Motion of Metal Rods in Viscous Medium · IZhO 2018 #1
Physics · fluid-mechanics
Problem
Experimental Setup: Use a glass tube (inner diameter D=4.6 mm) filled with liquid gel, mounted vertically with open end pointing upward. Metal rods of various diameters (2.5, 3.0, 3.5, 4.0 mm) and length 4 cm are available.
Part 1. Metal
1. Prove experimentally that the motion of the rod inside the tube is uniform. Use only metal rod of diameter of 4.0 mm in this case. Determine the velocity of the rod sinking in the gel as accurately as possible. Calculate the error of the velocity measured.
2. Measure the dependence of the velocity of the rods (with the same length) on their diameters. Plot a graph of the obtained dependence.
3. Theoretically, we can show that the velocity V of the rod depends on the thickness h of the gap between the tube walls and the lateral surface of the rod (if the gap is small compared to the radius of the tube) according to the law
V=Chγ (1)
where C is a constant.
Using your experimental data, check whether this dependence holds.
4. Determine the power index γ in formula (1) which most accurately fits the experimental data. Make error estimation of the obtained value of this power index γ.
5. Give a brief theoretical justification for the result obtained in Question 4.