## 4 Physical Model Experiments and Measuring Results  
In order to verify and analyze the ultrasound PIV method and the iterative multigrid deformation technique, we built a physical model system and carried out a series of experiments for the real-time measurement of velocity profile distribution. The schematic diagram of the ultrasound PIV measurement system is shown in Figure 6, and its physical model system for all physical model experiments is shown in Figure 7. Additionally, the measured velocities during the experiments are compared point-by-point with those of the acoustic Doppler current profilers (ADCP), and then the root mean square (RMS) error and average fluctuating velocity during the same experiments are analyzed. The physical model of the ultrasound PIV measurement system mainly includes a medical ultrasound machine (hardware) and an interface program including an inside improved PIV method (software). The steady flow of a fluid in a long glass channel with circulating water flow is shown in Figure 6. The size of the glass channel is 5.0 m \(\times\) 1.2 m \(\times\) 1.0 m (length \(\times\) width \(\times\) height). A convex or linear array probe with a frequency of 3.5 MHz is linked to the medical ultrasound machine. The frequency of ultrasonic waves from the probe can be 1 MHz, 2 MHz, 3.5 MHz, or 5 MHz. Higher frequency of the ultrasonic wave can improve the imaging precision of sediment-laden particles, but the detecting distance of the probe in silt carrying flow may be shorter. Therefore, we used a frequency 3.5 MHz probe during the model test. This system is installed near the water's surface of a circulating water channel. The ultrasound imaging region is about 35 cm \(\times\) 35 cm, which can be monitored by the array probe of the ultrasound system. Usually, the reliable depth of the measurement can be from 5 cm to 35 cm, and the measuring results can be shown directly in real-time. The array elements' imaging direction of the probe should stay in  
Figure 6: The schematic diagram of the ultrasound PIV measurement system. Figure 7: The physical model system for all the experiments. the same direction as the main flow. The probe is fixed in the water channel and primarily measures particles in the water flow as they move across the imaging area of the probe. The circulating water channel has a pump, which is used to maintain a steady flow with a fixed voltage during the whole experiment. The ultrasound system can obtain a series of ultrasonic images with a size of 640 \(\times\) 480 pixels. The spatial resolution of the ultrasonic image is about 32 \(\times\) 32 pixel/cm\({}^{2}\). The frame rate of the ultrasound system can be up to 60 frames/s. Some key properties and specifications of the experimental device are shown in Table 1.  
The processing software includes some PIV codes that can be referred to as the built-in software of the ultrasound imaging device, and the program of the PIV method is on the website. The software should include the following main features: (1) it can link a personal computer to the ultrasound imaging device directly by using a high-speed network card; (2) it can real-time display the ultrasound imaging results of silt carrying flow within sand particles in the personal computer; (3) it can real-time transform and process the image video by editing the interface program; (4) it can calculate the vector map and analyze flow field and depth-averaged velocity distribution by using the iterative multi-grid deformation technique and the related ultrasound PIV method. The program of our used ultrasound imaging measurement system is a piece of software specially designed for our research. The experiments on the real-time measurement of velocity profile distribution in silt carrying flow were carried out on the physical model system shown in Figure 7. The ultrasonic images are obtained by using the ultrasound PIV measurement system and the iterative multi-grid deformation technique.