(c) The pressure at the bottom of each arm is proportional to ρ and the mass of fluid in the horizontal portion of the tube is proportional to ρ, so ρ divides out and the results are independent of the
density of the fluid. The pressure at the bottom of a vertical arm is independent of the cross-sectional area
of the arm. Newton’s second law could be applied to a cross-sectional of fluid smaller than that of the
tubes. Therefore, the results are independent and of the size and shape of all parts of the tube.