Two large tanks are separated by a wall 20 cm thick, as shown in the figure below. One tank is filled with oil with ρoil = 876 kg/m3 and μoil = 0.45 Ns/m2. The other is filled with water with ρwater = 998 kg/m3 and μwater = 0.00100 Ns/m2. The depths of fluid in the two tanks are respectively 5 metres and 4 metres. A 90 cm diameter hole is drilled in the wall that separates the two tanks at a height of 3 metres above the bottom. An aluminum (ρaluminum = 2750 kg/m3) rod 90 cm in diameter and 80 cm long is placed in the hole, with equal amounts of the rod overhanging into the two tanks. There is no fluid between the aluminum rod and the wall (i.e. a perfect seal).
Find the force and moment (about the centre of the rod) that the wall exerts on the aluminum rod to ensure that the rod remains stationary
F = PA = [tex]\rho[/tex]ghA
The Attempt at a Solution
I started the problem by drawing a free body diagram of the pipe, I attached a picture.
F Roil and F Rwater are the resultant hydrostatic forces applied at the center of pressure by the liquid in the x direction. F Ry oil and F Rywater are the resultant hydrostatic forces applied at the center of pressure in the y direction. W is the weight of the rod in each liquid and Fb is the buoyant force.
After drawing a FBD I did a sum of forces about the x and y axis. Then I did a moment balance about point O, the red dot on the FBD picture. I haven't actually crunched out the numbers yet but based on my reasoning the wall wouldn't apply any force on the rod since it would be the forces and moments applied by the liquids on each side that would balance in order to keep the rod stationary. I have a feeling this isnt right though. Any help would be great.
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