The term manometer is derived from the ancient Greek words 'manós', meaning thin or rare, and 'métron' meaning measure. A manometer works on the principle of hydrostatic equilibrium and is used for measuring the pressure (static pressure) exerted by a still liquid or gas. Hydrostatic equilibrium states that the pressure at any point in a fluid at rest is equal, and its value is just the weight of the overlying fluid. The manometer is the simplest instrument used for gauge pressure (low-range pressure) measurements by balancing the pressure against the weight of a column of liquid. The action of all manometers depends on the effect of pressure exerted by a fluid at a depth. Following are the advantages of manometers:
- Simple and time-proven.
- They have high accuracy and sensitivity.
- Availability of a wide range of filling fluids of varying specific gravities.
- It has a reasonable cost.
- There are suitable for low pressure and low differential pressure applications.
1. Simple U-tube Manometer
A manometer is a device
to measure pressures. A common simple manometer consists of a U-shaped tube of
glass filled with some liquid. In its simplest form, this type of manometer
consists of an incompressible fluid like water or mercury. Typically it is
mercury because of its high density.
Consider a U-shaped tube
whose both ends are open to the atmosphere is filled with a liquid. The points
A and B, Fig. 1(a), are at atmospheric pressure and the same vertical height.
In another case, Fig. 1(b), consider that the left arm of the U-tube top end is
closed and there is a sample of gas in the closed end of the tube. The right
side of the tube remains open to the atmosphere. Point A, then, is at
atmospheric pressure. Point C is at the pressure of the gas in the closed end
of the tube. Point B has a pressure greater than atmospheric pressure due to the
weight of the column of liquid of height h. Point C is at the same height as B,
so it has the same pressure as point B. Thus, pressure at point C is equal to
the pressure of the gas in the closed end of the tube. The pressure of the gas
trapped in the closed end of the tube is greater than the atmospheric pressure
by the amount of pressure exerted by the column of liquid of height h.
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| Fig.1: Liquid and Gas at Atmospheric Pressure in U-tube Manometer |
Another possible arrangement of the manometer where the top of the left side of the tube is closed and the closed end of the tube contains a sample of gas or it contains a vacuum, Fig. 1(c). Point A is at atmospheric pressure. Point C is at some pressure if it contains gas in the closed end of the tube. Since point B is at the same height as point A, it is at atmospheric pressure. But the pressure at point B is also the sum of the pressure at point C and the pressure exerted by the weight of the column of liquid of height h in the tube. Thus, it can be concluded that pressure at point C is less than atmospheric pressure by the amount of pressure exerted by the column of liquid of height h. If the closed end of the tube contains a vacuum, then the pressure at point C is zero, and atmospheric pressure is equal to the pressure exerted by the weight of the column of liquid of height h. The U-tube manometer is inexpensive and does not need calibration.
Pressure is defined as
the force per area. The SI unit for pressure is the pascal, which is N/m2.
Another common unit for measuring atmospheric pressure is mm of mercury, whose
value is usually about 760 mm. If the closed end of the tube, Fig. 1(c),
contains a vacuum, the height h is about 760 mm. In many situations, measuring
pressures in units of length of the liquid in the manometer is perfectly
adequate.
The pressure measurement
in the manometer is calculated by considering a cylinder of liquid of height h
and area A. The weight of the cylinder is its mass ‘m’ times the acceleration
due to gravity ‘g’. This is the force exerted by the cylinder of liquid on
whatever is just below it. It is expressed as :
F = m g …. (1)
The pressure ‘P’ is this
force divided by the area ‘A’ of the face of the cylinder and is expressed as:
equation...(2)
The mass of the cylinder
is the density of the liquid ‘ρ’ times the volume ‘V’.
m = ρ × V ….(3)
The volume is the area
‘A’ of the face of the cylinder times its height ‘h’.
V = A × h ….(4)
P = ρ × h × g ….(5)
2. Differential U-tube Manometer
A differential manometer
is a device that measures the difference in pressure between two places. They
can range from simple to complex digital equipment. Standard manometers are
used to measure the pressure in a container by comparing it to normal
atmospheric pressure. Differential manometers are also used to compare the
pressure of two different containers. They are used to know which container has
greater pressure and how large the difference between the two is.
The simplest differential
manometer is a U-shaped tube with both ends at the same height. A liquid
usually used is water or mercury and it rests at the bottom of the tube. If one
end of the tube is in a place with higher air pressure, the pressure will push
down the liquid on that side of the tube. By measuring the difference between
the heights of liquid, it is possible to calculate the pressure difference. To
calculate the pressure difference, the height difference is multiplied by the
density of the gas and the acceleration due to gravity.
