The goal of this paper is to develop a procedure of calculating karst conduit fluxes using dye tracing results. The Green's function for the initial value problem is adapted by localized dilution at the juncture of conduit flows. Then the model is employed to simulate three breakthrough curves measured near Emerald Sink, Northwest Florida. The simulation of the tracing experiment from Cheryl Sink to Emerald Sink yields a recharge of 1.49 m(3)/s at Emerald Sink. For the oxbow that connects Cheryl Sink with Emerald Sink, the major shortcut and the long side convey about 90 and 10% of water, respectively. The simulations of other two experiments yield a consistent value for the flow from a tributary conduit into the main conduit 200 m downstream of Emerald Sink, being 1.9-2.0 m(3)/s. The proposed theory is novel and robust in that the peak arrival time, time width, and amplitude of the measured curves are fully utilized, and the resulting water fluxes are independent of conduit radius.