A system for measuring rheological characteristics for drilling muds without the use of a delicate, expensive, or labor-intensive viscometer is disclosed. The system includes a fluid diverter circuit which retrieves a sample of the drilling mud and stores it in a reservoir where the pressure and level of the drilling mud are measured. The reservoir drains through a measurement pipe which enables a calculation of a flow rate. With the dimensions of the measurement pipe, the pressure, and the flow rate, a rheological chart can be assembled. The system can iteratively measure pressure and from the iterative data achieve a non-Newtonian factor, n′, confirm entrance length of the measurement pipe, and confirm that the flow in the measurement pipe is laminar.