The Traffic Engineer for the city with consent of the City Council by resolution shall designate such unmetered parking zones in the city where it is determined that such zones shall be necessary to aid in the regulations, control and inspection of parking vehicles. The unmetered parking zones shall be identified by the appropriate parking sign giving notice of the time limits in said parking zone. Parking in excess of the time provided in said unmetered parking zones shall be an offense under this chapter and shall carry with it a penalty which shall be established by resolution of the City Council.
(`73 Code, 20.205, § 5)