A liquid of density `900(kg)/(m^(3))` is filled in a cylindrical tank of upper radius 0.9 m and lower radius 0.3 m A capillary tube of length 1 is attached at the bottom of the tank as shown in fig. 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 liquid is `8xx10^(-6)(m^(3))/(s)` and if capillary tube is detached, the liquid comes out from the tank with a velocity `10(m)/(s)`. then the coefficient viscosity of liquid is `(pia^(2)=10^(-6)m^(2)a^(2))/(l=2xx10^(-6)m)`.

Options

A. `eta=1.25xx10^(-3)N-(s)/(m^(2)`
B. `eta=2.50xx10^(-3)N-(s)/(m^(2)`
C. `eta=5.00xx10^(-3)N-(s)/(m^(2)`
D. `eta=7.25xx10^(-3)N-(s)/(m^(2)`

Answer

A

Explanation

Applying bemoullie's equation
`P+rhogh=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))`, but `v_(1)=((A_(2)v_(2))/(A_(1)))`
`DeltaP=P+rhogh,because(dV)/(dt)=(pia^(4)DeltaP)/(8etal)`