In the chapter Flash Facts - Friction, Drag, and Sound, James Kakalios examines the possibility of the crazy physics of the Flash, the supersonic superhero who, after lightning strike laboratory incident, gains the ability to travel incredible speeds. This in turn opens up a surprisingly diverse set of talents for him..
The most basic one is building-scaling. The author found that it is actually possible for the Flash to run up the side of a building. If you disregard the insane speed necessary to perform the feat, the physics mostly check out....mostly. In order to travel the vertical distance of the building, he needs to have a high enough velocity to overcome the gravity that pulls at him in the opposite direction, which can be put into the equation v2=(2gh). James Kakalios compares this to an earlier chapter on Superman, where to reach a height of 660ft, he would need to have an initial velocity of 140mph. This wouldn't be a problem for the Flash who can run near light speed.
However, one of the most important forces to the Flash in order for his power to be relevant is friction. Without friction, he could windmill as much as he liked and wouldn't get anywhere. One particular villain with ice powers was able to incapacitate him this way. In order to travel up the side of the building, he needs enough friction to propel him forwards, vertically. However this in itself is a problem because friction is proportional to the weight being exerted perpendicularly on a surface, and as the Flash runs up a wall, none of his weight is acting down into the wall. Technically there can't exist any friction and so his powers are negated.
This problem is solved by examining his stride length for the speed he's traveling. Friction becomes barely relevant when you realize that his feet would only touch the ground once every 660ft if he's traveling a mere 3600mph or 5250ft/s. This alone is enough to cover the height of the building in the Superman problem, between footfalls.
Regardless, he would get smashed into the side of the wall from the force of the sudden 90 degree change in direction.
Another thing the author examines is the realism in the physics of the Flash's famous ability to run on water. It turns out that water has a high enough viscosity that it doesn't have time to move out of the way of his feet. Similar to how falling into water from a height is always described as feeling like hitting cement, the impact is so sudden that it creates a high density region where there is contact with the water. It acts more like a solid at the speed that the Flash travels at. There is still the issue of gaining momentum through friction, but it could be possible if he created backwards spinning vortices similar to how a water-strider propels itself.
Kakalios, James. "Flash Facts - Friction, Drag, and Sound." The Physics of Superheroes. New York: Gotham, 2005. 57-68. Print.