# One-Dimensional Modeling of the Pressure Loss in Concrete Pumping and Experimental Verification
## 5 Analysis of Results
### Example Validation and Analysis  
Due to the coarse aggregate grading shape of S25-A25 concrete in reference [24] being unknown, the equivalent coarse aggregate diameter of 15.8 mm is adopted based on the data obtained from the experiment in the previous section. In the reference, the pumping pressure loss was measured by 170 m horizontal pumping circuit experiment and lubrication layer thickness of S50-A25 concrete using the ultrasonic velocity profile (UVP) method.  
The BSA2110 HP-D pump truck is used in the field, and the pump pipe with a diameter of 125 mm and a wall thickness of 7.7 mm is selected. A rheometer is used to measure the thickness of the lubricating layer. The material composition of S50-A25 concrete is shown in Table 3.  
The density of cement is 3150 kg/m\({}^{3}\), the density of coarse aggregate is 2610 kg/m\({}^{3}\), the density of mortar \(\rho\)s is 2100 kg/m\({}^{3}\), the size of sand is 0.08-5 mm, and the maximum aggregate size is 25 mm. To validation the accuracy of the model, the pressure loss measured in the pumping circuit experiment is compared with the calculation results of the pump pressure loss one dimensional flow model.  
In the literature, the pumping flow in the concrete conveying pipe is 42 m\({}^{3}\)/h, the viscosity of the lubricating layer is 2.50 Pa-s, measured by rheometer, and the thickness of the lubricating layer is 2.09 mm, measured by the ultrasonic (UVP) velocity profile method. According to Equation (15), the equivalent diameter is twice the thickness of the lubricating layer, and its value is 4.18 mm. According to Equation (18), the relative roughness of the coarse aggregates \(K_{d}\) is 3.7799. According to Equations (16)-(18), the Reynolds numbers \(R_{e}\) is 3.3392, and according to Equation (25), the resistance coefficient \(\lambda\) is 0.4021. According to Equation (27), the pressure loss per unit length is calculated by the pumping one-dimensional flow model as follows:  
\[\Delta p_{e}=0.02284\text{MPa}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cement CEMI52.5N** & **Fly Ash** & **Blast Furnace** & **Water-** & **Sand** & **Coarse** & **Maximum** \\ (kg/m\({}^{3}\)) & **(kg/m\({}^{3}\))** & **Slag (kg/m\({}^{3}\))** & **Reducing** & **(kg/m\({}^{3}\))** & **Aggregates** & **Aggregate Size** \\  & & & **Agent** & **(kg/m\({}^{3}\))** & **(mm)** \\ \hline
350 & 50 & 225 & 0.33 & 736 & 871 & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Content of each component in S25-A25 concrete.  
The measured pressure loss value in the reference is 0.02823, and the relative error between the measured value and the calculated value is 19.09%. The results show that the calculated pressure loss of the pumping one-dimensional model flow is basically the same as the actual pressure loss. These comparison results verify the feasibility of one-dimensional flow model pumping. The pressure loss mainly comes from the frictional resistance generated by the relative motion of each layer of mortar and the lubrication layer, as well as from the large number of vortices generated by large aggregate particles and the large wall roughness blocking effect. It is worth noting that the construction of the one-dimensional flow model in this study does not consider the transition region between the lubrication layer and the plunger layer. Therefore, the pressure loss caused by this part is ignored, which leads to the calculation result of the one-dimensional model flow model being smaller than the measured value.