There are two types of differential manometer namely:
- U-tube differential manometer.
- Inverted U-tube differential manometer.
There are two types of U-tube differential manometers.
- U-tube differential manometer at the same level.
- U-tube differential manometer at different levels.
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| Fig.1: U-Tube Differential Manometer at the Same Level |
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| Fig.2: U-Tube Differential Manometer at the Different Level |
The first type of manometer has two pipes in a parallel position, Fig.1. This type of manometer is used for measuring the fluid pressure difference between these two pipes arranged at the same level. The second type of manometer, Fig.2, is used where two pipes are at a different place and are not in parallel conditions. This type of manometer is used for measuring the fluid pressure between these two pipes arranged at different levels. Differential manometers have a wide range of uses in different disciplines. One example is that they can be used to measure the flow dynamics of gas by comparing the pressure at different points in the pipe.
3. Inverted
U-tube Manometer
The inverted U-tube
differential manometer is reciprocal of the U-tube differential manometer at a different
level. This type of manometer is used to measure the accuracy of small
differences if pressure is increased. Inverted U-tube manometer, Fig.1 is used
for measuring pressure differences in liquids. The space above the liquid in
the manometer is filled with air. To adjust the level of the liquid in the
manometer, a tap at the top is provided that admits or expels the air. The
pressure at the same level in a continuous body of static fluid is equal.
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| Fig.1: Inverted U-tube Manometer |
The pressure at level XX' is equated as follows:
For the left arm of the manometer:
Px = P1
− ρ g (h + a) … (1)
where Px is
pressure in the left arm at point X, P1 is pressure in the left arm
fluid, ρ is the density of the air and g is the gravitational force.
For the right arm of the manometer:
Px = P2
− (ρ g a + ρm g h) …. (2)
where ρm is the
density of mercury.
Since,
Px = Px'
…. (3)
P1 – ρ g (h +
a) = P2 − (ρ g a + ρm g h)
P1 – P2
= (ρ – ρm) g h …. (4)
If the manometric fluid
is chosen in such a way that ρm << ρ then,
P1 – P2
= ρ g h …. (5)
For an inverted U-tube
manometer, the manometric fluid is usually air.
4. Micromanometer
A micromanometer is used
for the accurate measurement of extremely small pressure differences. The
micromanometer is another variation of liquid column manometers based on the
principle of an inclined tube manometer. The meniscus of the inclined tube is at
a reference level as shown in Fig.1, viewing through a magnifier provided with
a cross hairline. This is done for the condition, P1 = P2.
The adjustment is done by moving the well up and down a micrometer. For the
condition when P1 ≠ P2, the shift in the meniscus
position is restored to zero by raising or lowering the well as before and the
difference between these two readings gives the pressure difference in terms of
height.
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| Fig.1: Micromanometer |
Micromanometer is a static fluid pressure difference measuring device. Its dynamics can rarely be ignored. Considering manometric fluid as a free body, the forces acting on it are
- The weight is distributed over the entire fluid.
- The drag force is due to its motion and the corresponding tube wall shearing stress.
- The force is due to differential pressure.
- Surface tension force at the two ends.
5. Inclined Manometer
For accurate measurement
of small pressure differences by an ordinary U-tube manometer, the ratio of a density
of mercury (ρm) to a density of water (ρw) must be close
to unity. This is not possible if the working fluid is a gas. A manometric
liquid of density very close to that of the working liquid and giving at the
same time a well-defined meniscus at the interface is not always possible. For
this purpose, an inclined tube manometer is used.
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| Fig.1: Inclined Tube Manometer |
If the transparent tube of a manometer, instead of being vertical, is set at an angle ‘θ’ to the horizontal, Fig.1, then a pressure difference corresponding to a vertical difference of levels ‘x’ gives a movement of the meniscus s = x / sin θ along the slope. If ‘θ’ is small, a considerable magnification of the movement of the meniscus may be achieved. Angles less than 50° are not usually satisfactory, because it becomes difficult to determine the exact position of the meniscus. One arm of this manometer is usually made large in cross-section than the other. When a pressure difference is applied across the manometer, the movement of the liquid surface in the wider arm is practically negligible compared to that occurring in the narrower arm. If the level of the surface in the wider arm is assumed constant, the displacement of the meniscus in the narrower limb needs only to be measured, and therefore only this arm is required to be transparent.