A variation in the yard requirement in any district so as to relieve unnecessary hardships and exceptional practical difficulties in cases when and where by reason of exceptional narrowness, shallowness, or other unusual characteristic of size or shape of a specific piece of property, at the time of the enactment of such regulation or restriction, or by reason of exceptional topographical conditions or other extraordinary situation or condition of such piece of property, or by reason of the use or development of property, immediately adjacent thereto, the strict application of each regulation or restriction would result in unnecessary hardship and exceptional practical difficulties upon the owner of such property. Such granting of variance shall comply, as nearly as possible, in every respect with the spirit, intent, and purpose of this chapter; it being the purpose of this provision to authorize the granting of variation only for reasons of demonstrable and unnecessary hardship and exceptional practical difficulties as distinguished from variations sought by applicants for purposes or reasons of convenience, profit, or caprice.