Q 6 A circular plate 2.5m diameter is immersed in water, its greatest and least depth below the free surface being 3m and 1m respectively. Find (i) The total pressure on one face of the plate and(ii) Position of centre of pressure (Dec 2013, July 2015) Ans: d = 2.5m, 2     Sin 1 2.5   53.13    1  1  2m h 2.52 4.909m2 A   d     2 4 4  2.54 1.917m4     IG 64 64 d  4 F = = 9.81×4.909×2 = 96.31 kN wA h Q 7 Prove that for a plate submerged in horizontal position in water the center of pressure is same as centroid of the plate. (July 2013, July 2015) Ans: Consider a plane horizontal surface Water immersed in a static fluid. As every point of the horizontal surface is at the same depth from the free surface of the liquid, the pressure intensity will be P Horizontal equal to p = g h, where is the  h ‘h Plane depth of surface (Refer Fig.). Surface Let be the Elemental area and ‘dA’ ‘A’ be the surface area c.p Area ‘A’ Then total force dP = p × dA  gAh P Fig. Total Pressure on a Horizontal Plane Surface The centre of pressure I Sin 2 For Horizontal surface  0 , substituting in Eq.(1)   h Eq.(1) hcp Ah
Q 6 A circular plate 2.5m diameter is immersed in water, its greatest and least depth below the free surface being 3m and 1m respectively. Find (i) The total pressure on one face of the plate and(ii) Position of centre of pressure (Dec 2013, July 2015) Ans: d = 2.5m,   Sin 1  2   2.5    53.13 h  1  1  2m A   d 2    2.52  4.909m2 4  IG  64 4 d 4    2.54  1.917m4 64 F = wA h = 9.81×4.909×2 = 96.31 kN Q 7 Prove that for a plate submerged in horizontal position in water the center of pressure is same as centroid of the plate. (July 2013, July 2015) Ans: Consider a plane horizontal surface immersed in a static fluid. As every point of the horizontal surface is at the Water same depth from the free surface of the liquid, the pressure intensity will be P equal to p =  g h, where ‘h is the h depth of surface (Refer Fig.). Horizontal Plane Surface Let ‘dA’ be the Elemental area and ‘A’ be the surface area Then total force dP = p × dA c.p Area ‘A’ P  gAh The centre of pressure Fig. Total Pressure on a Horizontal Plane Surface I Sin 2 hcp  h  Eq.(1) For Horizontal surface  0 , substituting in Eq.(1) Ah
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