Abstract The circulation in the liver is unique at macroscopic and microscopic levels. At the macroscopic level, there is an unusual presence of portal and arterial inputs rather than a single arterial input. At the microscopic level, a series of microenvironments in the acinar system is essential in controlling the functional characteristics of hepatic parenchymal cells. Since the hemodynamics is much less studied in the multifunctional liver, an attempt is made to study the hepatic hemodynamics in a segment of a hepatic lobular structure, that is made up of high-pressure oxygenated arteriole, low-pressure nutrient-rich portal venule, fenestrated sinusoidal space and hepatic venule. Our goal is to dispel some of the myths of this complex vascular bed by means of finite volume blood flow simulation. Flow features like high-velocity gradients near the fenestrations, flow reversal and Dean vortices in the sinusoidal space are analyzed within the non-Newtonian framework. Since no distinct exact or numerical solutions are available for this complex vascular bed, the present simulated results are compared with the available clinical observations. Results revealed that the pressure plays a key role in hepatic blood flow.