Per the screenshot in latter: 1571 page views per hour. That's 26 page views a minute, which is "a few dozen".

The screenshot is from the point the email was sent, not the point where the site went down.

We sometimes call his "the HN kiss of death", and we do this a lot to smaller visibility websites that never anticipate a few hundred/thousand hits within a couple of hours.

I usually go through the comments, then drop these URIs on my calendar and check them a couple of days later. By then the discussions have matured and the site is up and running (perhaps even the posts have been correct/enhanced with the HN comments).

18.000 visitors per day is 1 visitor every 5 seconds.

When you post stuff on HN, the visitors don't usually come in an orderly queue at the same rate for 24 hours. There is most likely a spike where most of the visitors open the site within a couple of hours, and then click around the other parts of the site. It can get pretty taxing pretty fast if you are serving for example images, and each page view triggers database queries.