We derive, without approximation, a closed-form macroscopic equation for finite Knudsen number flow using the Boltzmann–BGK kinetic theory with constant relaxation time. This general closed-form equation is specialized into a compact integro-differential equation for time-dependent isothermal unidirectional flows and results are presented for channel flow. This equation provides a clear demonstration of the effects of finite Knudsen number, and it also illustrates the limitations of the Boltzmann–BGK theory with constant relaxation time and bounce-back boundary conditions.