Engineering College

As shown in the figure below, a monometer is attached to a tank of gas in which the pressure is 104.0 kPa. The manometer liquid is mercury, with a density of 13.59 g/cm 3 . If g = 9.81 m/s 2 and the atmospheric pressure is 101.33 kPa, calculate (a) the difference in mercury levels in the manometer, in cm, and (b) the gage pressure of the gas, in kPa.

As Shown In The Figure Below, A Monometer Is Attached To A Tank Of Gas In Which The Pressure Is 104.0

Answers

Answer 1

Answer:

a) The difference in mercury levels in the manometer is 2 centimeters.

b) The gage of the gas is 2.670 kilopascals.  

Explanation:

a) Pressure in gases is absolute. A manometer helps to determine the hydrostatic difference between pressure of the gas ([tex]P_{g}[/tex]) and atmospheric pressure ([tex]P_{atm}[/tex]), both measured in pascals. A kilopascal equals 1000 pascals and 1 meter equals 100 centimeters. That is:

[tex]P_{g}-P_{atm} = \rho \cdot g \cdot L[/tex] (1)

Where:

[tex]\rho[/tex] - Density of mercury, measured in kilograms per cubic meter.

[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.

[tex]L[/tex] - Difference in mercury levels, measured in meters.

If we know that [tex]P_{g} = 104000\,Pa[/tex], [tex]P_{atm} = 101330\,Pa[/tex], [tex]\rho = 13590\,\frac{kg}{m^{3}}[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], the difference in mercury levels in the manometer is:

[tex]L = \frac{P_{g}-P_{atm}}{\rho\cdot g}[/tex]

[tex]L = \frac{104000\,Pa-101330\,Pa}{\left(13590\,\frac{kg}{m^{3}} \right)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}[/tex]

[tex]L = 0.020\,m[/tex]

[tex]L = 2\,cm[/tex]

The difference in mercury levels in the manometer is 2 centimeters.

b) The gage pressure is the difference between gas pressure and atmospheric pressure: ([tex]P_{g} = 104000\,Pa[/tex], [tex]P_{atm} = 101330\,Pa[/tex])

[tex]P_{gage} = P_{g}-P_{atm}[/tex] (2)

[tex]P_{gage} = 104000\,Pa-101330\,Pa[/tex]

[tex]P_{gage} = 2670\,Pa[/tex]

[tex]P_{gage} = 2.670\,kPa[/tex]

The gage of the gas is 2.670 kilopascals.

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