Is 1 hour of shisha as harmful as smoking 100 cigarettes?
There are studies supporting the idea that this is probably close to the right order of magnitude.
The US Centers for Disease Control and Prevention claim
The amount of smoke inhaled during a typical hookah session is about 90,000 milliliters (ml), compared with 500–600 ml inhaled when smoking a cigarette.
based on Cobb CO, Ward KD, Maziak W, Shihadeh AL, Eissenberg T. Waterpipe Tobacco Smoking: An Emerging Health Crisis in the United States. American Journal of Health Behavior 2010;34(3):275–85
90,000 / 550 is 163 cigarettes.
The CDC document mentions several health risks arising from the way that the Shisha heats the tobacco and states that the smoke contains high levels of toxins after passing through the water. However I didn't see any quantitative comparison in the CDC document of toxicity of the smoke compared to cigarettes.
However the referenced study contains this statement
these data suggest that, relative to a single cigarette (about 500 ml of smoke, see Table 1), a single waterpipe use episode (about 90,000 ml of smoke, see Table 1) is associated with 1.7 times the nicotine, 8.4 times the CO, and 36.0 times the tar. Although extrapolating this type of smoke content analysis to actual cigarette or waterpipe smokers has important limitations (see 23,49), these data suggest that waterpipe tobacco smoking is likely associated with substantial toxicant exposure.
This suggests the harm might, at worst, be equivalent to smoking 36 cigarettes - if tar is the major cause of harm and if harm is linearly proportional to exposure.
Volumes of smoke
Cobb et al says:
As seen in Table 1, data collected from actual waterpipe tobacco smokers in natural settings show that a waterpipe use episode typically involves almost 200 puffs, with an average puff volume exceeding 500 ml.22,24 Thus, compared to a cigarette, which involves inhalation of approximately 500–600 ml of smoke (ie, 10–13 puffs of about 50 ml, on average
Breland AB, Kleykamp BA, Eissenberg T. Clinical laboratory evaluation of potential reduced exposure products for smokers. Nicotine Tob Res. 2006;8(6):727–738. [PubMed]
Djordjevic MV, Stellman SD, Zang E. Doses of nicotine and lung carcinogens delivered to cigarette smokers. J Natl Cancer Inst. 2000;92(2):106–111. [PubMed]
There is an FTC machine smoking protocol (for e.g. measuring toxins delivered to a smoker from smoking a cigarette). This specifies 35ml 2-second puffs once a minute until 23mm butt length remains.
Djordjevic et al performed measurements with pressure transducers on 133 smokers and found puffs of around 46ml at around 20 second intervals.
A 2009 study: Waterpipe tobacco and cigarette smoking: direct comparison of toxicant exposure.
Mean total puff volume was 48.6 L for waterpipe use as compared to 1.0 L for cigarette smoking (p<0.001).
These numbers seem broadly consistent with a total volume of 500ml of smoke inhaled per cigarette.