Question

A circular plate 3m in diameter is submerged in water so that the greatest and least depths below the free surface are 2.0m and 1.0m respectively. Find (i) the total pressure force on one side of the plate and (ii) the position of the centre of pressure.

Answer 1

Explanation:

Given A circular plate 3 m in diameter is submerged in water so that the greatest and least depths below the free surface are 2.0 m and 1.0 m respectively. Find (i) the total pressure force on one side of the plate and (ii) the position of the centre of pressure.

• Given diameter of plate d = 3 m
• Therefore Area A = π d^2 / 4
•                              = π x (3)^2 / 4
•                              = 9 x 3.14 / 4
•                             = 7.065 m^2
• Now distance of centre of gravity from free surface  
• Diameter of C.G from free surface
•         = h bar = CD + GC sin theta  
•                   = 1 + 1 sin theta
• So sin theta = AB/BC = 2 – DC / 3
•                                   = 2 – 1 / 3
•                                  = 0.333
• So h bar =1 + 1 x 0.333
•             = 1.333
• Now total pressure F = ρ g A h bar
•                                 = 1000 x 9.8 x 7.065 x 1.333
•                           F = 92,292.92 N
• Centre of pressure h* = I G sin^2 theta / Ah bar + h bar.
• So I G = π / 64 (d)^4
•          = 3.14 / 64 x (3)^4
•          = 3.974
• Now h* = 3.974 (0.333)^2 / 7.065 x 1.333 + 1.333
•                                         = 1.333 + 0.0467
•                                          = 1.379 m

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https://brainly.in/question/19851460

Answer 2

Answer:

1.379m will be the correct answer hope it helps you