This work presents a simplified model for the rapid computation of the yearly solar fraction of direct solar water heating systems using on-off control. Thermal stratification was included using a simple one-dimensional multi-node model. A time-step dependency analysis showed that a time step of 0.05 h is a good compromise between accuracy and computation speed. The solar fraction increases with collector flow rate when the flow rate is low. In fully-mixed storage, the solar fraction keeps increasing with flow rate, although with a decreasing rate of increase. However, in stratified storage, the solar fraction reaches a maximum at an optimum flow rate, before it starts decreasing with flow rate. When the number of tank nodes increases from 1 to 4, the maximum solar fraction increases 5-28 %; this increase is superior for less efficient collectors and lower collector areas. In low-stratified systems, the optimum flow rate is the maximum allowed by the system. However, in stratified systems, the optimum flow rate is reduced to values of 0.006-0.016 m(3) h(-1) per square meter of collector area. Unless the tank walls are covered by a rather thick layer of thermal insulation (about 0.2 m), storage tank losses cannot be ignored. (C) 2020 Elsevier Ltd. All rights reserved.