When two or more persons, joint owners in an irrigation ditch or reservoir, not incorporated, or their lessees, are unable to agree relative to the division or distribution of water received through their ditch or from their reservoir, and where there is no disagreement as to the ownership of said water, it shall be lawful for any such owner or owners, his or her or their lessee or lessees, or either of them, to apply to the department, in writing, setting forth such fact and giving such information as shall enable the department to estimate the probable expense of such service, asking the department to appoint some suitable person to take charge of such ditch or reservoir for the purpose of making a just division or distribution of the water from the same to the parties entitled to the use thereof. The department shall upon the receipt of such application notify the applicant of the probable expense of such division and upon receipt of certified check for said amount, the department shall appoint a suitable person to make such division. The person so appointed shall take exclusive charge of such ditch or reservoir for the purpose of dividing the water therefrom in accordance with the established rights of the diverters therefrom, and continue the said work until the necessity therefor shall cease to exist. The expense of such investigation and division shall be a charge upon all of the co-owners and the person advancing the payment to the department shall be entitled to recover in any court of competent jurisdiction from his or her co-owners their proportionate share of the expense.