Pressure measurement Lecture 2 drainage design

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Pressure measurement

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Resultant Force and Centre of Pressure on a submerged plane surface in a liquid

The term ∑𝑧𝛿𝐴 the 1^st Moment of Area of the plane PQ about the free surface
∑𝑧𝛿𝐴 = AZ

where A is the area of the plane and Z is the depth to the centroid, G
This can also be written in terms of distance from point O (Z=𝑥sin𝜃)
∑𝑧𝛿𝐴 = A𝑥sin𝜃

So, resultant force on a plane, R=𝝆𝒈𝑨𝒛 = 𝝆𝒈𝑨𝒙sin𝜽
This resultant force acts at right angles to the plane through the center of pressure, C, at a depth D.
The moment of R about any point will be equal to the sum of the moments of the forces on all the
elements δA of the plane about the same point…..