# Thrust and Centre of Pressure

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The name "centre of pressure (COP)" indicates representative pressure will act through this point for a vertical plane inside liquid.
If so, then total thrust= vertical area of the plane x pressure at COP.
But this does not match with the books.
All books say, total force (the thrust)= vertical area of the plane X pressure at centroid.
I do not understand this.

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Ray Vickson
Homework Helper
Dearly Missed
The name "centre of pressure (COP)" indicates representative pressure will act through this point for a vertical plane inside liquid.
If so, then total thrust= vertical area of the plane x pressure at COP.
But this does not match with the books.
All books say, total force (the thrust)= vertical area of the plane X pressure at centroid.
I do not understand this.
Please name some of these books.

Chestermiller
Mentor
[Moderator's note: This thread was created by moving posts from another thread, hence no homework template]

The name "centre of pressure (COP)" indicates representative pressure will act through this point for a vertical plane inside liquid.
If so, then total thrust= vertical area of the plane x pressure at COP.
But this does not match with the books.
All books say, total force (the thrust)= vertical area of the plane X pressure at centroid.
I do not understand this.
The force on the vertical plane will indeed be equal to the vertical area times the pressure at the centroid. However, if a force of this magnitude were applied on the opposite side of the plate to try to keep it in equilibrium, the plate would not be in equilibrium; it would rotate. This is because the moment balance on the plate (treated as a rigid body) would not be satisfied. In order to satisfy the moment balance, the force would have to be applied somewhat below the centroid (at 1/3 of the way up). This is because the average pressure on the bottom half of the plate is higher than the average pressure on the top half of the plate.

haruspex