August 21, 2017 at 2:42 p.m. is when the solar eclipse will be at its maximum in Washington, D.C. with 81% blockage.
While it won't get dark here, there should be noticeable dimming from about 2:12 p.m. to 3:12 p.m. Even though the eclipse begins at 1:17 p.m. and ends at 4:01 p.m., the 30 minutes either side of maximum looks to be the point at which noticeable dimming will occur.
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I've used the program Stellarium, which is an open source planetarium software which can be found at Stellarium.org. This software gives, in my opinion, a very realistic depiction of what the sky will look like at any given time, for any given place on earth.
The first image below is for August 22, 2017 at 2:42 p.m. over Washington, D.C. While not exactly the same as on the 21st, it's close enough for our needs.
This next image shows the dimming that will occur at 2:42 p.m. on the 21st. It looks equivalent to a moderate to thick overcast.
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Finally, to check how realistic Stellarium is, I looked at the depiction for Charleston, SC at 2:47 p.m. on the 21st. Charleston will be in the path of totality. Not only does it show the darkness, but the software also displays what planets and stars will be visible.
Please remember not to look directly at the sun. Only legitimate safety glasses, welders goggles that are #12 glass or higher, or a pinhole projector are the only safe ways to see the eclipse.