The water management engineer shall have charge of the construction of the plan of water management. He shall make monthly estimates of the amount of work done and shall furnish one copy to the contractor and file the other with the secretary of the board of commissioners, and the commissioners shall within five days after the filing of such estimates meet and direct the secretary to draw a warrant in favor of such contractor for not more than 90 percent of the work done according to the specifications and contract; and, upon the presentation of such warrant, properly signed by the president and secretary, to the treasurer of the district, he shall pay the amount due thereon. When the work is fully completed and accepted by the water management engineer, he shall make an estimate for the whole amount due, including the amounts withheld on previous monthly estimates, which shall be paid from the water management fund as provided in this section. In case the water management district installs the works of improvement with the assistance of some organization or agency, engineering services may be furnished by the cooperating organization or agency as set out above, with any additional duties being performed as required due to the two groups working together.