Using water pressure on drains sounds funny, but it can work. Yes you can, but you may need to get some special tooling. A tool called a drain bladder can be attached to a hose to clean out a drain.
For related information, see the articles 'How To Clean a Drain', 'Using a Snake on a Drain' and 'Troubleshooting Plumbing Pipes'.
Water Pressure Cautions
You need to use some caution when using pressure on a drain. A big concern with using water pressure is that you are introducing more water into the drain. If the drain does not open up, you could have a bigger mess on your hands.
Do not try to use pressure on the compression fittings under your sinks. You could blow them apart and make bigger mess. The same rules apply for putting pressure on a line as do a plunger. You will need to close off any other drains that are on the clogged side of the blockage.
A blow bag is a simple device that fits into the drain and expands when you attach a garden hose to it. The water pressure builds up inside the pipe and the clog breaks free and is washed away. When it works properly, this method can be less messy than a snake. Unfortunately, it does not work for all types of clogs. Tree roots would be an example. Pressure will not remove them.
Using a Drain Bladder
Insert the blow bag with a garden hose attached to it, into the pipe in question. Turn the water on and wait for the bag to expand. Remember, you are introducing more water into this situation. Make sure you have stopped up any other drains connected to this line. If you don't the water will just come out there.
Not much else to do, just give it some time. You should be able to hear the water running freely in the line when the clog has been removed. Using water pressure on drains is not hard, but it can be messy.
Another pressure device is a water ram. This is not a common item in most homes. Think of it as a plunger on steroids. It sends a blast of air into the pipe that is hopefully strong enough to break up the clog. This method can work for clogs that are too difficult for a plunger.
Caution on the use of pressure is warranted with this device. The pressure will blow out at the weakest point. This could be the fittings on another sink or a corroded section of pipe in your basement.
A water ram will cost hundreds of dollars to purchase. Not normal homeowner fare. You may be able to rent one locally if you want to try this route. Get some instructions for its use if you do.
Using water pressure can be an effective way to clean a drain. The added water can help to wash all of the blockage down the drain. This method is not used as much as other methods and can sometimes cause additional problems.
If you were not successful in unclogging your drain, see the articles 'How To Clean a Drain', 'Using a Snake on a Drain' and 'Troubleshooting Plumbing Pipes'.