM tube. The suitable inner diameter d of the
measuring tubes
is 2 ~ 3mm. All measuring tubes are coupled with each other in a bundle.
According to the invention, a system is a little complex, but the accuracy of
the water
depth measurement is very higher independent of the weather change. It is also
not necessary
to use an expensive pressure transducer. The invention has an advantage in
that a pressure
transducer not only having an inferior property but also being cheaper can be
used.
On the other hand, when the bubble water level measuring system is mounted,
there
are cases that the measuring tubes l and 2i are mounted vertically and along
the slope of a
reservoir bank.
As shown in Fig. 8A, even though the measuring tube is vertically mounted, it
is
slanted at an angle a. The water column pressure yhoi is as follows:
7~~ot cosy (33)
21
CA 02405620 2005-02-28
Wherein, h'oi is a length of a water column in the reference measuring tube 2i
slanted at the angle cc, and yhoi is a water column pressure of h'oi.
As shown in Fig. 8B, if a bundle of the measuring tubes are mounted along the
slope
of the reservoir bank, yhoi is as follows:
f~~z = Y~o~ ~'a~a,(34)
Wherein, ~3 is an average gradient angle. h'oi is exactly confirmable by an
amount
of water vi filled in the reference measuring tube 2i, but cc and,.l3 can't be
exactly measured. If
an angle error a of mounting the measuring tube is 1 ~ 3°, a water
depth measuring
supplementary error is -0.03 ~ -0.3cm. Unless the mounting angle error exceeds
2°, the
supplementary error is ignorable. If the measuring tube is mounted at the
gradient angle ~3 and
the gradient angle ~i is not exactly determined, the measuring error of the
water depth hx
becomes larger. However, there have been cases where it is not possible to
measure the
gradient angle (3. The result of measuring the water column pressure yhoi of
the reference
measuring tube 2i is as follows:
Pmi = yhoi + E~i = yh'oiSin(3 + ~Di
Herein, what is exactly known is only h'oi. Therefore, in order to find the
yhoi, the
EBI gets calculated, exactly. For preparing these cases, the curve or table of
Op=f(t;P) is
written in advance in a manner that a pressure transducer having a higher
accuracy is
corrected and checked. The water column pressure Pmi is measured by the
pressure
transducer, Bpa-ygHo is calculated and yhoi is calculated as follows:
~o; = Pm= - yep; + ~P~ - y~ ~p ~ (35)
As described above, according to the invention, reference water column
pressure
measuring tubes of n>_2 in a U shape are disposed at the same length along
with a water depth
measuring tube, an amount of water is filled in the reference water column
pressure
measuring tubes, compressed gas is supplied to the reference water column
pressure
measuring tubes from one side tube thereof for a short time period and the
water is pushed up
in the other tube to form the water column pressures ~yh0l, yh02...yhOn and
measure the water
depth.
Accordingly, the invention is mostly used in using the measurement of the
water
depth, water level in a reservoir, a lake and an underground water and can
measure the water
depth, water level in a higher accuracy compensating for errors caused due to
the
22
CA 02405620 2005-02-28
circumferential environment such as a temperature, an altitude difference, a
water specific
gravity, etc. at once.
23
