Is it unethical to hire students for private consulting work?
I'm at a University at the moment where this sort of thing is quite common - and indeed, my previous institution had another department where a relationship like this one actually led to a major company that hires a large number of graduates. It isn't inherently unethical, but you need to make sure that business interests and academic ones are kept separate. It might, for example, be wise to have an uninvolved faculty member serving as co-supervisor. My institution's stance:

Protecting the Interests of Students and Trainees:
The impact of a perceived or actual conflict of interest or commitment of faculty members on their students (including post-doctoral fellows and other trainees) is of special concern to the university.  In particular, the university is  committed to maintaining the content and quality of the educational experience for students whose research is sponsored by a for-profit business and whose faculty advisors have a financial interest or a  management role in that business.  The concern is even greater if the dissertation work could potentially affect the value of a company in which the faculty member has an ownership or managerial interest.
For example, a faculty member who pressures a student to complete work related to the faculty member’s company could easily affect the student’s completion of graduate studies in a timely and appropriate way, thereby putting the faculty member’s interest in obtaining proprietary results ahead of the student’s academic or scholarly research activities.   The concern is similar for the involvement of students in faculty consulting or other external activities.  The risks and benefits of such involvement must be carefully weighed by departmental administrators responsible for evaluating the disclosure and approving the request, particularly where the involvement may be longer term and/or more time consuming.
University policy recognizes that the involvement of students in faculty-owned or managed businesses or consulting may yield substantial benefit to the student, provided that certain conditions are met.
Faculty members must disclose the proposed involvement of students in their external activities or in company-sponsored research.
Faculty members who intend to serve as PI or co-PI on sponsored projects and have graduate students or trainees conduct a portion of the research under their supervision must develop a conflict of interest management plan to address protections for these early career scholars.  See Example 2 under Managing Conflicts of Interest for appropriate strategies.
Students and postdoctoral trainees have the right to be fully informed about the source of their funding, the nature of the faculty member’s personal interest or involvement, and, if relevant, any agreements concerning data collection, copyright, or patent protection arising from the research.  Departmental and college-level administrators review the risks and protections with the student using the Research Agreement for Students and Postdoctoral Associates.