It is known that some flagellated bacteria like Serratia marcescens, when deposited and affixed onto a surface to form a "bacterial carpet", self-organize in a collective motion of the flagella that is capable of pumping fluid through microfluidic channels. We set up a continuum model comprising two macroscopic variables that is capable of describing this self-organization mechanism as well as quantifying it to the extent that an agreement with the experimentally observed channel width dependence of the pumping is reached. The activity is introduced through a collective angular velocity of the helical flagella rotation, which is an example of a dynamic macroscopic preferred direction. Our model supports and quantifies the view that the self-coordination is due to a positive feedback loop between the bacterial flagella and the local flow generated by their rotation. Moreover, our results indicate that this biological active system is operating close to the self-organization threshold.