1. (a) Describe how a barometer measures atmospheric pressure. 15 r A manometer
ID: 1770930 • Letter: 1
Question
1. (a) Describe how a barometer measures atmospheric pressure. 15 r A manometer is connected to a vessel containing air. The vertical leg of the manometer connected to the vessel has a diameter of 25 mm and the other vertical leg, open to the atmosphere, has a diameter of 6 mm. The manometer fluid is mercury (density = 13,600 kg/m3). (b) i. What is the pressure in the vessel when the mercury menisci in the leg connected to the vessel is higher than that open to atmosphere by 10 cm? [5 ii. The pressure in the vessel is increased by 10 kPa. What is the new reading of the mercury manometer? [4 What is the change in height of mercury in the smaller diameter leg? [6 ili.Explanation / Answer
Solution (a);
The simplest kind of barometer is a tall closed tube standing upside down in a bath of mercury (a dense liquid metal at room temperature) so the liquid rises partly up the tube a bit like it does in a thermometer. We use mercury in barometers because it's more convenient than using water. Water is less dense (less heavy, in effect) than mercury so air pressure will lift a certain volume of water much higher up a tube than the same volume of mercury. In other words, if you use water, you need a really tall tube and your barometer will be so enormous as to be impractical. But if you use mercury, you can get by with a much smaller piece of equipment. A piece of apparatus like this is called a Torricellian barometer for Italian mathematician Evangelista Torricelli (1608–1647), a pupil of Galileo's, who invented the first instrument of this kind in 1643.
At sea level, the atmosphere will push down on a pool of mercury and make it rise up in a tube to a height of approximately 760mm (roughly 30in). We call this air pressure one atmosphere (1 atm). Go up a mountain, and take your Torricellian barometer with you, and you'll find the pressure falls the higher you up go. The atmosphere no longer pushes down on the mercury quite so much so it doesn't rise so far in the tube. Maybe it'll rise to more like 65cm (25 in). The pressure on top of Mount Everest is slightly less than a third of normal atmospheric pressure at sea level (roughly 0.3 atm).
solution (b-1)
If ‘dm‘is the manometric fluid density, ‘d1’ is the density of the fluid over the manometer, ‘P2’ is the atmospheric pressure (for general measurement of gas pressure) and ‘P1’ is the gas pressure
If a1 and a2 are the areas of the well and the capillary, and if (h1-h2) is the difference in height in the well due to the pressure difference (p1-p2) as shown, at balance, then
p1-p2 = dm.h (1+a2/a1)
p1-p2 = 13600x0.1x(1+36/625)
p1-p2=1438.33 pa
p2= -1438.33+P1
Solution (b-2)
p1-p2 = dm.h (1+a2/a1)
h= (p1-p2)/dm(1+a2/a1)
h= (10000-1438)/13600x1.058
h= 60 cm
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