This paper focuses on modeling the fate of effluent from diffuse seafloor hydrothermal activity after it has been vented into the water column. The model was formulated using a number of simplifying assumptions which permit direct application of this model to field measurements. I have limited the configurations to those where the hydrothermal outflow velocities are smaller than horizontal current. I assume that the entrainment of ambient seawater into the plume is constant over the length of the plume. This permits formulation of a first-order relation for the rise height and dilution in a diffuse hydrothermal plume as a function of downstream distance. The analytic model is compared with a simple laboratory simulation of the hydrothermal flow. The results suggest that diffuse hydrothermal effluent will penetrate to a height in the water column that is proportional to the overall dimension of the diffuse vent patch, multiplied by a dimensionless plume intensity parameter. I also show relations for plume dilution which will be compared with field data in part 2 of this work. ¿ American Geophysical Union 1994