We show how to compute \(O(\sqrt{\log n})\)-approximations to SPARSEST CUT and BALANCED SEPARATOR problems in \(\tilde{O}(n^2)\) time, thus improving upon the recent algorithm of Arora, Rao and Vazirani (2004). Their algorithm uses semidefinite programming and required \(\tilde{O}(n^{4.5})\) time. Our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs. The existence of expander flows was also established by Arora, Rao, and Vazirani.