A liquid of density 900 ` kg//m^3 ` is filled in a cylindrical tank open from top of upper radius 0.9 m and lower radius 0.3 m. A capillary tube of length l is attached at the bottom of the tank as shown in the figure. The capillary has outer radius 0.002 m and inner radius a.
When pressure p is applied at the top of the tank volume flow rate of the liquid is ` 8 xx 10 ^(-6 ) m^3// s ` and if capillary tube is detached, the liquid comes out from the tank with a velocity 10 m/s
[Given : ` pi a ^2 = 10 ^(-6) m^ 2 and a ^ 2//1 = 2 xx 10 ^(-6) m ]`
Determine the coefficient of viscosity in SI units when the capillary tube is attached :

Options

A. ` (1)/(720) `
B. ` (1)/(360)`
C. `(1)/(180)`
D. `(1)/(90)`

Answer

A

Explanation

By Poiseuille’s equation, the rate of flow of liquid in the capillary tube ` Q = (pi (Delta p ) a ^4 )/(8 eta 1 ) `
` therefore 8 xx 10 ^(-6) = ((pi a ^ 2 ) (Delta p ) )/(8 eta ) ((a^ 2 )/(1)) " " therefore eta = ((pi a ^ 2) (Delta p) ((a^ 2)/(1)))/(8 xx 8 xx 10 ^(-6) ) `
Substituting the values, we have ` eta = ((10^(-6))((4)/(9) xx 10 ^(5)) (2 xx 10 ^(-6)))/( 8 xx 8 xx 10 ^(-6) ) = (1)/(720) N - s //m^2 `