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That's a good question, and an important one. But how often to change the water depends on several factors and the circumstances of each household. We, the owners of the Petwant Water Fountain, have a short-haired orange tabby who (sometimes) responds to the name Jago. He has an 11-cup fountain and uses it a lot. We rarely need to top it up, we clean the fountain and do a complete water change once a week. But if we had another cat, the watering, cleaning and water changes would be more frequent.
We've had clients with two, five or even eighteen cats. They absolutely and very definitely need to change the water in the cat waterer more often. Or, they need multiple cat fountains, and the frequency of each fountain can be greatly reduced.
So while there is no formula that we know of based on cat count and water volume, we have found that there are reliable visual clues. When the water level is near the top of the pump and you start hearing the pump, you've run it a little out and need to top it up. If you start to hear the pump despite a lot of water in the fountain, it's time to clean the pump, and it's also a good time to clean the bowl.
If you start to see foam or white bubbles on the surface of the water, it's about a day or two past the best time to clean the fountain and change the water. This is usually consistent, so if you changed the water six days ago and you see white foam or bubbles that are not just a result of the water being oxidized and not dissipating, changing the water every four or five days would be a solid determination . The foam or white bubbles come from organic matter dissolved in the water - cat food, saliva, etc. Chances are your cat will continue to use this to drink from the fountain, but he doesn't want to. No doubt the water had no smell and tasted as fresh as he'd like, but it wasn't harmful at this stage. So while how often you need to change the water in your pet fountain varies widely, you can learn the signs and act accordingly.
Top up the pump when the water level starts to drop to about a half inch from the top of the pump. Clean the fountain every 3 to 4 days for multiple cats and every 5 to 6 days for a single cat. Allows for the number of cats you have to count and whether they are long-haired or short-haired. Long-haired cats generally require more frequent cleanings.