24ohh...ya i took only one side of cylinder..
so I just need to multiply my result with 2 naa ??
Suppose that a bubble has the shape of a long cylinder, rather than that of a sphere. Determine an expression for the difference between the inside and outside pressures; express your answer in terms of the surface tension γ and the radius R of the cylinder
PS: Solving this question explains a lot of very basic things about surface tension :) .. Do not ignore ;)
Source: Internet...
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18 Answers
3@eure that i know ......ur looking only at the force coused by T in that interface .... that 2r is part of the actual surface of bubble .. there is no proj here .....
24
62The answer will be like this..
You have all made some slight mistakes..
Eureka has taken only one film...
WHile IITimcomin has made a mistake of taking force due to pressure as P(2piRL) The logic of which is nto clear to me..
According to me the method should be
Pi-Po(2RL) = T(2L+2L+4r+4R)
So Pi-Po = T (2L+4R) / LR = 2T/R + 4T/L
since L is very large, it is same as 2T/R
(Here I have assumed pure cyllindrical shape which may not be ture.. but it wont matter because the lenght is very large in comparison to the radius...)
24Anyways answer remians same..becoz answer didnt depend on that term (L→∞)[3]
1@eureka surface tenion is like kind of internal force in between the two halves.......so it go to act over the perimeter of the rectangle ......:)
3xyz he said ur ans is rong cuz u didnt take L>>R... else it shud be right!!!!
24@xyz
Tension force wont act on projection.....it will act on pure bubble surface
so pure bubble surface will have perimeter...Ï€R+Ï€R+2L
62are you sure karna... (It is given that L is very large... )
So the answer will be independent of L
Try again.. (not that this needs to be necessariliy true)
1@eureka how are u taking the perimeter to be 2pir+2l.........
the cross section will be a rectangle of dimensions 2r and l
corect me if i am wrong
24@ iitimcomin
Tension force wont act on projection.....it will act on pure bubble surface
@xyz
ur terms are diff
1even i have done the same thing in first post...but nishant sir has told that its wrong
3eure u made a mistake...
it should be
T(2(2R+L))..........its the perimeter of the recangle u get as crossection.... think abt it.....
so taking R<<L u get T/R..........[FOR LIQUID]........
so for soaP... u get 2T/R!!!
#6 is another way f doin it u get same ans...[1]
24Cutting the cylinder through middle
Pout(2RL)+T(Ï€R+Ï€R+2L)=P(2RL)
=>(P-Pout)=T(2Ï€R+2L)2RL
=>(P-Pout)=T(Ï€R+L)RL
=>(P-Pout)=T[Ï€L+1R]
L→∞
=>(P-Pout)=TR
Correct soln
Pout(2RL)+T(2R+2R+2L)=P(2RL)
=>(P-Pout)=T(4R+2L)2RL
=>(P-Pout)=T(2R+L)RL
=>(P-Pout)=T[2L+1R]
L→∞
=>(P-Pout)=TR
also edit :
Put γ in palce of T
3me getting Pex=2Y/R
Since the L>>>R
we have Y.(πLΔr+πΔLR)=(ΔP).(2ΠLrΔr+πΔLR)
which yields us ΔP=2Y/r
3let there be excess pressure .P ... inside .....
therefore .. we have ..
P(2piRL)dr = 2T(2piLdr + 2piRdr)
P = 2T(L+R)/(RL)
if L>>R
we have P = 2T/R