White is a brilliant color, but it has the severe liability of putting even the slightest bit of grime on full public display. This is a real problem for white brick exterior surfaces, which require regular cleaning. Powerwashing will do the job, but also opens the risk of driving water into any cracks in the brick or mortar. The best way to do the job is to use muriatic acid, but that poses its own special problems.
Lay out dropcloths or tarps -- preferably acid-resistant plastic -- around the base of the wall. In a pinch, regualr tarps or dropcloths will work, as long as there are no big acid spills.
Prepare the wall by soaking it with water. There is no need for anything special; a garden hose will do for this job.
If you have not already done so, put on your acid-resistant clothing, goggles and respirator. Also set your baking soda in a handy place. This will neutralize a bad spill, especially if the acid gets on your skin.
Fill one bucket with a mixture of ammonia and water. The proper proportion is one cup of ammonia per gallon of water.
Mix the muriatic acid with water in a 5-gallon plastic bucket. The standard mix is 1 part acid to 10 parts water. If your acid is concentrated or diluted, though, it might require a different ratio. Check the instructions on the label before proceeding.
Decide if the wind is too high for spraying the acid. This is a pure judgment call on your part. If you think the wind will spray acid everywhere, switch from a sprayer to a brush.
Using either the sprayer or the brush, apply the acid to the wall in small sections of between 3 feet by 3 feet and 6 feet by 6 feet. How large depends on how quickly you can apply the acid, as it should stay on the wall no more than two or three3 minutes. Keep in mind that the acid will eventually damage the sprayer or brush, so they may need to be replaced during the course of a long job.
Rinse the wall by first scrubbing it with the brush using the water and ammonia mixture. Once finished rinsing, get out the hose and spray the work area.
Continue section by section until the wall is cleaned.