Atmospheric Pressure and Gauge Pressure

      
Introduction

The pressure of a gas can be measured several ways.

The open-tube manometer to the left measures a difference in pressure.  

P = P _atmospheric  ^{+ g /\h}

^{where /\h = h} _left  -  h _right  

/\h will be negative if the pressure of the gas is less than the atmospheric pressure.

The Bourdon gauge to the left uses the effect of pressure on the flexible tube to measure pressure.  As the pressure increases, the tube straightens out.  The gauge has to be calibrated with known pressures.

This gauge is used to measure the difference in pressure between the air in a tire and the atmospheric pressure.

The air in the tire pushes against a piston that compresses a spring.  
  

                    F
Since P  =  -----    and F = kX   a known area makes it possible to calculate P.
                    A
      

 Since the tire gauge and some others measure the difference in the air pressure and the pressure of the gas, they give a gauge pressure, P _G.

The Pressure of the gas is the sum of the gauge pressure, P_G, and the atmospheric pressure, P_A.

P  =  P_G  +  P _A  

The barometer to the left was the first type used to measured atmospheric pressure.  The first barometers used water as the fluid and were over 33 feet tall.  To make the barometer, a long tube was attached to the side of a building.  The tube had a spigot at the top and was filled from the top leaving the bottom in a bucket of water.  When the tube was full of water, the spigot at the top was closed.  A near vacuum was created at the top.  There was water vapor above the water but no air.

The weight of the fluid inside the barometer was equal to the weight of the air above the barometer.  

Mercury was used later instead of water.  Since mercury's density is 13.6 times greater than water, the tube could be much shorter making the barometer more practical.  In addition, the vapor pressure of mercury is much less than the vapor pressure of water.  Thus a smaller correction had to be made to take into account the vapor pressure.  Mercury is poisonous and mercury barometers are being phased out of normal usage.

The aneroid barometer to the left is much cheaper while still giving good results.  It also avoids the problem of mercury poisoning while adding more durability.

More sophisticated barometers use electronics to measure the distortion of a thin, flexible diaphragm.  

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Problems

1.	Calculate the density of the oil.  Hint, the pressure at points a and b are the same.
2.	Calculate the pressure of the gas.
3.	The gauge pressure in each of four tires of an automobile is 200. kPa.  If each tire has a footprint of 200. cm2, what is the mass of the car?
4.	Calculate the minimum gauge pressure needed in a water pipe leading into a building if water is to come out of a faucet on the twelfth floor, 35 m above.

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Answers

1.	Calculate the density of the oil.  Hint, the pressure at points a and b are the same.
	m oil  =  m water  above point b m = V x D      thus         Because of uniform diameters, height is proportional to volume. h oil x D oil  =  h water x D water        Solve for D oil.                         h water x D water           (26.3 cm  -  8.89 cm) x 1.00 g/cm3   D oil  =  ------------------------  =  -----------------------------------------------  =  0.662 g/cm3                         h oil                                       26.3 cm 3
2.	Calculate the pressure of the gas.
	P  =  773 torr  +  325 mm Hg  -  145 mm Hg  =  953 torr
3.	The gauge pressure in each of four tires of an automobile is 200. kPa.  If each tire has a footprint of 200. cm2, what is the mass of the car?
	1 m  =  100 cm      =>    1 m2  =  ( 100 cm )2  =  10000 cm2                                 1 m2  200. cm3  x  -----------------  =  0.0200 m2    x  4  =  0.0800 m2  =  A                       10000 cm2                  F P  =  -----   =>    F  =  P x A  =  200. x 103 N m -2  x  0.0800 m2  =  1.60 x 104 N           A                                      F         1.60 x 104 N F = mg   =>  m  =  ----  =  ---------------------  =  1630 kg                                 g          9.80 m s -2
4.	Calculate the minimum gauge pressure needed in a water pipe leading into a building if water is to come out of a faucet on the twelfth floor, 35 m above.
	The gauge pressure is due to the height of water.    P = gh  =  1.00 x 103 kg/m2  x  9.80 m s -2  x  35 m  =  3.43 x 10 5 Pa  =  343 kPa

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