1. Pressure Measurements
Pressure measurements related to the fluid systems are the topic of this chapter.
Absolute pressure refers to the absolute value of the force per unit area exerted on the containing wall by a fluid.
Gage pressure represents the difference between the absolute pressure and the local atmospheric (atm) pressure.
Vacuum represents the amount by which the atmospheric pressure exceeds the absolute pressure

2. Pressure Measurements
Atmospheric pressure
Negative gage pressure or vacuum
Positive gage pressure
P(absolute)

3. Pressure Measurements2
The standard SI unit for pressure is the (N/m ) or Pascal (Pa).
1 atm = x10 Pa
= 760 mmHg
Fluid pressure results from a momentum exchange between the molecules of the fluid and a containing wall.

4. Pressure Measurements
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5. Pressure Measurement
The mean free path is defined as the average distance a molecule travels between collisions. For an ideal gas whose molecules act approximately like billiard balls.
where r is the effective radius of the molecule and λ is the mean free path.
It is clear that the mean free path increases with a decrease in the gas density.
Phil. U., M Eng Dep., Measurements, Chap#6

6. Pressure Measurement
For air the relation for mean free path reduces to
Phil. U., M Eng Dep., Measurements, Chap#6

7. Dynamic Response Considerations
The transient response of pressure-measuring instruments is dependent on two factors:
1-the response of the transducer element that senses the pressure.
2- The response of the pressure-transmitting fluid and the connecting tubing.
The fluctuating pressure has a frequency of ω and an amplitude of p0 and is impressed on the tube of length L and radius r.

8. Dynamic Response Considerations
Phil. U., M Eng Dep., Measurements, Chap#6

10. Mechanical Pressure- Measurements devices
Mechanical devices offer the simplest means for pressure measurements.
The barometer is a device used to measure the atmospheric pressure
Consider the U-tube manometer shown in figure 6.3. A pressure balance of the tube columns dictates that:
P – Pa = gh(m - f)

11. Mechanical Pressure-Measurement Devices
Phil. U., M Eng Dep., Measurements, Chap#6

13. Pressure Measurement p (absolute) = p (gage) + p (atm)
The local atmospheric pressure must be obtained from a local measurement near the place where the gage pressure is measured. Such a measurement might be performed with a mercury barometer.
For altitudes between 0 and 36,000 ft the standard atmosphere is expressed by
Phil. U., M Eng Dep., Measurements, Chap#6

14. Pressure Measurement
For altitudes between 0 and 36,000 ft the standard atmosphere is expressed by
Phil. U., M Eng Dep., Measurements, Chap#6

15. Dead-Weight Tester
The dead-weight tester is a device used for balancing a fluid pressure with a known weight.

16. Dead-Weight Tester
The accuracies of dead-weight testers are limited by two factors:
(1) the friction between the cylinder and the piston
(2) the uncertainty in the area of the piston.
Phil. U., M Eng Dep., Measurements, Chap#6

17. Dead-Weight Tester The smaller the clearance, the more
closely the effective area will approximate the cross-sectional area of the piston.
It can be shown1 that the percentage error due to the clearance varies according to

18. Bourdon-Tube Pressure Gage

19. Bourdon-Tube Pressure Gage
Bourdon-tube pressure gages enjoy a wide range of application where consistent, inexpensive measurements of static pressure are desired.
They are commercially available in many sizes (1- to 16-in diameter) and accuracies
The Heise gage2 is an extremely accurate bourdon-tube gage with an accuracy of 0.1 percent of full-scale reading

20. Diaphragm and Bellows Gages
Diaphragm and bellows gages measures pressure based on sensing the elastic deformation of materials as a result of pressure.
The diaphragm deflection will be according to the pressure difference. The deflection is measured by appropriate displacement transducers or strain gages

21. Diaphragm and Bellows Gages
Electrical-resistance strain gages may also be installed on the diaphragm, as shown in Fig The output of these gages is a function of the local strain, which, in turn, may be related to the diaphragm deflection and pressure differential.
The deflection generally follows a linear variation with p when the deflection is less than one-third the diaphragm thickness
Phil. U., M Eng Dep., Measurements, Chap#6

23. Diaphragm and Bellows Gages
Consider figure 6.12 for a bellows gage.
The pressure difference causes the bellows movements which may be converted into electrical or mechanical signal.
The bellows gage is generally unsuitable for transient measurements because of the larger relative motion and mass involved.

24. Phil. U., M Eng Dep., Measurements, Chap#6

25. The LVDT
The linear variable differential transducer (LVDT) assembled with a diaphragm can be used as a differential pressure gage. (see figure 6.14)
The displacement of the core is connected with the diaphragm movement, which is in turn, indicates the pressure difference P2-P1.

27. The LVDT
The natural frequency of a circular diaphragm fixed at its perimeter is given by Hetenyi [5] as

28. The LVDT
Phil. U., M Eng Dep., Measurements, Chap#6

29. The Bridgman Gage
It is known that the resistance of fine wires changes with the pressure according to:
R = R1 (b + P)
where: R1: is the resistance at 1 atm
b: pressure coefficient of the resistance
This gage can measure pressures as high as 100,000 atm
the gage can be used for high-pressure measurement with an accuracy of 0.1 percent. The transient response of the gage is exceedingly good

30. MCLEOD GAGE
Phil. U., M Eng Dep., Measurements, Chap#6

31. MCLEOD GAGE
A known volume gas (with low pressure) is compressed to a smaller volume (with high pressure), and using the resulting volume a.nd pressure, the initial pressure can be calculated
he reference capillary tube has a point called zero reference point. This reference column is connected to a bulb and measuring capillary and the place of connection of the bulb with reference column is called as cut off point. (It is called the cut off point.
Phil. U., M Eng Dep., Measurements, Chap#6

32. MCLEOD GAGE
Now as V1,V2 and P2 are known, the applied pressure P1 can be calculated using Boyle’s Law given by; P1V1 = P2V2 Let the volume of the bulb from the cutoff point upto the beginning of the measuring capillary tube = V Let area of cross – section of the measuring capillary tube = a  Let height of measuring capillary tube = hc.
Phil. U., M Eng Dep., Measurements, Chap#6