An apparatus for mixing fluids includes at least one noncircular orifice having unequal major and minor axis dimensions, with the major axis dimension being less than approximately 5 times the minor axis dimension. A first fluid is emitted from the orifice as a jet for mixing with another fluid in a region downstream of the orifice. The mixing region extends downstream a distance at least equal to the minor axis dimension, and then either terminates in a wall in the path of the jet or continues downstream to a total distance of at least approximately 3 times the minor axis dimension. The mixing region has a lateral width of at least 2(a+0.4x) in a direction parallel to the major axis and a lateral width of at least 2(b+0.4x) in a direction parallel to the minor axis, where a and b are one-half the major and minor axis dimensions, respectively, and x is the distance downstream of the orifice.