l am looking for a snorkel, preferably cheap if possible, that does not allow water in even when totally submersed a few foot under water.Also is there a special name for this type of snorkel?Thanks for your help.

Yes, it is called a scuba tank.

Aqualung Air Dry Snorkel. The spray-proof cap reduces the possibility of water from waves and spray getting into the snorkel. l think this would be ur best option although the Price is £18.95.

Happy snorkeling :)

best to just learn how to expel the water from the snokel. is this for you or a child?

It is called a dry snorkel. They have a float valve on the barrel end that shuts a split second before u go under or a wave hits high enough to reach the barrel end. Many will also have a purge valve near the mouthpiece to let u expell any water or condensation while still under. There r many on the market from $25 to $80 . My fav is the Ocean Master, since they make great gear but u also pay for that. They're around $70 .
The cheapest I've seen is the Spirit Ultra dry at about $25, but u also get what u pay for & since l have not tried one personally, l can not vouch for them.
Your best bet? Hit a dive shop & bring ur mask with you. You will be able to see which ones offer best fit without putting it in ur mouth, but rigged to the mask on ur face if it is not in a blister package & what is avaliable locally to u in ur price range. At the very least, if the snorkel is blister packaged, u can compare mask, head shape & fit better than u would by just buying blind without opening the pack.