How large is Waterdeep?

I’m going to be running Waterdeep: Dragon Heist for my group soon. As part of this I would like to work out how long it would take characters to travel around the city on foot, both from top to bottom, and from side to side. In order to do this I need to figure out the scale of the city.

There is a wonderful map provided with the adventure, however it has no scale attached to it, or at least none I can find!

Is there official material which details the size of Waterdeep in geographic terms?