I've been in that situation and it's stayed with me for 20 years:
Was working as a design engineer in a nuclear environment when I was asked by my boss what the clearance from a robotised brush-head was from the top of a spent fissile material container at a certain point in a decontamination procedure. I tried to fluff my way out of the question by saying 'er, it's around about 2mm at that point'. ofc i didn't know exactly, but with that he said at the top of his voice and in front of about 30 other engineers in a big open plan office 'We don't do 'aroundabout' 'ere lad! This is nuclear engineering, we deal in micron tolerances, not 'aroundabout!'
OMG, the shame of it. I wish the ground would have opened up and swallowed me. And of course colleagues took advantage for months later: 'I'll have a coffee please Chris, with aroundabout 2 sugars, ta'. :lol: Bastids. haha.
Lesson learned. If you don't know the answer, don't make it up.
:roll: