Whenever it shall become necessary for the city to take or damage private property for the purpose of establishing, laying out, extending and widening streets and other public highways and places within the city, or for the purpose of securing rights-of-way for drains, sewers and aqueducts, and for the purpose of widening, straightening or diverting the channels of streams and the improvement of waterfronts, or any other public purpose, and the city council cannot agree with the owner thereof as to the price to be paid, the city council may proceed to acquire, take or damage the same in the manner provided by chapter 8.12 RCW or by chapter 8.20 RCW.