No, Viagra isn't water-soluble and won't dissolve well in water. In fact, it's possible that breaking up the pill and trying to dissolve it might actually make it less effective. However, it is recommended that you take Viagra with water since it can help the pill move through your digestive system easier.
Indigestion or an upset stomach can be a side effect of Viagra and some people have found that taking Viagra with a glass of water reduced the chances of digestive issues.
If you have trouble swallowing Viagra, consider investing in a pill splitter that can cleanly divide your pills in half without the risk of shattering the pill or creating excessive dust after the break. Pill splitters are also much safer than trying to do it yourself with a sharp knife.