An apparatus and method for determining the viscosity of a fluid over plural shear rates caused by a decreasing pressure differential by monitoring the movement of the fluid through a riser tube and a capillary tube. The movement can be monitored by detecting the changing weight of the fluid, using a precision balance or load cell, as it moves through the riser tube and capillary tube into a fluid collector; or, alternatively, the movement can be monitored by detecting the changing level of a fluid column in the riser tube using a column level detector. A processor then uses the changing weight or height data, along with the dimensions of the capillary tube and a dimension of the riser tube, to determine the viscosity of the fluid. In addition, apparatus and methods for determining fluid viscosity online and fluid mixture homogeneity online are also described.