Answer
(Fatwa: 1191/969/D=1431)
It is wajib to perform the tawaf of Hajj and Umrah with wudhu. One dam (slaughtering of an animal) is wajib if it is done without wudhu. You poured water over your whole body before performing tawaf, so it is hoped that the water must have reached to the parts washable in wudhu. So, if nothing happened which invalidates wudhu, you will be considered in the state of wudhu and your tawaf will be complete and dam will not be wajib. However, if the water did not reach to all wudhu parts or after pouring water your wudhu broke, then one dam (slaughtering of one goat or sheep) shall be wajib, which should be slaughtered within the boundary of haram.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband