Meriam MANOMETERS - Manual (Page 3)

Gravity at a known latitude is:
g
x
= 980.616 (1 - .0026373cos2x + .0000059cos 2 2x)
g
x
= gravity value at latitude x, sea level (cm/s 2 )
x = latitude (degrees)
The relationship for inland values of gravity at elevations
above sea level is:
g
t
= g
x
- 0.000094H+ 0.00003408 (H-H 1 ) (cm/sec 2 )
H = elevation (feet) above mean sea level
H 1 = average elevation (feet) of the general terrain within a
radius of 100 miles of the point
The second term may be eliminated when H 1 is unknown, but
the accuracy of the gravity determination will decrease. The
degree of inaccuracy is determined by how far H 1 varies from
H. In mountainous terrain this error could be large.
For every different set of conditions the significance of the
corrections vary. Whether these corrections can be overlooked
or not depends upon the accuracy requirements.
Other corrections do exist, but are generally outside the
resolution of the instrument. For information on these
considerations consult Meriam.
8. Accuracy
A manometer, when used properly, is a very accurate
instrument. NIST recognizes the U-type manometer as a
primary standard due to its inherent accuracy and simplicity
of operation. The manometer has no moving parts subject
to wear, age, or fatigue. It is simply a determination of the
height of a liquid column. When the previously mentioned
corrections are accounted for the uncertainty of a manometer
reading is ± 1/2 the smallest graduation. This is due to your
eyes ability to interpolate between the graduations.
9. Trouble Shooting
When properly selected and used, the manometer is a very
accurate standard. It can, however, present what appears
to be incorrect indications. These are generally the result
of misapplied or improperly used pressures, or incorrectly
evaluated indication.
No Reading — Pressure is not being applied to either, or both,
sides of the instrument. Check for plugged or leaking pressure
lines. Check internal passages of the meter for foreign
particles, which may be blocking flow. Be sure atmospheric
pressure connection is vented to atmosphere. Check for proper
zero setting.
High Reading — Specific gravity of the indicating fluid may
be too low; check scale legend and provide correct indicating
fluid. With tank gauges, tank contents fluid density may be too
great. If the low pressure line is above atmospheric pressure
Using this method is very accurate when density/
temperature relationships are known. Data is readily
available for water and mercury.
Density (g/cm 3 ) as a function of temperature (C°) for
mercury:
= 13.556786 (1-0.0001818 (T- 15.5556) )
Density (g/cm3) as a function of temperature (C°) for
water:
= 0.9998395 + 6.7982999 x 10 -5 (T)
-9.1060255 x 10 -6 (T 2 ) + 1.0052729 x 10 -7 (T 3 )
-1.1267135 x 10 -9 (T 4 ) + 6.5917956 x lO -12 (T 5 )
For other fluids, manometer scales and fluid densities
may be formulated to read inches of water or mercury at
a set temperature. This temperature is usually ambient
temperature. This decreases the error due to the temperature
change, because most manometers are used at or close to
ambient temperature. In some work direct readings close
to design temperature are accurate enough. The manometer
still only reads correctly at one temperature, and for precise
work the temperature corrections can not be overlooked.
Gravity Corrections
The gravity correction arises because gravity at the location
of the instrument governs the weight of the liquid column.
Like the fluid density correction, the gravity correction is a
ratio.
(Standard) ρ
o
g
o
h
o
= (Ambient) ρ
t
g
t
h
t
h
o
= x h
t
g
o
= standard gravity - 980.665 cm/s 2
(45.54° N latitude & sea level)
g
t
= gravity at the instruments location
A 10° change in latitude at sea level will introduce
approximately 0.1% error in reading. At the Equator (0°) the
error is approximately 0.25%, An increase in elevation of
5000 ft will introduce an error of approximately 0.05%.
Gravity values have been determined by the U.S. Coast and
Geodetic Survey at many points in the United States. Using
these values, the U.S. Geodetic Survey may interpolate and
obtain a gravity value sufficient for most work. To obtain
a gravity report, the instrumentʼs latitude, longitude, and
elevation are needed. For precise work you must have the
value of the gravity measured at the instrumentʼs location.
Where a high degree of accuracy is not necessary and the
value of local gravity has not been determined, local gravity
can be calculated.
g
t
ρ
t
g
o
ρ
o