Lecture 4. Pressure

4.1 Pressure and it units Pressure = “the normal (perpendicular) force per unit area” Pressure at the bottom of the static (nonmoving) column of liquid p = pressure at the bottom of the column of liquid F = force A = area ρ = density of fluid g = acceleration of gravity h = height of the fluid column p 0 = atmospheric pressure at the top of the column of liquid “ρgh” is sometimes called “head of liquid”, simply expressed as height of liquids e.g. 50 cm Hg

Pressure Unit SI system (some common nonstandard units) – bar : 100 kPa = 1 bar – kg f /cm 2 : often called just “kilos” – Torr : 760 Torr = 1 atm AE system – mm Hg – in. Hg – ft H 2 O – in. H 2 O – atm – lb f /in 2 : psi or often called just “pounds”

4.2 Pressure Measurement Barometer use for measuring atmospheric pressure (Fig. 5.3, p.104) -> barometric / atmospheric pressure

Standard Atmosphere Atmospheric pressure : variable Standard atmosphere : defined as “the pressure in a standard gravitational field equivalent to 1 atm or 760 mmHg at 0 o C. Standard atmosphere : – atm mmHg – ft H 2 O x10 5 Pa or N/m 2 – in. Hg kPa – psia (pounds force per square inch) -> Without barometric/atmospheric pressure, one usually assume that barometric pressure equals the standard pressure.

Relative/Gauge Pressure Open-end manometer (Fig. 5.2a, p.103)

Relative/Gauge Pressure Open-end manometer (Fig. 5.9, p.114)

Relative/Gauge Pressure Bourdon gauge pressure-measuring devices (Bourdon gauge) (Fig. 5.4, p.105) (not always relative pressure)

Absolute Pressure Close-end manometer (Fig.5.2b, p.103) Barometer (Fig. 5.3, p.104)

Absolute pressure (above atmospheric pressure) = gauge pressure + (barometric/atmospheric pressure) Absolute pressure (below atmospheric pressure) = (barometric/atmospheric pressure) - vacuum Barometric/ atmospheric pressure Perfect vacuum Gauge pressure Vacuum Absolute pressure

Notes psia = pound force per square inch absolute psig = pound force per square inch gauge psi -> use common sense to which is being measured! Other pressure units -> be certain to carefully specify “gauge” or “absolute” -> 300 kPa absolute -> 12 cmHg gauge

Examples Lecture 4.2 (E5.2, DMH) The pressure gauge on a tank of CO 2 used to fill soda-water bottles reads 51.0 psi. At the same time the barometer reads 28.0 in. Hg. What is the absolute pressure in the tank in psia? (See Figure E5.2, p.110) Ans psia psia = 64.8 psia

Examples Lecture 4.2 (E5.3, DMH) Small animals such as mice can live (although not comfortably) at reduced air pressures down to 20 kPa absolute. In a test, a mercury manometer attached to a tank, as shown in Figure E5.3, reads 64.5 cm Hg and the barometer reads 100 kPa. Will the mice survive? Ans. 100 kPa – 86 kPa = 14 kPa absolute -> probably not!

4.3 Differential Pressure Measurements Differential Pressure Manometer (Fig. 5.9, p.114)

4.3 Differential Pressure Measurements Differential Pressure Manometer (Fig. 5.10, p.115)

Examples Lecture 4.3 (E5.4, DMH) In measuring the flow of fluid in a pipeline as shown in Figure E5.4, a differential manometer was used to determine the pressure difference across the orifice plate. The flow rate was to be calibrated with the observed pressure drop (difference). Calculate the pressure drop p 1 -p 2 in pascals for the manometer reading in Figure E5.4. Ans Pa

Examples Lecture 4.3 (E5.5, DMH) Air is flowing through a duct under a draft of 4.0 cm H 2 O. The barometer indicates that the atmospheric pressure is 730 mm Hg. What is the absolute pressure of the air in inches of mercury? (See Figure E5.5) Ans in. Hg – 0.12 in. Hg = 28.6 in. Hg absolute

Problems Chapter 5 P1, 5.3 P2, , 5.16, 5.22, 5.26, 5.32