Can one reverse a hash with partial plaintext knowledge?
For an ideal hash function, the fastest way to compute a first or second preimage is through a brute-force attack. That is, if there's no structural weaknesses in the design of the hash function, your best bet is to mount a brute-force attack.

The knowledge of the message size (n bits) and some parts of it (m bits) will certainly reduce the complexity of finding a preimage under the brute force attack: The worst-case complexity will reduce from 2n to 2n-m. 

A space-time trade-off over the brute-force attack is by exploiting rainbow tables. I believe  the partial knowledge of the preimage may prove useful in mounting this attack too.