Calculate the pressure inside a small air bubble of radius $0.01 mm$ situated at a depth of $h = 20 m$ below the free surface of liquid of density $ρ_{1} = 10^{3} k g / m^{3}, ρ_{2} = 800 km / m^{3}$ and surface tension $T_{2} = 7.5 \times 10^{- 2} N / m$ . The thickness of the first liquid is $h_{1} = 15 m$ and $h_{2} = 25 m$ .

Question

Calculate the pressure inside a small air bubble of radius

0.01 mm

situated at a depth of

h = 20 m

below the free surface of liquid of density

ρ_{1} = 10^{3} k g / m^{3}, ρ_{2} = 800 km / m^{3}

and surface tension

T_{2} = 7.5 \times 10^{- 2} N / m

. The thickness of the first liquid is

h_{1} = 15 m

and

h_{2} = 25 m

.

Filo · Accepted Answer

Given :   R=0.01mm =0.00001m                h=20 m             h1​=15 m            ρ1​ =103 kg/m3                       ρ2​ =800 kg/m3                 T2​ =0.075 N/mFrom the figure,       x =h−h1​ =20−15 =5 mPressure just outside the bubble         P=Po​+ρ1​gh1​+ρgx∴     P=105+103(10)(15)+800(10)(5) =2.9×105 N/m2Thus pressure inside the air bubble        Pi​ =P+R2T2​​∴     Pi​ = 2.9×105+0.000012×0.075​ =3.05×105 N/m2

Question Text	Calculate the pressure inside a small air bubble of radius $0.01 mm$ situated at a depth of $h = 20 m$ below the free surface of liquid of density $ρ_{1} = 10^{3} k g / m^{3}, ρ_{2} = 800 km / m^{3}$ and surface tension $T_{2} = 7.5 \times 10^{- 2} N / m$ . The thickness of the first liquid is $h_{1} = 15 m$ and $h_{2} = 25 m$ .
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Calculate the pressure inside a small air bubble of radius 0.01mm situated at a depth of h=20m below the free surface of liquid of density ρ1​=103kg/m3,ρ2​=800km/m3 and surface tension T2​=7.5×10−2N/m. The thickness of the first liquid is h1​=15m and h2​=25m.

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