Emergency shower for nitric acid spills
If you spill nitric acid onto the table, you yourself are unharmed and you can use a cool head to decide what to do next. If the spill is small, pour water on it to both dilute it and dilute the heat — remember water has a high specific heat capacity. If the spill is larger, I would probably try adding sodium hydrogencarbonate to react away the acid before wiping it up. Adding larger amounts of water will work, too, but you need to get them from somewhere and then need to get rid of the resulting puddle.

If the spill is on you you want to get the acid off your clothes and body immediately. The quickest and most effective solution is to pour water over your head and lots of it. This is what the emergency showers are for. Lots, here, has two functions: it not only quickly dilutes the acid to a less harmful concentration but also (because it is washing down) serves well to actually remove the heat — remember again that water has a high specific heat capacity. Emergency showers have a high throughput for exactly this reason.