Pressure “F” is the applied force, and “A”

Pressure is defined as simply the amount of force that is applied
in a direction perpendicular to a unit of area of an object. Pressure is one of
many properties in the study of fluid, similar to temperature, density,
viscosity and more. Pressure is defined with the following equation:

In the above equation, “p”
represents pressure which is usually measured in SI unit of Pascal or imperial
unit of psi. The “F” is the applied force, and “A” is the area
orthogonal to the direction of the applied force.

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When working with pressure it is vital to understand the terms
involved. We can measure the pressure two different ways, both are correct but
relative to different points. When we measure pressure relative to a perfect
vacuum, we call it the absolute pressure. When pressure is measured
relative to the pressure presented in the surrounding environment (atmospheric
pressure), we call that the gauge pressure. With this being said, if a
gauge pressure is read at zero that means the pressure is equal to the local
atmospheric pressure. Due to the fact that gauge pressure is a relative
quantity, it can be either positive or negative depending on weather the
pressure is above or below the surrounding pressure. Absolute pressures, contrary
to gauge pressures, are always positive. The following is a graphic
illustration that shows the difference between the two pressures.  

 

 

 

Figure 1: Illustration of gauge pressure vs absolute pressure

 

            Hydrostatic
gauge, mechanical gauge, pressure gauge are all examples of instruments that
allow us to measure the pressure of a fluid. The first one is the hydrostatic
gauge. It is a column of fluid usually in form of a “U”. Pressure can be
applied to both openings of the U-tube, the side that has the higher pressure
will push the manometer fluid further down. This gives us the following
equation:

 

In this case p is
the density of the fluid inside the manometer, g represents the constant
gravity, and h is the height displaced by the fluid due to the pressure
difference.

 

Manometers are used because they are low-cost, effective, and easy
to fabricate. As long as the fluid is not soluble in the manometer and is
maintained above freezing point as well as be able to move freely in the tube,
then it will behave linearly. These conditions are very common which makes it a
good tool. However there are a few evident disadvantages to this tool. One of
which is that because the fluid oscillates with a difference in pressure, it
can’t be used to measure time-varying pressures. The glass U-tube is also is
not a convenient object to carry around.

 

Figure 2: Example of a U-tube Manometer

 

Mechanical gauges are more convenient. They are simply a metallic
tubing with an elastic material that resists the force exerted by the fluid
pressure. The elastic material gets stretched when pressure is applied to it.
As a result, the elastic material when stretched, regulates a needle that
indicates the pressure and gives a reading. When the pressure rises, the more
the elastic material gets stretched, thus rotating the needle to a higher
pressure reading. On the contrary, when the pressure is reduced, the elastic
material retracts and reduces the reading until it reaches the zero gauge
reading (atmospheric pressure).

 

A common example of a mechanical gauge is a Bourdon gauge. Bourdon
gauges are more effective than the manometer, it is very reliable if calibrated
correctly and much more smaller and convenient. Similar to the manometer
however, it isn’t recommended to measure fast changing pressure because of the
flow oscillation. Something important to note with Bourdon gauges is that it
must be calibrated. De-calibration is a situation where physical properties of
an instrument is altered which then affects the results. The results will be
false because de-calibration means the instrument is now relative to another
reference point. De-calibration in a Bourdon gauge can be mainly caused by
fatigue and corrosion in the metal.

 

 

Figure 3: Example of Bourdon gauge

 

Lastly we have the pressure transducer. The instruments exceeds
the performance of both the Bourdon gauge and the manometer because of its
precision. This is due to the fact that it is an electromechanical device
because it is designed with a diaphragm and a sensing element. The force
created by the pressure from the fluid is captured by the diaphragm. This force
will strain or displace the diaphragm and convert it into an electrical signal
thanks to the electrical element. The reading of the pressure magnitude that
converts to electrical signal is directly proportional to the applied pressure.

 

Pressure transducers contain moving mechanical parts just like the
Bourdon gauge. This requires calibration procedure every now and then to
prevent false readings caused by de-calibration. Pressure transducers are
advantageous compared to the Bourdon gauge and the manometer in that they can
be used to measure time-varying fluid pressures thanks to its electrical
element. The electrical elements are good because they are sensitive and have
good repeatability but this comes at a high cost.

