Question 3.P.24: Determine the vertical and horizontal forces on the cylinder......
Determine the vertical and horizontal forces on the cylinder shown in Fig. P. 3.24. The cylinder is in equilibrium.
The horizontal force can be calculated as the sum of forces due to the oil and due to the water on projected area. Consider 1 m length.
The horizontal force on AB and BC are equal and opposite.
The other horizontal force due to oil on CD is
= 9810 × 0.91 × (1.25/ 2) × 1.25 × 1
= 6974.3 N and this force acts at
[(1.25/2) + 1 × 1 × 1.25³ × 2/12 × 1.25 × 1.25 × 1) = 0.833 m from the top surface
The vertical upward force equals the weight of water displaced + weight of oil displaced (AEDG + CDG)
= [9810 × (π × 1.25²/2)] + [(1.25 × 1.25) + π × 1.25²/4) × 0.91 × 9810]
= (24077 + 24904) N
Total upward force = 48981 N
Workout the resultant as an exercise.