In the rapidly evolving landscape of education, digital technologies have repeatedly disrupted traditional pedagogical methods. This paper explores the latest of these disruptions: the potential integration of large language models (LLMs) and chatbots into graduate engineering education. We begin by tracing historical and technological disruptions to provide context and then introduce key terms such as machine learning and deep learning and the underlying mechanisms of recent advancements, namely attention/transformer models and graphics processing units. The heart of our investigation lies in the application of an LLM-based chatbot in a graduate fluid mechanics course. We developed a question bank from the course material and assessed the chatbot's ability to provide accurate, insightful responses. The results are encouraging, demonstrating not only the bot's ability to effectively answer complex questions but also the potential advantages of chatbot usage in the classroom, such as the promotion of self-paced learning, the provision of instantaneous feedback, and the reduction of instructors' workload. The study also examines the transformative effect of intelligent prompting on enhancing the chatbot's performance. Furthermore, we demonstrate how powerful plugins like Wolfram Alpha for mathematical problem-solving and code interpretation can significantly extend the chatbot's capabilities, transforming it into a comprehensive educational tool. While acknowledging the challenges and ethical implications surrounding the use of such AI models in education, we advocate for a balanced approach. The use of LLMs and chatbots in graduate education can be greatly beneficial but requires ongoing evaluation and adaptation to ensure ethical and efficient use.