 

Figure 4: Example of Pressure Transducer

 

 Theoretical Background

The main objective of this lab is to have a
fully idea about pressure and the concept of it, also how it related to fluid
with a liberated bourdon gauge and calibrate bourdon gauge with knowing the
weight. To be more specific, the definition of pressure is the amount of force
that been applied on a specific area. Also, it is measured in either Pascal
(Pa) or Pounds per square inch (psi). Pressure is considered to be one of the
most important properties of fluid.

 

 

 Figure 5: Graphical
representation of gauge pressure and absolute pressure

 

Pressure relative to a perfect vacuum (absolute zero
pressure) is called absolute pressure.  
 pressure
relative to the pressure presented in the Surrounding environment such as
atmospheric pressure, this is called the gauge pressure.

 

 

 

Experimental Unit

A Dead-weight Piston Gauge (HM150.02) was used in this experiment
and consists of two units, the Bourdon Gauge (2) used to measure pressure and a
Dead-Weight Piston (8) to calibrate the device. The Bourdon gauge measures the
hydraulic pressure inside the dead-weight piston. The Gauge is connected to the
piston by a pipeline containing hydraulic oil. The Piston is loaded (3) with
weights (4) to increase the internal pressure and this is used to calibrate the
Gauge. A hand wheel (6) is used to adjust the oil level inside the piston so
the piston has a large enough stroke to handle the added weights. The Device is
also equipped with an overflow valve (5) in case of oil overflow.

Figure 6: Dead-Weight
Piston Gauge (HM150.02)

 

Procedure

The experiment started by pressing the piston out of the cylinder
using the hand wheel. Next the piston and weight support are removed. Oil is
added to the open cylinder until the cylinder is filled to the edge. The hand
wheel was used to adjust the oil level and to zero the Bourdon Gauge. The
weight support was placed back into the cylinder of the Bourdon gauge once it
had been zeroes. The piston was lowered by unscrewing the counterbalance
cylinder until it was freely suspended. Weight was loaded onto the weight
support, beginning with the thin disk and then more weight was added using the
larger disks in each trial. At each trial as more weight was added, readings of
the pressure were taken. The experiment ended when the reading was taken with
the last weight loaded. The readings collected were used to compare to the
theoretical values using the equations as stated in the results section.

 

Results and Discussion

Table 1: Bourdon Gauge
readings

         
                                               Mass of Weight Support kg

0.385

Trial #

Total Mass of piston kg

Cumulative Pressure to Loaded mass bar pm

Bourdon Gauge Reading bar pa

Relative Error %

1

0

0

0

0

2

0.385

 0.333

0.31

 7.17

3

0.578

 0.501

0.49

 2.26

4

1.152

 0.999

0.85

 14.9

5

1.726

 1.50

1.40

 6.49

6

2.300

 2.00

1.85

 7.27

7

2.874

 2.49

2.40

 3.73

 

Sources of Error

          The output information from the lab may have been affected by
reduced efficiency of the machine. All experimental devices lose efficiency due
to time and constant usage. This may be the reason to a small amount of error
occurring when performing the lab.

 

 

 

 

Conclusion

 

Pressure is unquestionably one of the fundamental properties of
fluid mechanics, therefore a general understanding of pressure would be
required in order to succeed. The experiment which was conducted would serve as
an aid for the better understanding of the concept of pressure.  After
calculating the results from the experiment, it was clear that a similar trend
was followed throughout the experiment. As the total mass of the piston
increased, the cumulative pressure to the loaded mass increased as well. The
trend holds true due to the fact that having a higher mass would therefore
cause a greater value for the applied force. Analyzing the equation, the direct
relationship between increase of mass and increase of cumulative pressure
becomes quite evident. A greater understanding of the basic concept of pressure
was gained during this experiment, as well as basic knowledge of using a
Bourdon Gauge. The knowledge gained from this experiment will be quite helpful
for the near future. 

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