Given the barometric pressure of 14.7 psia (29.92 in Hg abs) make these conversion: a) 80 psig to psia and to atmosphere, b) 20 in. Hg vacuum to in Hg abs and to psia, c) 10 psia to psi vacuum and to Pa
The Correct Answer and Explanation is:
Let’s go through each of the conversions one by one, explaining the steps involved:
a) 80 psig to psia and to atmosphere
- psig to psia:
To convert from psig (pounds per square inch gauge) to psia (pounds per square inch absolute), we need to add the barometric pressure (14.7 psia). The equation is: psia=psig+atmospheric pressure\text{psia} = \text{psig} + \text{atmospheric pressure}psia=psig+atmospheric pressure So: 80 psig+14.7 psia=94.7 psia80 \, \text{psig} + 14.7 \, \text{psia} = 94.7 \, \text{psia}80psig+14.7psia=94.7psia Therefore, 80 psig is equivalent to 94.7 psia. - psia to atmosphere:
1 atmosphere (atm) is equal to 14.7 psia. To convert from psia to atmospheres, we divide by 14.7: 94.7 psia14.7 psia/atm=6.44 atm\frac{94.7 \, \text{psia}}{14.7 \, \text{psia/atm}} = 6.44 \, \text{atm}14.7psia/atm94.7psia=6.44atm Therefore, 80 psig is equivalent to 6.44 atm.
b) 20 in. Hg vacuum to in Hg abs and to psia
- in Hg vacuum to in Hg abs:
To convert from in Hg vacuum to in Hg absolute, we subtract the vacuum pressure from standard atmospheric pressure, which is 29.92 in Hg. The formula is: in Hg abs=29.92 in Hg−20 in Hg vacuum\text{in Hg abs} = 29.92 \, \text{in Hg} – 20 \, \text{in Hg vacuum}in Hg abs=29.92in Hg−20in Hg vacuum So: 29.92 in Hg−20 in Hg=9.92 in Hg abs29.92 \, \text{in Hg} – 20 \, \text{in Hg} = 9.92 \, \text{in Hg abs}29.92in Hg−20in Hg=9.92in Hg abs Therefore, 20 in. Hg vacuum is equivalent to 9.92 in. Hg absolute. - in Hg abs to psia:
1 in Hg is equal to 0.4912 psia. To convert 9.92 in. Hg absolute to psia: 9.92 in Hg abs×0.4912 psia/in Hg=4.87 psia9.92 \, \text{in Hg abs} \times 0.4912 \, \text{psia/in Hg} = 4.87 \, \text{psia}9.92in Hg abs×0.4912psia/in Hg=4.87psia Therefore, 20 in. Hg vacuum is equivalent to 4.87 psia.
c) 10 psia to psi vacuum and to Pa
- psia to psi vacuum:
To convert from psia to psi vacuum, we subtract the absolute pressure from atmospheric pressure (14.7 psia): psi vacuum=14.7 psia−10 psia\text{psi vacuum} = 14.7 \, \text{psia} – 10 \, \text{psia}psi vacuum=14.7psia−10psia So: 14.7 psia−10 psia=4.7 psi vacuum14.7 \, \text{psia} – 10 \, \text{psia} = 4.7 \, \text{psi vacuum}14.7psia−10psia=4.7psi vacuum Therefore, 10 psia is equivalent to 4.7 psi vacuum. - psia to Pa:
1 psia is equal to 6894.76 Pa (since 1 psi = 6894.76 Pa). To convert 10 psia to Pascals: 10 psia×6894.76 Pa/psia=68,947.6 Pa10 \, \text{psia} \times 6894.76 \, \text{Pa/psia} = 68,947.6 \, \text{Pa}10psia×6894.76Pa/psia=68,947.6Pa Therefore, 10 psia is equivalent to 68,947.6 Pa.
Summary of Results:
- a) 80 psig is equal to:
- 94.7 psia
- 6.44 atm
- b) 20 in. Hg vacuum is equal to:
- 9.92 in. Hg absolute
- 4.87 psia
- c) 10 psia is equal to:
- 4.7 psi vacuum
- 68,947.6 Pa
