A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar＇s macrodispersion.