If you are a domain expert in a particular area, then you have a right (and a professional obligation) to use/share your expertise for the benefit of the company you are working for. This is especially true if that is specifically what they hired you to do.
If you know you are right, or something someone else is doing is wrong, because of your training or prior experience, then it it important to communicate it clearly, confidently and concisely. Use a fairly dead-pan/neutral tone of voice - state what you know as a matter of fact and try to avoid sounding 'cocky' or haughty.
It is important to be firm, because if you try to be too 'diplomatic' or somehow downplay your knowledge by being 'gracious', then there is a risk you will come across as uncertain or unconfident, which may be doing a disservice to your expertise and may undermine your position as a subject-matter expert.
It is important to be factual and to try not to state professional opinion as fact. Be clear about what is scientific fact and what is based on your personal former experiences. Also, be prepared to back up your input with references or examples, e.g. "No, that's not how 1D adiabatic flow theory works - I can point you to a good reference text book that explains that" or "No, I don't think that's going to work, because I did a series of lab tests in this previous job that were very similar".
In terms of being 'diplomatic' if you need to correct someone, it might be helpful to have a conversation with them in private, rather than showing them up or embarrassing them in front of a large group. Although, sometimes correcting someone in a large meeting is necessary, if there is a serious conceptual error that is underpinning the whole thing.
Also, be open-minded and listen to other people too. Don't just assume that because you have more prior experience in this area, that you will always be right. No-one ever knows everything about anything. It is quite possible that someone else may come up with some cool new idea or a new way of doing something, that you may not have considered or come across before. It is by sharing your knowledge, but also being willing to take on board other people's suggestions and ideas that you will build a level of respect within your organization.
So, be firm and confident when you know (100%) you are right, but also be honest and open-minded in areas you are less sure about.
You say in your question that many of your coworkers are more senior than you and may have more experience in the company. In that case, the approach I would take is to present your input as a recommendation, clearly and confidently: "Based on my past experience and training, my recommendation is X". It can also be good to put this in writing (perhaps in an e-mail). Then, let them choose what to do with it. If they ignore your advice (and you were right), chances are they will make some mistake, which will become apparent later on, and you will be vindicated. In this way, you can gradually build your reputation in the company and your coworkers should come to appreciate your expertise in that area.
However, if your coworkers are being downright unprofessional, to the point where they are being rude; not letting you speak; or even bullying you, then I would probably discuss that with your Manager.