Let's use dimensional analysis to determine the equation for the flow rate Q of a fluid in a pipe. The flow rate Q has dimensions of volume per time. It is inversely proportional to L, the length of the tube (so you double the tube length, the flow rate halves). The flow rate also depends on the following three other quantities: the pressure difference AP between the ends of the pipe, the radius of the pipe R, and the viscosity of the fluid n. The pressure difference is a force per area (and force has units of kg · m/s²). The viscosity has units of kg /(m ·s).

Fig: 1