An engineering model of a transient laminar flow from a pressurised vessel through a long microchannel under a condition of a rapid valve opening at a channel outlet is developed. A valve at the channel outlet, which is opening with a given speed, is modelled as a time-dependent boundary condition. Transient flows are investigated numerically by the method of characteristics. The calculations show that variations of pressure and velocity distributions along the channel over time, caused by a transient flow regime, decrease with a decrease in the channel diameter and the channel length, an increase in the time of valve opening and an increase in the fluid viscosity. (c) 2012 Canadian Society for Chemical Engineering