Any applicant for a permit to construct, develop, install, or modify a private water system required by rules adopted by the director of health under section 3701.347 of the Revised Code may apply to the board of health of the city or general health district administering and enforcing the private water supply program in the health district in which the private water system is or is to be located or, if the health district is not administering and enforcing the program, may apply to the department of health for a variance from such rules governing the design, construction, development, installation, or modification of private water systems. The application for a variance shall be made in writing and shall include a statement of the particular rule or rules from which a variance is sought, a description of the proposed system or modification, and the necessity for the variance. The board of health or the department of health shall not grant a variance unless the applicant demonstrates that:

(A) There will be an unusual and unnecessary hardship in complying with the rules from which the variance is sought;

(B) Contamination of the private water system will not occur as a result of construction and operation of the system as proposed by the variance application;

(C) The health of persons using water from the private water system will not be endangered as a result of construction and operation of the system as proposed by the variance application; and

(D) No other technically feasible and economically reasonable means exist for obtaining water from the proposed type of water source.