"consistent purpose" is correct and can be used in written English.
You can use it to refer to an unchanging goal or intention. For example, "He maintained a consistent purpose throughout the project, despite the challenges he faced."
Venice, he writes, was a "joint-stock company" run by unromantic opportunists for a "frighteningly consistent" purpose: the ruthless pursuit of material gain.
Mr. Davis, who is also a painter, approaches the medium with large and consistent purpose as well as skill, exploiting its intimacy and diaristic potential in a narrative that is both self-revealing and archetypal.
But that phenomenon is at most an indirect result of the council rather than something the council pursued with consistent purpose.
We do not employ the MacPherson definition of racist incidents, when it comes to antisemitism, because we believe it to be too subjective for consistent analytical purposes.
They were also, for each discussion thread, asked to provide feedback in a manner consistent with this purpose; for example, to provide their "impression of the design," what they perceive to be "good / bad" in the design, or to "suggest changes".
According to the ICO's CCTV code of practice, the disclosure of footage must be "consistent with the purpose(s) for which the system was established".
From our analysis to date it appears that the aluminum tubes would be consistent with the purpose stated by Iraq and, unless modified, would not be suitable for manufacturing centrifuges; however, we are still investigating this issue.
In return, the university promised to spend future income generated by the endowment in ways "consistent with the purpose of the chair".
