# One-Dimensional Modeling of the Pressure Loss in Concrete Pumping and Experimental Verification
## 5 Analysis of Results
### Analysis of Experimental Results
Based on the coarse aggregate particles extracted, the average mass of 18 aggregate particles is measured to be 138.60 g. A HandySCAN noncontact 3D laser scanner combined with Geomagic Design X (v.19.0.2) software is used to statistically determine that the average surface area of the 18 coarse aggregate particles is 22,335.89 mm\({}^{2}\), the average density of the aggregate particles is 2360 kg/m\({}^{3}\), and, according to Equations (21) and (24), the equivalent particle size of the coarse aggregates \(K\) is 15.80 mm. The time required for cement mortar to slump 100 mm is 0.08 s. According to Equation (19), the mortar kinematic viscosity coefficient u is 10.6 Pa-s. According to Equations (16)-(18), the Reynolds number \(R_{e}\) is 0.611, and the relative roughness of the coarse aggregates \(K_{d}\) is 2.393 mm. Thus, according to Equation (25), the resistance coefficient \(\lambda\) is 0.66. Based on the pipeline length \(l\), the pumping velocity \(v\), the mortar kinematic viscosity coefficient u, and the mortar density \(\rho s\), the pressure loss per unit length is calculated by the pumping one-dimensional flow model as follows:  
\[\Delta p_{m}=0.022\text{ MPa}\]  
When a pump truck pumps concrete, the force conditions close to the pumping inlet of the pipeline generated by the impact of the plunger pump and concrete reflux are complex. A straight pumping pipe section with a relatively stable concrete flow pattern is selected for the stress-strain test. The strain monitoring system is mainly composed of three parts: resistive strain gauges, a DHDAS dynamic signal acquisition system, and a data storage system. Additional lab equipment includes 502 glues, sandpaper, a level, alcohol, connecting wires, 703 silica gel, etc. During the pumping of concrete by the pump truck, the pipeline near the pumping inlet is subjected to the impact of the plunger pump and the return flow of concrete,  
Figure 5: Actual aggregate particle modeling and size distribution. which makes the force situation complicated. In this paper, the pumping straight pipe section with relatively stable concrete flow pattern is selected to carry out the strain test. The height of the pipeline with strain gauge is 70 m above the ground, and the distance between the two monitoring points is 1.5 m. The type of resistance strain gauge is BX120-3 AA, and the strain gauge arrangement is bidirectional vertical circumferential and axial arrangement. After pasting firmly on site, the pasting quality of the strain gauge is checked. If the deviation is too large, polishing and pasting is repeated, and if the paste quality is good, the strain gauge is waterproof and insulated with 703 silica gel. Considering the temperature compensation, a PC computer and DHDAS dynamic signal acquisition and analysis software are used to collect data on the strain of the monitored pipe section, and the sampling frequency is 50 Hz. The testing of pump tube strain is repeated many times, and the circumferential and axial strain changes monitored at the two monitoring points are shown in Figure 6.  
The experimental results show that the circumferential strain varies between 84 and 93 \(\upmu\)m, and the axial strain varies between 13 and 22 \(\upmu\)m. Taking the values of the stable section and analyzing them, the circumferential strain at measurement point 1 is 87.4 \(\upmu\)m and the axial strain is 17.4 \(\upmu\)m, whereas the circumferential strain at measurement point 2 is 85.2 \(\upmu\)m and the axial strain is 15.6 \(\upmu\)m. The calculated circumferential pressure at measurement points 1 is 6.566 MPa, and that at measurement point 2 is 6.372 MPa. According to Equations (28)-(32), the pressure loss per unit length is obtained as follows:  
\[\Delta p_{e}=0.0263\ \text{MPa}\]  
The pressure loss per unit length values obtained from empirical equations, the one-dimensional flow model, and experiments are compared. The smallest pressure loss is obtained with the empirical formulas, which is approximately 62.0% of the actual measured pressure loss.