Is the curve a spiral? And what spiral?

[dodonaomik]

Homework Statement

The problem: the distribution of pressure of the left side of the circular cylinder

Homework Equations

ρ= the density of water
γ=ρg
P=ρgh
circle O = a long wooden circular cylinder

The Attempt at a Solution

MY QUESTION:
Please see the curve indicated by the green/purple circle in the above picture.
Is the curve a spiral? And what spiral?
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[dodonaomik]

A sketch map

 

[dodonaomik]

I was ever sure the curve isn't an Archimedean spiral by calculation and verification.
Please see the following 2 figures.
(Of course, I may be wrong!)