a high density liquid (such as mercury) for large pressure differences. One end of the tube is open to the atmosphere and the other end is connected to the system whose pressure we want to measure [see Fig. . (b)].
The pressure P at A is equal to pressure at point B. What we normally measure is the gauge pressure, which is P − P a , given by Eq. ( . ) and is proportional to manometer height h .
Pressure is same at the same level on both sides of the U-tube containing a fluid. For liquids, the density varies very little over wide ranges in pressure and temperature and we can treat it safely as a constant for our present purposes. Gases on the other hand, exhibits large variations of densities with changes in pressure and temperature. Unlike gases, liquids are, therefore, largely treated as incompressible.
Example . The density of the atmosphere at sea level is . kg/m . Assume that it does not change with altitude.
Then how high would the atmosphere extend? Answer We use Eq. ( . ) ρ gh = .
kg m – × . m s × h m = . × Pa ∴ h = m ≈ km In reality the density of air decreases with height. So does the value of g .
The atmospheric cover extends with decreasing pressure over km. We should also note that the sea level atmospheric pressure is not always mm of Hg. A drop in the Hg level by mm or more is a sign of an approaching storm. Example .
At a depth of m in an ocean (a) what is the absolute pressure? (b) What is the gauge pressure? (c) Find the force acting on the window of area cm × cm of a submarine at this depth, the interior of which is maintained at sea- level atmospheric pressure. (The density of sea water is .