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Liquid pressure and thrust. Centres of pressure 267
Fig. 30.1
Resultant thrust on the whole area are
wg Z1dA

Z1 dA ZEAE
but and
It should be noted that this formula gives only the magnitude of the resultant thrust. It does not indicate the point at which the resultant thrust may be considered to act.
The centre of pressure
The centre of pressure is the point at which the resultant thrust on an immersed surface may be considered to act. Its position may be found as follows:
(i) For a rectangular lamina immersed with one side in the surface of the liquid.
In Figure 30.2, each particle of the strip GH is approximately at the same depth and therefore, the pressure intensity is nearly the same on each particle. Hence the resultant thrust on each strip will act at its mid-point. The resultant of the thrusts on all of the strips in the lamina will act at a point on EF.
w g Z1dA w gEZEAE
; Resultant thrust Density g Depth of centroid Area

w g Z1 dA