Q#45
A vertical tube, closed at one end, is immersed in water. A column of air is trapped inside the tube.
The density of water is 1000 kg m-3.
What is the difference between the pressure of the air in the tube and the atmospheric pressure?
A 1960 Pa B 2940 Pa C 4910 Pa D 7850 Pa
Solution:
Answer: C.
At any specific depth in a liquid, the pressure is the same for any point at the same level.
Also at any point, pressure is due to the liquid ABOVE the point.
Consider the liquid in the vertical tube.
The pressure acting on the liquid in the tube is due to the air above only.
But as we know (from the first sentence above), the pressure at a level in the liquid is the same at the same depth in the liquid. Thus,
Pressure of air in tube (Pair) = Pressure due to (20 + 30 =) 50 cm depth of liquid outside tube + Atmospheric pressure Patm
{In the tube, the pressure is due to air above. But at the same level outside the tube, there is 50.0 cm of liquid above a point at this level. Atmospheric pressure acts on the water surface.}
Pair = Pressure due to (20 + 30 =) 50 cm depth of liquid + Patm
Pair – Patm = Pressure due to (20 + 30 =) 50 cm depth of liquid
Pair – Patm = hρg = 0.50 × 1000 × 9.81
Pair – Patm = 4905 Pa = 4910 Pa
This is the difference between the pressure of air in the tube and the atmospheric pressure.
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