Calibration Of Pressure Gauge Using Dead Weight Apparatus

EXPERIMENT NO. 3 CALIBRATION OF PRESSURE GAUGE USING DEAD WEIGHT APPARATUS

1. Objective: The objective of this experiment is to produce a calibration curve of a bourdon gauge.

2. Apparatus/Equipment: Hydraulics Bench Bourdon Gauge (see photo) Dead Weight Calibrator (see photo)

Description of Apparatus: The Dead Weight Calibrator apparatus comprises a precision round piston and cylinder (see Figure 3.1). Weights can be added to the piston so a number of pressures can be produced within the cylinder. The cylinder is mounted on a baseboard which is supported on leveling screws and equipped with a spirit level.

Pressure gauge is a simple device and normally very reliable in service. The basic element of the gauge is a curved elastic tube, usually brass or stainless steel which changes its geometry when filled fluid under pressure. This deformation is transmitted by a linkage to the gauge pointer which in turn indicates the gauge reading. The gauge to be calibrated is connected to the cylinder of the Dead Weight Apparatus by a flexible tube. Water is then allowed to enter into the connected system through the inlet of the gauge and let it

flows into the hose connecting the gauge and the cylinder of the Dead Weight Apparatus. Drain is provided for water from the cylinder after passing the piston.

3. Theory: Bourdon gauge is a simple device and normally very reliable in service. The basic element of the gauge is a curved elastic tube, usually brass or stainless steel which changes its geometry when filled with fluid under pressure. This deformation is transmitted by a linkage to the gauge pointer. Pressure (p) is force distributed over a surface, that is, p=

F A

where

F = force A = area

In here the load placed on the piston is the force, F, and the cross-sectional area of the piston that is in contact with the liquid (water) is the area, A.

4. Procedure 1) The pressure gauge and dead weight apparatus were connected to the water supply of the hydraulic bench. 2) The pump was turned on to allow water to flow through the gauge and dead weight apparatus. The gauge reading corresponding to the weight of the piston was noted. 3) Calibration weights were added and the corresponding gauge reading was read. 4) The cylindrical pressure was computed by dividing the total weight (weight of piston + calibration weight) by the area of the piston.

5. Results Diameter of Piston (m)

Mass of Piston (kg)

Area of Piston (m2)

Mass of Weight (kg)

Total Mass (kg)

Gauge G

Cylinder Pressure, P

Absolute Gauge Error

Trial 1

(kPa)

(kPa)

Reading

% Gauge Error

(kPa)

0.5

0.01767

0.000245

0.0

0.5

20

20.020

0.02

0.099

0.5

0.01767

0.000245

0.5

1.0

40

40.040

0.04

0.099

0.5

0.01767

0.000245

1.0

2.0

75

80.082

5.082

6.346

0.5

0.01767

0.000245

1.0

3.0

115

120.122

5.122

4.264

0.5

0.01767

0.000245

2.0

5.0

190

200.204

10.204

5.097

0.5

0.01767

0.000245

2.0

7.0

270

280.286

10.286

3.670

𝐹

Sample Computations:

Cylinder Pressure (P) = 𝐴

D= Diameter of Piston = 0.01767 m = G= Average Gauge Reading1 = 28.5kPa

0.5𝑘𝑔×9.81m/𝑠 2 0.245×10−3

×

1𝑘N 1000N

= 20.02 kPa 𝜋

Area of Piston = 4 (𝐷 2 ) =

Absolute Gauge Error = / P-G / =/ 20.02 kPa- 20 kPa /

𝜋

(0.01767 2 ) 4

= 0.02 kPa

= 0.245 × 10−3 m2 Total mass = Mass of Weight + Mass of Piston

% Gauge Error =

/ P−G / 𝑃

× 100

= 0.0 kg + 0.5kg = (0.02/20.02) x 100 = 0.5 kg = 0.099 %

Graph of Absolute Gauge Error vs Gauge Reading 12

Absolute Gauge Error (kPa)

10 8

6 4 2 0 0

50

100

-2

150

200

250

300

250

300

Gauge Reading (kPa)

Graph of Percent Gauge Error vs Gauge Reading 7

Percent Gauge Error (%)

6 5 4 3 2 1 0

0 -1

50

100

150 Gauge Reading (kPa)

200

6. Discussion of Results When applied with a series of weights in intervals of 0.5, 1 and 2 kg, both the gauge pressure and theoretical pressure increased, and as weights were taken off, also in intervals, both gauge pressure and theoretical pressure decreased. This is the expected result. The percent gauge error ranged from 0.099% to 6.346%. These results also show that the percent error varied widely. This means that the gauge is rather inaccurate, and probably needs recalibration. However, its inaccuracy varies with respect to the pressure acting on it. The higher the total weight, the larger the error; the error increased as more weights were added. The first graph on the previous page plots the average gauge reading against the absolute gauge error, both in kPa. For the most part, the graph’s slope is positive, denoting direct proportionality. The second graph plots the average gauge reading against the percent gauge reading in kPa. 7.

Conclusion The results show a minimal range of error, the maximum value of which is over 6 percent. This error is due to three factors – temperature, vibration, and pulsation. These effects are due to the unstable position of the equipment. This may also affect the position of the pointer of the gauge. Air bubbles were also found inside the tubes which are more compressible than water and thus this may also affect the gauge reading. The gauge readings were rather inaccurate when loaded with heavier weights, but became more accurate as pressure decreased, as can be observed by looking at the graphs on the previous page. However, a noticeable “jump” occurred in the third set-up this might be due to human error -wrong reading of the gauge. The positive slope of the graph indicates that the pressure and the error are directly proportional. It is also notable that a large reference or absolute gauge error associates with a high percent error. This is expected, since the percent error is the absolute error divided by the theoretical pressure of the weights. The absolute error is higher at lower cylindrical pressures, so the generated quotient would be high; the absolute error is low when heavier weights were loaded, so a small absolute error divided by a large cylindrical pressure gives a small percentage. The relative height between the dead-weight calibrator and the gauge is important in the calibration. This is through analysis of the hydrostatic equation that states that pressure equals specific weight multiplied by the depth – in other words, pressure is a function of the depth. If the connection of the gauge to the hose were positioned at a lower altitude than the surface where the water meets the piston, there is depth relative to the surface of the fluid where pressure is minimum. Pressure increases as altitude decreases, so the lower the gauge relative to the calibrator, the higher the pressure reading in the gauge.