The behaviour of wet agglomerates in which the particles are joined by discrete pendular bridges depends not only on the forces developed at the contact points, but also on the rupture energy of each bridge. While the rupture energy may be computed exactly by employing the Laplace-Young equation, this involves lengthy numerical integration procedures. An alternative approach is adopted here in order to obtain a closed-form approximate solution which greatly simplifies engineering calculations. As in previous studies, the shape of the bridge is approximated as a toroid. In order to simplify the rupture energy calculation, the bridge half-filling angle is taken as independent of surface separation, with a value corresponding to that at the rupture distance. The effect of this simplification is examined for the case of two equi-sized particles with zero contact angle, and it is shown that the solution underestimates the exact values by less than 14%.