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4.th week

Units and scales of pressure measurements

Pressure can be expressed with reference to any datum.

The usual datums are:

1. Absolute zero.

2. Local atmospheric pressure.

Absolute pressure: is the pressure when expressed as difference between its value and a complete vacuum.

Gage pressure: is the pressure when expressed as difference between its value and the local atmospheric pressure.

Negative, Suction, or Vacuum pressure: is the pressure below local atmospheric pressure with reference to gage

pressure.

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Types of pressure gages

1. The Bourdon gage: it is the device used for measuring gage

pressures. The red.pressure element is a hollow, curved, flat metallic

tube closed at one end; the other end is connected to the pressure to be

measured. the gage pressure measures pressure relative to the medium

surrounding the tube, which is the local atmosphere.

2. The mercury barometer: it is used to measure atmospheric pressure.

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MANOMETERS

In Fig(b). The meniscus can come to rest below A, as shown. Since the

pressure at the meniscus is zero gage and since pressure decreases with

elevation:

Fig(c) showed the manometer which is used for high negative or positive

gage pressure. a liquid with high specific weight is employed. It must be

immiscible in the first fluid. The pressure at A can be calculated as

follows:

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Where:PA= unknown pressure at A.

h1= height of liquid of the manometer.

h2= height of liquid want to measure its pressure in the

manometer.

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Differential Manometer:

Example 1:

EXAMPLE 2.

The classic use of a manometer is when two U-tube legs are of equal

length, as in Fig. E2.3, and the measurement involves a pressure

difference across two horizontal points. The typical application is to

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measure pressure change across a flow device, as shown. Derive a

formula for the pressure difference pa - pb in terms of the system

parameters in Fig.

Solution

Using our “up-down” concept as in Eq. (2.32), start at (a), evaluate

pressure changes around the U-tube, and end up at (b):

pa +ρ1gL +ρ1gh -ρ2gh -ρ1gL = pb

or pa - pb = (ρ2-ρ1)gh

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Fig. 2.10 A complicated multiple-fluid manometer to relate

PA to PB.

Example:

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Micromanometers

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Example:

The Inclined manometer:

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Fig. 2.6: a modern portable

barometer, with digital readout, uses

the resonating silicon element .

Solved problems

Ex1: A closed tank contains 1.5 m of SAE 30 oil, 1 m of water, 20 cm of

mercury, and an air space on top, all at 20C. If pbottom 60 kPa, what is

the pressure in the air space? γoil=8720N/m3, γwater=9790N/m3,

γmercury=133100N/m3.

Solution: Apply the hydrostatic formula down through the three layers of

fluid:

P bottom = Pair + γoil * hoil + γwater *hwater+ γ mercury *h mercury

60000 Pa= Pair + (8720 N/m )(1.5 m)+ (9790)(1.0 m) +(133100)(0.2 m)

Solve for the pressure in the air space: Pair 10500 Pa Ans.

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Ex2: