= Solution
On the translating <circular cylinder> $r=a$, the preceding <velocity potential> and <streamfunction> give
$$
\phi=-Ua\cos\theta,\qquad d\psi=Ua\cos\theta\,d\theta.
$$
Using the <boundary integral for kinetic energy of planar potential flow>,
$$
T=-\frac\rho2\int_0^{2\pi}(-U^2a^2\cos^2\theta)\,d\theta
=\frac{\rho\pi a^2U^2}{2}.
$$
Therefore
$$
\boxed{T=\frac12MU^2,\qquad M=\rho\pi a^2.}
$$
As a direct check, $|\mathbf u|^2=U^2a^4/r^4$, and integration over $r>a$ gives the same result.
The fluid <kinetic energy> has the same dependence on body speed as the <kinetic energy> of an extra mass $M$ carried by the body. Thus $M$ is its <added mass>, here equal to the mass of displaced fluid per unit cylinder length. For a cylinder of physical mass per length $m$, the combined <kinetic energy> is $\tfrac12(m+M)U^2$. Accelerating the body requires accelerating the surrounding <fluid>, producing the inertial reaction $-M\dot U$ along the direction of motion. This is the <added mass of a circular cylinder>.
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