# 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.

## Answers and Replies

Ray Vickson
Science Advisor
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
Science Advisor
Homework Helper
Gold Member
2020 Award
The name "centre of pressure (COP)" indicates representative pressure will act through this point
Not representative pressure, no.
As Chestermiller posts, a "representative" force acts at the centre of pressure, in the sense that if you were to insert a rigid plate in that vertical plane and apply the right force at that point then equilibrium would be achieved against the forces on the other side of the plate.
If by "representative pressure" you mean total force divided by area then that equals the pressure to be found at the centroid.