摘   要：对赫巴流体在圆管内的层流流动问题进行理论分析，建立了流体在圆管截面上的流速分布、剪应力分布、流核速度、壁面剪应力、体积流量、平均流速、等效黏度等若干物理量的解析表达式和数值求解策略；以实际新拌混凝土的赫巴流体参数为例，考察了单位管长压降与平均流速之间的关系。
Abstract: The steady-state, laminar flow problem of a Herschel-Bulkley (HB) fluid through a long circular pipe, a problem analogous to the Hagen-Poiseuille flow of a Newtonian fluid, was studied. The HB fluid model is a three-parameter, yield-power law model, where the three parameters are the yield stress, the fluid consistency index, and the flow behavior index, and certain special parameter values, the HB model can be simplified to the Bingham fluid model, the power-law fluid model and the simple Newtonian model, and is believed to better describe the rheological behaviors of complex fluids like sewage sludges, drilling fluids, cements pastes, mortars, and fresh concretes than the simpler Bingham or power-law fluid models. Rigorous analytical expressions are derived for the velocity profile, shear stress distribution, yield radius, average flow velocity, Metzner-Reed model parameters, etc. A numerical recipe is reported, and as a demonstration on the application side, the flow of a fresh concrete is investigated and is discussed in the context of concrete pumping. To simplify the relationship between pressure drop and average velocity, the concept of “equivalent fluid viscosity” is introduced.