In general, when calculating caloric requirements for animals, we can apply what's known as Kleiber's law. Kleiber's law states that the food requirements of various animals scale by the mass of the animal to the $\frac{3}{4}$ power. This value is then multiplied by a constant that's dependent on the type of animal.
To compute a dragon the size of Smaug's caloric intake, then, we can start by computing his weight. According to this source, Smaug was around 60 meters long. A tyrannosaurus rex, by comparison, is a little over 12 meters long. Smaug had a long tail, though. (About 2/3rds of his length is tail), while t-rexes look to only be about half tail. If we compute weight based on body length, we'd then have Smaug's 20 meter body compared to about 6 meters for our t-rex. If we assume weight scales with the cube of body length, we can then figure Smaug's weight to be around $\frac{20}{6}^3 = 37$ times the weight of a t-rex. The more bird-like assumptions about dinosaurs put the weight of a t-rex at about 4.5 tonnes. Since Smaug flies, we can assume that his weight is probably similarly proportioned to his mass, perhaps a bit less. Since 37*9 is 166.5, we'll round down to a respectable 150 tonnes for Smaug. This is comparable to the weight of a blue whale (190 tonnes), which, while only about half as long as our dragon, is significantly more densely built.
Now let's apply Kleiber's law. First, let's get some base data on how much animals eat
- A 290 gram barn owl needs the eat about 72.9g of small mammals per day. (About 120 kCal)
- A 20kg crocodile needs to eat about 2kg of meat per week. (About 470 kCal/day)
These numbers give us estimates for about how much reptiles that are fairly stationary (our dragons sleep a lot) and flying birds (dragons fly around to catch food) need to eat. We can scale these numbers up to get some estimates on how much our dragons need to eat per day. The data I found is specified per day (or per week) rather than per hour, but we can extrapolate based on the activities of our sample animals what sort of activities these things correspond to.
Bird-like dragons
Our dragons weigh as much as around 500,000 owls. Based on Kleiber's law, they should then eat about 20,000 times as much food, for a total of 2.3 million Calories/day. Smaug ate ponies in the lord of the rings, so we can say that this is about 8 ponies worth of meat, for comparison. This activity level corresponds to a bird that hunts quite a bit, so this is probably a fair estimate for the activity level of a dragon while scouting or hunting.
Reptile-like dragons
If their caloric requirements are closer to those of crocodiles, they'll need a bit less. A dragon weighs 7500 times more than a 20kg croc, and so should need about 806 times the food as one. This comes out to a mere 380,000 Calories per day, or a bit more than one pony per day. This is more like a dragon that's sitting around snoozing on some gold or schmoozing with other dragons and the odd invisible hobbit.
Final estimate
In summary, if our dragons eat about as much as owls (relative to weight) while they hunt, but only hunt once a week and snooze like crocs the rest of the time, they'll need an average of around 655000 Calories per day. That's about two ponies per day, so once a week a dragon will need to go out and eat a small herd of them before going back to snooze on its pile of gold.