# One-Dimensional Modeling of the Pressure Loss in Concrete Pumping and Experimental Verification
## 3 Concrete Pumping One-Dimensional Flow Model Construction  
According to the analysis of the rheological behavior in concrete pumping, the concrete in the pumping pipe is divided into a lubrication layer and a plunger layer. The flow behavior of the lubrication layer is similar to that of mortar, and the plunger layer as a whole moves forward in the pumping pipe direction in the form of a plunger flow. In other words, the fluid medium in the lubrication layer is mainly mortar, and the fluid medium in the plunger layer is mainly a mixture of aggregate particles and mortar. The lubrication layer gradually transitions to the plunger layer when coarse aggregate particles begin to appear in the bottom layer of the pumping pipe. Due to the viscosity of concrete, the flow velocity of the lubrication layer in contact with the pumping pipe wall is zero, and the flow velocity of the lubrication layer in contact with the plunger layer is the concrete pumping flow rate. The aggregate particles and the mortar in the plunger layer flow forward as a whole in the form of a plunger flow. There is no relative motion between the aggregate particles and the mortar in the plunger layer, and the friction between the aggregate particles and the mortar can be neglected. Therefore, the concrete pumping pressure loss is mainly concentrated in the lubrication layer region, for example, in the friction between the lubrication layer and the pipe wall, the friction between the lubrication layer and plunger layer due to their relative movement, and the friction of the mortar in the lubrication layer generated by slip. The specific factors affecting the pumping pressure loss include the pipe wall roughness, lubrication layer thickness, aggregate particle shape and size, lubrication layer kinematic viscosity coefficient, Reynolds number, and concrete pumping speed. Because the roughness of the pipe wall is much smaller than the coarse aggregate particle size, the frictional resistance generated by the pipe wall is less than the viscous force between the coarse aggregate particles and the lubrication layer, and the pipe wall frictional resistance is ignored in this paper. To analyze the effect of coarse aggregate particles on pressure loss facilitation, it is assumed that the coarse aggregate particles occupy the critical layer of the lubrication layer and the plunger layer and that coarse aggregate particles of various shapes are equivalent to spherical particles with equal particle sizes. According to the above assumptions, a typical straight pipe is taken as an example to establish a one-dimensional flow model for concrete pumping, as shown in Figure 2. In the figure, \(v\) is the concrete pumping flow rate, \(l\) is the length between the selected control region cross-flow section 1 and cross-flow section 2, \(z_{1}\) is the height of the axis of cross-flow section 1 from the reference datum, \(z_{2}\) is the height of the axis of cross-flow section 2 from the reference datum, \(p_{1}\) is the average pressure in cross-flow section 1, \(p_{2}\) is the average pressure in cross-flow section 2, \(d\) is the inner diameter of the pumping pipeline, \(\delta\) is the thickness of the lubrication layer, \(K\) is the equivalent particle size of the coarse aggregate particles, and \(\tau_{0}\) is the viscous force of the lubrication layer and the plunger layer.