## 5 Results and Discussion
### Measurement Uncertainty Evaluation  
The velocity calculation equation based on DPIV is Equation (25):  
\[|v|=\gamma\frac{\Delta pixel}{\Delta t}, \tag{25}\]  
where, \(\gamma\) is camera calibration factor, \(\Delta pixel\) is the pixel value of particles movement in two adjacent frames of images, and \(\Delta t\) is the time difference between two frames of images. Figure 12: Measurement results under different working conditions. (**a**) Flow velocity field of \(28.3\times 10^{-3}\) m/s-70%. (**b**) Flow velocity field of \(37.7\times 10^{-3}\) m/s-70%. (**c**) Flow velocity field of \(51.9\times 10^{-3}\) m/s-70%. (**d**) Flow velocity field of \(47.2\times 10^{-3}\) m/s-90%. (**e**) Flow velocity field of \(47.2\times 10^{-3}\) m/s-80%. (**f**) Flow velocity field of \(47.2\times 10^{-3}\) m/s-70%. To evaluate the uncertainty measurement of oil-water two-phase immiscible flow velocity, the above equation is equivalent to  
\[|v|=\frac{4(\Delta Q_{W}+\Delta Q_{O})}{\pi D^{2}\Delta t}, \tag{26}\]  
where, \(\Delta Q_{W}\) is the water phase flow rate, \(\Delta Q_{O}\) is the oil phase flow rate, and \(D\) is pipe inner diameter. In the calculation process, the measurement of oil-water two-phase immiscible flow velocity is obtained according to Equation (25), not Equation (26). According to Equation (25), flow velocity measurement errors are divided into two categories: One is instrument calibration error, which is mainly composed of object distance error, camera tilt error, and camera manufacturing error; the other is the geometric error and control error of measurement system. According to the above analysis, the measurement uncertainty of oil-water two-phase immiscible flow measurement mainly includes the following. (1) Measurement uncertainty \(u_{w}\) caused by the control error of water phase flow velocity \(\Delta Q_{W}\). The maximum value of this error is 0.1%, the error approximately follows uniform distribution, and the maximum flow velocity of water phase is 3.20 m\({}^{3}\)/h. Therefore, the measurement uncertainty caused by this part is calculated as  
\[u_{w}=\left(0.072\times 10^{-3}\right)/\sqrt{3}\;\mathrm{m/s}, \tag{27}\]  
(2) Measurement uncertainty \(u_{o}\) caused by the control error of water phase flow rate \(\Delta Q_{O}\)  
The maximum value of this error is 0.1%, the error approximately follows uniform distribution, and the maximum flow velocity of oil phase is 1.38 m\({}^{3}\)/h. Therefore, the measurement uncertainty caused by this part is calculated as  
\[u_{o}=\left(0.032\times 10^{-3}\right)/\sqrt{3}\;\mathrm{m/s}, \tag{28}\]  
(3) Measurement uncertainty \(u_{D}\) caused by the error of pipe inner diameter \(D\)  
The maximum value of this error is 0.1 mm, pipe inner diameter \(D\) is 125 mm, and the error approximately follows uniform distribution. Therefore, the measurement uncertainty caused by this part is  
\[u_{D}=\left(0.003\times 10^{-3}\right)/\sqrt{3}\;\mathrm{m/s}, \tag{29}\]  
(4) Measurement uncertainty \(u_{\Delta t}\) caused by the error of time difference \(\Delta t\) of per camera frame  
The maximum value of this error is 0.05%, the error approximately follows uniform distribution, and the time difference of each frame is 0.001. Therefore, the measurement uncertainty caused by this part is  
\[u_{D}=\left(0.002\times 10^{-3}\right)/\sqrt{3}\;\mathrm{m/s}, \tag{30}\]  
(5) Measurement uncertainty \(u_{\gamma}\) caused by the error of camera calibration \(\gamma\)  
Object distance error is 1 mm, object distance is 0.5 m, the tilt angle error of the camera is 0.01\({}^{\circ}\), the camera design angle is 0\({}^{\circ}\), and the errors are within the limits permitted of the measurement procedure. Therefore, the measurement uncertainty of this part according to the manufacturer is  
\[u_{\gamma}=(0.05\%+\mathrm{L}\times 0.005\%)\mathrm{V_{max}}=0.059\times 10^{- 3}\;\mathrm{m/s} \tag{31}\]  
where, \(L\) is object distance, \(V\mathrm{max}\) is the max flow velocity, and the value is 0.113 m/s.