Wow, that new UT engineering center is definitely going to be a highrise, and the design is very nice. Looking at the renderings of it, the Ernest Cockrell Jr Hall Tower is located to the north of it. That building is 172 feet with 11 floors, so I would estimate this new building will probably be around 160 feet tall. It'll be immediately south of that taller building and north of the Engineering-Science Building. It looks like they'll demolish that skinny little tower between those two buildings, and possibly even the Engineering-Science Building, which is itself a highrise - 118 feet tall.
Here's the PDF with more details and a larger rendering.
http://texasexes.org/userdocs/eercalcalde.pdf
Those links bring up some points. UT has lacked very many upgrades to its campus facilities. Most of the buildings that are "new" are pushing 40+ years old. When you look at the campuses of other major universities, they've added new buildings to replace their old buildings which are actually costing them more money to maintain because they are older and falling apart. Texas A&M is one university to look at. They've added several new major campus buildings for their programs. It's kind of shocking actually that our state's flagship school hasn't added much in the last 30 to 40 years. We've only just recently started to see new buildings being built at UT, but this is the first major one.
To put this into perspective, if it gets built at that size and height, it will be tallest building built on campus since 1973. And that year, the Capitol was still the tallest building in Austin. There has only been one single highrise built on campus since 2007, and that is the Almetris Duren Residence Hall near 26th & Guadalupe. Before that the last highrise to be built on campus was the Robert Moore Lee Hall in 1974.
By the way, at 160 feet tall today that building would be the 65th tallest building in Austin.