Upon final determination of the location, nature and size of the proposed project, the governing body of the city shall by resolution direct the city engineer, or some other competent engineer, to prepare detailed plans of the contemplated project and a final cost estimate which shall include the advertising, appraising, engineering, printing and such other expenses as in the judgment of the engineer is necessary or essential to the completion of the project and the payment of the cost thereof. The plans and estimates shall be filed with the clerk of the city upon their completion.