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The lower end of a capillary tube of dia...

The lower end of a capillary tube of diameter 2.00 mm is dipped 8.00 cm below the surface of water in a beaker. What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at the temperature of the experiments is `7.30 xx 10^(-2) "N/m"`. 1 atmospheric pressure `=1.01 xx 10^(5) Pa` density of water `=7000" kg/m"^(3), g="9.80 ms"^(-2)`. Also calculate the excess pressure.

Text Solution

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Given, `r=(2.00 mm)/(2)=1.00 mm`
`=1.00 xx 10^(-3)m`
`h=8.00 cm =8 xx 10^(-2) m`
`sigma=7.30 xx 10^(-2) N//m`
`P_("atm")=1.01 xx 10^(5) Pa`
`p=1000 kg//m^(3), g=9.80 m//s^(2)`
Excess pressure inside the bubble is
`p=(2sigma)/(r)=(2 xx 7.30 xx 10^(-2))/(1 xx 10^(-3)) =146 Pa`
Pressure required in the tube=Atmospheric pressure +Pressure due to water column
`=P_("atm")+hpg`
`=1.01 xx 10^(5)+8 xx 10^(-2) xx 10^(-3) xx 9.80`
`=1.01 xx 10^(5) +0.00784 xx 10^(5)`
`=1.01784 xx 10^(5) Pa`
Pressure inside the bubble =Pressure outside the tube +Exces pressure
`=1.01784 xx 10^(5)+146`
`=1.0193 xx 10^(5) Pa or`
`=1.02 xx 10^(5) Pa`
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