A seal assembly includes an annular base, a spring, a shoe, a first channel, a seal cover, and a seal. The spring includes a beam and is connected to the annular base. The shoe is disposed radially inward of the annular base and connected to the spring. The shoe includes an upstream portion, a downstream portion, and a lip connected to and extending radially outward from the upstream portion of the shoe. The spring extends from the annular base to the shoe. The first channel is positioned between the shoe and the beam of the spring. The seal is disposed between the seal cover and the shoe such that a downstream face of the seal is in contact with an upstream face of the shoe.