How to judge length of exams when teaching undergraduate engineering I am a first-time lecturer for an American university (am a PhD student), and am giving midterm and final exams in the course, which comprises an introduction to engineering and how to work with systems in a methodological way. 

I am designing the midterm exam for the course, and the students have an allotted 50 minutes to complete it. Most of the questions are brief short-answer questions (around 2-3 sentences for an answer is sufficient), followed by some multiple choice and fill-in-the-blank questions.

I took the midterm by myself and timed the length of completion, which was around 12 minutes for me. From other professors that I have taken classes from, this seems to be the standard (i.e., if the professor can complete the exam in 1/4 of the allotted time, then it is an appropriate length).

Does this seem reasonable? I'd like to hear some related experiences from other instructors.
The "1/4" rule of thumb is reasonable in a lot of cases, but it can be unreasonable for particular groups of students.  In a very low level course (like yours) it may take students much more than 4 times as long as you to do the test.  In an upper level course the students might be able to do the test in something less than 4 times as long you take.  

As an example, my rule of thumb for lower level undergraduate math courses (calculus, intro to linear algebra, and differential equations) is 1/8 rather than 1/4.  I've been teaching mathematics for almost 30 years, so solving these kinds of problems is second nature, and I'm mostly limited by the speed of my handwriting in producing a set of solutions.  It also helps that unlike my students, I can do arithmetic and algebra in my head without having to pull out a calculator.  

I would suggest that you discuss the exam with a professor or TA who has previously taught the course and see whether they think it might be too long.