Repeat problem 7 accounting for the friction loss from the vessel to the tube, assuming a loss coefficient of 0.50 at the contraction.

problem 7,

You are given a liquid and are asked to find its viscosity. Its density is known to be $0.97 \mathrm{~g} / \mathrm{cm}^{3}$. You place the fluid in an open vessel to which a $20 \mathrm{~cm}$ long vertical tube with an inside diameter of $2 \mathrm{~mm}$ is attached to the bottom (see Figure P6.6). When the depth of the liquid in the container is $6 \mathrm{~cm}$, you find that it drains out through the tube at a rate of $2.5 \mathrm{~cm}^{3} / \mathrm{s}$. If the diameter of the open vessel is much larger than that of the tube and friction loss from the vessel to the tube is negligible, what is the fluid viscosity?