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Unformatted text preview: Fluids Pressure Applications RHJansen Example 1 A gas is trapped in the bulb on the left by water (gray). The unknown gas has enough pressure to cause the water to form a column that is h = 40 cm tall at point B. a. What is this device called? Open tube manometer b. Write an equation relating PA to PB . Points A and B are at the same height. The same height means the same pressure. A B h PA = RHJansen Example 1 A gas is trapped in the bulb on the left by water (gray). The unknown gas has enough pressure to cause the water to form a column that is h = 40 cm tall at point B. c. Substitute pressure equations for PA and PB , and solve for the pressure of the trapped gas. A B h PA = Pgas = Pgas = + 0 The fluid above each point causes the pressure on that point. The trapped gas is above point A. A column of water and the atmosphere is above point B. RHJansen Substitute values and solve. See next slide. Example 1 A gas is trapped in the bulb on the left by water (gray). The unknown gas has enough pressure to cause the water to form a column that is h = 40 cm tall at point B. c. Substitute pressure equations for PA and PB , and then solve for the pressure of the trapped gas. A B h Pgas = + 0
5 5 Some of these values are memorized Pgas = (1 10 ) + (1000 ) ( 9.8) ( 0.40 ) Pgas = 1.04 10 RHJansen Example 2 A column of mercury is trapped inside a tube. The space above the fluid column is a vacuum. The bottom of the tube is immersed in a dish open to the air. The purpose is to find the atmospheric pressure at point A. The fluid is mercury and the column is h = 78 cm tall. h A B a. What is this device called? Barometer b. Write an equation relating PA to PB . Points A and B are at the same height. The same height means the same pressure. PA = RHJansen Example 2 A column of mercury is trapped inside a tube. The space above the fluid column is a vacuum. The bottom of the tube is immersed in a dish open to the air. The purpose is to find the atmospheric pressure at point A. The fluid is mercury and the column is h = 78 cm tall. h A B c. Substitute pressure equations for PA and PB , and solve for the pressure of the trapped gas. PA = P0 = Pgas = Substitute values and solve. The fluid above each point causes the pressure on that point. The atmosphere is above point A. A column of mercury is above point B. (the space above is a vacuum and has no pressure) RHJansen Example 2 A column of mercury is trapped inside a tube. The space above the fluid column is a vacuum. The bottom of the tube is immersed in a dish open to the air. The purpose is to find the atmospheric pressure at point A. The fluid is mercury and the column is h = 78 cm tall. h A B c. Substitute pressure equations for PA and PB , and solve for the pressure of the trapped gas. P0 = P0 = (13.6 103 ) ( 9.8) ( 0.78) The atmospheric pressure is 10000 Pa under standard conditions. Sometimes the real pressure is higher or lower than standard. Barometers are used to find the exact atmospheric pressure, this helps in predicting the weather. RHJansen P0 = 1.04 10 5 Example 3 water reservoir A pump in a fresh
pumps water uphill into a holding tank. The height between the surface of the tank and the surface of the reservoir is 10 m. Determine th pressure of the pump to keep water flowing into the tank at constant velocity. P0 P0 h
pump P Ppump + = + 0 0 Ppump = Ppump = (1000 ) ( 9.8) (10 ) Ppump = 98000 P If the pump is turned off the water will go no higher than this point. So the pressure of the pump pushing up the hill must equal pressure of the water above this point. Atmospheric pressure is pushing on the reservoir and tank RHJansen ...
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 Spring '08
 Packard
 Physics

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