What risks does using a predictable IV bring?

Background: I am interested in writing an encrypting swap driver for
Linux using a fast cipher in CBC mode keyed from /dev/random at boot
time.

I considered using a hash of the block number of the swap partition
and some extra bytes pulled from /dev/random as the IV, but this may
be overkill. 

Would the system be weakened if I was to use just the block number?

Regards,
Damien Miller

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