Fluid Mechanics Viscosity Question 319
Question: The lower end of a capillary tube of radius 2.00mm is dipped 10.00cm below the surface of water in a beaker. Calculate the pressure within a bubble blown at its end in water, in excess of atmospheric pressure. [Surface tension of water$ 72\times {{10}^{-3}}N/m $ ]
Options:
A) $ 718N{{m}^{-2}} $
B) $ 912N{{m}^{-2}} $
C) $ 1160N{{m}^{-2}} $
D) $ 1052N{{m}^{-2}} $
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Answer:
Correct Answer: D
Solution:
[d] The pressure at a point just outside the bubble $ p_{0}=P_{atm}+h\rho g=P_{atm}+10\times {{10}^{-2}}\times 10^{3}\times 9.8 $ $ =P_{atm}+980N{{m}^{-2}} $ Now excess pressure within the bubble compared to a point just outside $ =\frac{2T}{R}=\frac{2\times 72\times {{10}^{-3}}}{2\times {{10}^{-3}}}72N{{m}^{-2}} $ $ \therefore $ Inside pressure = excess pressure + outside pressure $ =P_{atm}+980+72=P_{atm}+1052N{{m}^{-2}} $ $ \therefore $ Pressure within the bubble in excess of atmospheric pressure$ =1052N{{m}^{-2}} $ .
BETA
