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Grade: 11
a soap bubble if radius 4 cm and surface tension 30 dyne / cm, is blown at the end of a tube of length 10 cm and internal radius 0.20 cm . if viscousity of air is 1.89 * 10^-4 poise, find the time taken by the bubble to be reduced to a radius of 2 cm.
2 years ago

Answers : (1)

Sunder Muthukumaran
28 Points
Let the Volume flowing per unit time be Vt
To find the Vt ,
Use Poiseulle’s Formula  V=   \frac{\Pi Pr^{4}}{8\eta L} (L – Length of tube , r – radius of tube . P – excess pressure on bubble )
Then , 
Find the difference in Volume ; \Delta V = V_{2}- V_{1}
                                                           = \frac{4\Pi }{3}((R_{2})^{3}-(R_{1})^{3})
For excess pressure use ;
Now for the time ,
By dividing the \frac{\Delta V}{V_{t}}   = Change in voume ÷ Rate of flow   = Time taken
( which is similar to where we divide x/v for t , that is distance / velocity = Time) , (Here velocity is rate of flow of volume , and X is Change in volume )
Use the given values and solve for time .
Regards ,
11th Grade
2 years ago
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