精确计算Bingham流体圆管层流压降及速度分布规律的新方法

Bingham(宾汉)模型情况下，多采用通用公式进行圆管层流压降的解析计算，即将Bingham模型本构方程代入粘性流体圆管层流流动通用公式进行计算，仅能得到压降的解析解.新方法结合Bingham流体本构方程与运动方程，建立有关力学平衡方程，并运用代数方程的根式解理论对圆管层流流动时的非线性方程进行求解，可直接求得Bingham流体圆管层流压降及速度流核区半径的解析解，进一步可求得圆管层流速度解析解；Bingham流体圆管层流速度的直接影响因素为流量、塑性粘度和屈服值，研究发现速度流核宽度与屈服值成正比，与流量及塑性粘度成反比，且流核的宽度越大，流核区的速度越小.

A New Method for Accurate Calculation of the Bingham Fluid Axial Laminar Flow Pressure Drop and Velocity Distribution in Circular Pipes

Based on the Bingham model, the analytical calculations of axial laminar flow pressure drop in circular pipes often involve the general formula for viscous fluid, with the Bingham fluid constitutive equations introduced into the calculation to get only the analytical solution of pressure drop. A new method combining the Bingham fluid constitutive equation and the motion equation to establish the mechanical equilibrium equations was proposed, to solve the circular pipe laminar flow nonlinear equations according to the algebraic equation radical solution theory, and directly get the analytical solution of the axial laminar flow pressure drop, the velocity flow core zone radius and the flow velocity. The results show that, the direct influential factors on the Bingham fluid pipe laminar flow velocity are flow rate, plastic viscosity and yield value, and the flow core zone width is proportional to the yield value and inversely proportional to the flow velocity or the plastic viscosity. Besides, the wider the velocity flow core zone is, the lower the flow velocity in the core zone is.