  The correlation between the mean transverse momentum of outgoing particles,
$\langle p_t \rangle$, and the magnitude of anisotropic flow, $v_n$, has
recently been measured in Pb+Pb collisions at the CERN Large Hadron Collider,
as a function of the collision centrality. We confirm the previous observation
that event-by-event hydrodynamics predicts a correlation between $v_n$ and
$\langle p_t \rangle$ that is similar to that measured in data. We show that
the magnitude of this correlation can be directly predicted from the initial
condition of the hydrodynamic calculation, for $n=2,3$, if one replaces $v_n$
by the corresponding initial-state anisotropy, $\varepsilon_n$, and $\langle
p_t\rangle$ by the total energy per unit rapidity of the fluid at the beginning
of the hydrodynamic expansion.
