chap09 - PROBLEM 9.1 FIND SOLUTION Absolute pressure...

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PROBLEM 9.1 FIND: Convert to units of gauge pressure in N/m 2 SOLUTION Absolute pressure reference scale: 1 atm abs = 14.69 psia = 101.325 kPa abs = 101,325 N/m 2 abs 1 atm abs = 760 mm Hg abs = 406 in H 2 O abs Conversion factors: 14.69 psi = 101.325 kPa = 101,325 N/m 2 14.69 psi = 1 atm = 29.92 in Hg = 406 in H 2 O = 760 mm Hg 1 bar = 14.505 lb/in 2 = 100,000 N/m 2 p(gauge) = p(absolute) – p(reference) Using p(reference) = 101,325 N/m 2 : (a) 10.8 psia x 101325 N/m 2 /14.69 psi = 74 442 N/m 2 abs p = 74,442 – 101,325 N/m 2 = -26,883 N/m 2 = -26.883 kPa (b) 1.75 bars abs x 100,000 N/m 2 = 175,000 N/m 2 abs p = 175,000 – 101,325 N/m 2 = 73,675 N/m 2 = 73.675 kPa (c) 30.36 in H 2 O abs x 101,325 N/m 2 /406 in H 2 O = 7,577 N/m 2 abs p = 7,577 – 101,325 N/m 2 = -93,748 N/m 2 = - 93.748 kPa (d) 791 mm Hg abs x 101,325 N/m 2 /760mm Hg = 105,458 N/m 2 abs p = 105,458 – 101,325 N/m 2 = 4,133 N/m 2 = 4,133 kPa COMMENT Note that gauge pressure can be negative or positive relative to the reference pressure. Absolute pressure, which is measured relative to a perfect vacuum, is always a positive value.
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PROBLEM 9.2 FIND: Convert into absolute pressure SOLUTION p(absolute) = p(gauge) + p(reference) where here: p(reference) = 1 atm abs. Absolute pressure reference scale: 1 atm abs = 14.69 psia = 101.325 kPa abs = 101,325 N/m 2 abs 1 atm abs = 760 mm Hg abs = 406 in H 2 O abs Conversion factors: 14.69 psi = 101.325 kPa = 101,325 N/m 2 14.69 psi = 1 atm = 29.92 in Hg = 406 in H 2 O = 760 mm Hg (a) -0.55 psi + 14.69 psia = 14.14 psia = 0.963 atm abs (b) 100 mm Hg + 760 mm Hg abs = 860 mm Hg abs = 1.13 atm abs (c) 98.6 kPa + 101.325 kPa abs = 199.925 kPa abs = 1.97 atm abs (d) 7.62 cm H 2 O + 760 mm H 2 O abs = 836.2 mm H 2 O abs = 1.10 atm abs
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PROBLEM 9.3 KNOWN: H = 250 cm H 2 O p atm = 101.3 kPa abs FIND: The tank pressure p 1 . PROPERTIES: γ H2O = 997 kg/m 3 SOLUTION Referring to Figure 9.5 (manometer) p 1 – p 2 = p 1 - p atm p 1 = p atm + γ H2O H = 101,325 N/m 2 abs + (997 kg/m 3 )(250cm)(1m/100cm)(1N/kg-m/s 2 ) = 103,818 N/m 2 abs or = 0 N/m 2 + (997 kg/m 3 )(250cm)(1m/100cm)(1N/kg-m/s 2 ) = 2493 N/m 2
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