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.

Shown in the figure is a container whose top and botoom diameters are

1.	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.
Answer» Solution :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`