'you obviously know' is correct and can be used in written English.
You can use it when you want to emphasize that something is known or obvious to someone. For example: "You obviously know why I'm here - let's get started."
"After a game," Coughlin says, "you obviously know what happened.
"You obviously know a lot about sex," he said.
HENDRIK HERTZBERG: You obviously know what you're talking about.
But, obviously, watching it back you obviously know exactly what is going to happen.
You obviously know very little about the evolution of the human rights movement, and chose to demagogue serious groups like Amnesty International that are committed to fighting powerlessness around the world.
"I was in the back of the class, where the teacher couldn't see my feet, but my upper body was doing things I've seen Fred Astaire and Gene Kelly do, so the teacher said, 'You obviously know the steps.' Before long, I began to feel panic, then I started freezing up.
(January 11 is my birthday which you obviously knew already, so those few weeks after Christmas have an expectant patina of fallen tinsel and cupcake icing for me).
You obviously knew you would face a lot of criticism, just given the optics of how famous you are and the fact that you don't make music that often.
"They obviously know you can't take people from off the street and put them into permanent housing, but they are disingenuous with their criticism," Mr. McDonald said.
Don't let the circa-1997 Compaq 5800-series computer in the logo fool you, friends, these people obviously know their target audience.
The person you're kissing obviously knows you have braces and they know they have to be careful otherwise they wouldn't be kissing you.
