PSU Sizes are standard & will fit in any PC case except the slim type:
Anyway, here is the dimension of the current PSU in your case:
150mm x 140mm x 86mm (5.9 x 5.5 x 3.4 inches)
Here is that of the corsair:
5.9"(W) x 3.4"(H) x 6.3"(L)
The W & H are the same ( standard ) & the corsair is a bit longer but it should fit. To be safe, you can try to measure along your current PSU if there is any obstruction encountered by the extra 0.8" in length.
If there is obstruction, you can choose this instead:http://www.newegg.com/Product/Product.aspx?Item=N82E16817139028
It is exactly the same size as your current PSU. Slightly less capacity than before but still more than enough for the XFX 6870.