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Shown in the figure is a container whose...

Shown in the figure is a container whose top and botoom diameters are D and d respectively. At the bottom of the container, there is a capillary tube of outer radius b and inner radius a.
The volume flow rate in the capillary is Q. If the capillary is removed the liquid comes out with a velocity of `v_0`. The density of the liquid is given as `rho`. Calculate the coefficient of viscosity `eta`.

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
KEY CONCEPT: When the tube is not there, using Bernoulli's theorem
`P+P_0+1/2rhov_1^2+rhogH=1/2rhov_0^2+P_0`
`impliesP+rhogH=1/2rho(v_0^2-v_1^2)`
But according to equation of continuity
`v_1=(A_2v_0)/(A_1)`
`:.P+rhogH=1/2rho[v_0^2-(A_2/A_1v_0)^2]`
`P+rhogH=1/2rhov_0^2[1-(A_2/A_1)^2]`
Here, `P+rhogH=DeltaP`
According to Poisseuille's equation
`Q=(pi(DeltaP)a^4)/(8etal)=eta=(pi(DeltaP)a^4)/(8Ql)`
`:. eta=(pi(P+rhogH)a^4)/(8Ql)=(pi)/(8Ql)xx1/2rhov_0^2[1-(A_2/A_1)^2]xxa^4`
Where `A_2/A_1=d^2/D^2`
`eta=(pi)/(8Ql)xx1/2rhov_0^2[1-d^4/D^4]xxa^4`
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Shown in the figure is a container whose top and bottom diameters are D and d respectively At the bottom of the container these is a cappillary tube of outer radius b and inner radius a. the volume flow rate in the capillary is Q. if the capillary is removed the liquid comes out with a velocity of v_(0) . The density of the liquid is given as calculate the coefficient of viscosity eta (given pia^(2)=10^(-6)m^(2) and (a^(2))/(l)=2xx10^(-6)m ]

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Knowledge Check

  • The rate of flow of a liquid through a capillary tube is

    A
    directly proportional to the length of tube.
    B
    inversely proportional to the difference of pressure between the ends of the tube.
    C
    directly proportional to the `4^(th)` power of the radius of the tube.
    D
    independent of the nature of the liquid.

  • If a liquid does not wet the material of a capillary tube, then the liquid in it

    A
    rises
    B
    falls
    C
    neither rises nor falls
    D
    starts freezing .

  • The rise of a liquid in a capillary tube is due to:

    A
    osmosis
    B
    surface tension (c) viscosity
    C
    viscosity
    D
    diffusion

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