Measurement of PressureManometry

• Use liquid column in vertical or inclined tubes

• Hg barometer is an example of one type of manometer

• Measure

• 3 common types of manometers including the U-tube manometer, piezometer, inclined manometer Measurement of Pressure Manometry

0p h p 1Ap h

•Piezometer is simple and accurate

•Piezometer is only suitable if the pressure in the container is greater than atmospheric pressure

•Fluid in the container in which the pressure is measured must be a liquid rather than gas

Figure 2.9 (p. 51)

Piezometer tube.

Figure 2.10 (p. 51)

Simple U-tube manometer.

1 2 0Ap h h

2 1Ap h h

Example 1

• A manometer is used to measure the pressure in tank as shown. If the local atmospheric pressure is 96 kPa, determine the absolute pressure within the tank.

Example 2A closed tank contains compressed air and oil (SGoil=0.90)

as Is shown in the Figure. h1=36 in., h2=6 in, h3=9 in.

Determine the pressure reading (in psi) of the gage using

the U-tube Hg manometer

Figure 2.11 (p. 53)

Differential U-tube manometer.

1 2 3A Bp h h h p

• suitable to measure the pressure difference between two points

2 3 1A Bp p h h h

Figure 2.12 (p. 54)Inclined-tube manometer

1 2 3sinA Bp h l h p

Suitable to measure small pressure changes

Often used to measure small difference in gas pressures

2 3 1sinA Bp p l h h

2 sinA Bp p l

2 sinA Bp p

l

Other Pressure Measurement Devices

• Mechanical and electronic pressure measuring devices

Figure 2.13 (p. 55)

(a) Liquid-filled Bourdon pressure gages forv arious pressure ranges. (b) Internal elements of Bourdon gages. The “C-shaped” Bourdon tube is shown on the left, and the “coiled spring” Bourdon tube for high pressures of 1000 psi and above is shown on the right. (Photographs courtesy of Weiss Instruments, Inc.)

Pressure Transducer• Pressure is measured as an electrical output for continuous

monitoring.

Figure 2.15a (p. 57)

(a) Two different sized strain-gage pressure transducers(Spectramed Models P10EZ and P23XL) commonly used to measure physiological pressures. Plastic domes are filled with fluid and connected to blood vessels through a needle or catheter. (Photograph courtesy of Spectramed, Inc.

Figure 2.14 (p. 56)

Pressure transducer which combines a linear variabledifferential transformer (LVDT) with a Bourdon gage.(From Ref. 4, used by permission.)

Hydrostatic force on a Submerged PlaneSurface

Figure 2.16 (p. 58)

(a) Pressure distribution and resultant hydrostatic force on the bottom of an open tank. (b) Pressure distribution on the ends of an open tank.

Figure 2.17 (p. 58)

Notation for hydrostatic force on an inclined plane surface of arbitrary shape.

Hydrostatic force on an inclined surface

dA,or dAR

A

dF h F h sin dA; sin

A

y h y

sin dAR

A

F y

dA c

A

y y A

R cF h A

First moment of the area

Hydrostatic force on a curved surface

Figure 2.23 (p. 67)

Hydrostatic force on a curved surface.