Without the accompanying neither, it can be difficult to know whether or not to use nor.
Is this correct, or should or be used here instead?
We do not have the equipment needed to measure buoyancy nor air volume.
- We do not have the equipment needed to measure buoyancy nor/or air volume.
Either "nor" or "or" can be used.
It is up to the style you wish to follow as to which one might be preferable.
Your example is somewhat similar to the examples in CGEL, page 1309:
Nor appears as a coordinator paired correlatively with neither ([50.i]), or non-correlatively as a variant of or in negative contexts ([50.ii]):
i.a-b . . .
ii.a The change won't be as abrupt as in 1958 nor as severe as in 1959.
ii.b No state shall have a share less than 50% nor more than 70%.
ii.c Serious art is not for the lazy, nor for the untrained.
In [ii] nor could be replaced by or, which is much more common: the version with nor perhaps gives added emphasis to the negation. . . . The difference is that in [i] all the coordinates are marked as negative, whereas in the non-correlative [ii] the first coordinate (as abrupt as in 1958, etc.) is not marked as negative within the coordination itself, but falls within the scope of a preceding negative.
Your example is similar to those in [50.ii] in that your first coordinate ("buoyancy") falls within the scope of the negative "not".
Note that CGEL is the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language.
'Nor' is accepted but uncommon, 'or' is generally used.
Usage Note: When using neither in a balanced construction that negates two parts of a sentence, nor (not or) must be used in the second clause: She is neither able nor (not or) willing to go.
Similarly, when negating the second of two negative independent clauses, nor (not or) must be used: He cannot find anyone now, nor does he expect to find anyone in the future; Jane will never compromise with Bill, nor will Bill compromise with Jane.
However, when a verb is negated by not or never, and is followed by a verb phrase that is also to be negated (but not an entire clause), either or or nor can be used: He will not permit the change, or (or nor) even consider it. In noun phrases of the type no this or that, or is actually more common than nor: He has no experience or interest (less frequently nor interest) in chemistry. Or is also more common than nor when such a noun phrase, adjective phrase, or adverb phrase is introduced by not: He is not a philosopher or a statesman. They were not rich or happy.
Source: Collins Dictionary.
No, you wouldn't use nor in this way, it's kind of a double-negative. It could be:
We have the equipment needed to measure neither buoyancy nor air volume.
I find this stilted, however, and some would prefer:
We do not have the equipment needed to measure either buoyancy or air volume.
However, what you're REALLY trying to say is:
We have neither the equipment needed to measure buoyancy nor the equipment needed to measure air volume.
This can be shortened by having the repetitive sections be assumed:
We have neither the equipment needed to measure buoyancy nor (the equipment needed to measure) air volume.
So it becomes:
We have neither the equipment needed to measure buoyancy nor air volume.
State the whole sentence more actively:
'We don't have the equipment needed to measure buoyancy and air volume.'
The only thing wrong with the sentence is verb placement. It is this that makes the use of 'nor' or 'or' superfluous and creates the problem.