## 4 Pressure Loss Correction Model for Bend Section
### Verification of Pressure Loss in Bend Section  
To validate the effectiveness of the equivalent pressure loss model for the elbow section, this study uses the field parameters from [26]. A high-rise residential building has 25 floors, with a total height of 75 m. The first vertical bend of concrete pumping is selected for strain monitoring, and the project adopts the Zoomlion ZL140 THBE-10022R truck-mounted pump (Zoomlion Heavy Industry Science and Technology Co., Ltd., Changsha, China). The project adopts the ZLJ140 THBE-10022R truck-mounted pump; the maximum theoretical conveying capacity is 100 m\({}^{3}\)/h, the concrete cylinder diameter is 200 mm, and the cylinder stroke is 1650 mm. The specific experimental results refer to those in [26]. The geometric model matches the one described in Section 3.2 of this paper. The elbow has a horizontal inclination angle of 90\({}^{\circ}\), an opening angle of 90\({}^{\circ}\), an inner diameter of 125 mm, and a curvature radius of 1000 mm. The pump truck operates at a pressure of 20 MPa, with the total height of the residential building under construction being 75 m. The concrete has a slump of 238 mm and an expansion of 415 mm. According to the converted horizontal length method outlined in the Technical Regulations for Concrete Pumping Construction (JGJ/T10-2011), the pressure loss of a curved pipe with a tension angle of 90\({}^{\circ}\) is equivalent to that of a 9 m long horizontal straight pipe. Figure 11: The curve of the distribution of pressure loss in concrete pumping with the flow rate. Using [PERSON]'s empirical formula, the pressure loss \(\Delta p_{c}\) per unit length of a horizontal straight pipe is:  
\[\Delta p_{c}=\frac{2}{R}[k_{1}+k_{2}(1+t_{2}/t_{1})v]\alpha \tag{20}\]  
where \(\alpha\) is the ratio of radial pressure and axial pressure, usually taken as 0.90; \(R\) is the inner diameter of the pipe; \(k_{1}\) is the resistance coefficient produced by the concrete sticking to the pipe; \(k_{2}\) is the resistance coefficient produced by the uneven speed of concrete in the pipe section; \(t_{1}\) is the pumping piston reciprocating motion to promote the time of concrete; \(t_{2}\) is the time of the distribution valve conversion; \(t_{2}/t_{1}\) is generally taken as 0.3. \(k_{1}\) and \(k_{2}\) are related to the concrete mixing ratio, pipe wall smoothness, and other factors related to the engineering of commonly used concrete; slump S is used for calculation. The type of concrete conveyed by the pump truck is C45. The kinematic viscosity coefficient of the concrete mortar is 10.6 m\({}^{2}\)/s, and the density of the aggregate particles is 2182 kg/m\({}^{3}\). The thickness of the lubrication layer in the pumped straight pipe section is 2.1 mm, the equivalent diameter is 4.2 mm, and the relative roughness between the lubrication layer and the plunger layer is 3.76 mm. For a pumping flow rate of 0.63 m/s, the pressure loss per unit length, calculated using [PERSON]'s empirical formula, is 0.0056 MPa. When the pumping flow rates are 0.77 m/s and 0.89 m/s, [PERSON]'s empirical formula calculates the pressure losses per unit length as 0.0065 MPa and 0.0072 MPa, respectively. This paper uses a one-dimensional flow model to calculate the pressure loss in the elbow section. For comparison, the pressure loss in the straight pipe section is also calculated using this model. The results show that, for pumping flow rates of 0.63 m/s, 0.77 m/s, and 0.89 m/s, the pressure losses per unit length are 0.0224 MPa, 0.0214 MPa, and 0.0219 MPa, respectively. These values are higher than those calculated using Morinage's empirical formula. The values of the pressure loss in bends calculated using Morinage's empirical formula and the pressure loss in straight pipe sections determined by the one-dimensional flow model are referenced. The results, using the converted horizontal length method and the modified one-dimensional flow model formula, are presented in Table 5. The experimental test values are sourced from [26].