A closed form expression for the exact distribution of the Mann-Whitney-Wilcoxon $U$ test has been derived. From this, expressions for the exact power of the $U$ test for exponential and rectangular alternatives have been derived. Several determinations of the power of combined sample sizes of 11, 15 and 21 have been compared with the corresponding determinations of the power of Mood's median test procedure. Also, the asymptotic efficiency of the $U$ test relative to Mood's median test for exponential and rectangular translation alternatives is considered.
George E. Haynam. Zakkula Govindarajulu. "Exact Power of Mann-Whitney Test for Exponential and Rectangular Alternatives." Ann. Math. Statist. 37 (4) 945 - 953, August, 1966. https://doi.org/10.1214/aoms/1177699375