## 4 Results and Discussion
### The Effects of the Material and Riblets on Cavitation-Induced Erosion Depth and Cross-Section  
The previous section provides precise information concerning the effects of the material and riblets on cavitation-induced erosion morphology; however, the exact amount of cross-sectional area of erosion remains unclear, and the depth of erosion is expressed within the range of 330-450 \(\upmu\)m and 315-316 \(\upmu\)m for flat and ribleted surfaces, respectively. In this regard, this section offers a three-dimensional map of the eroded surface and a diagram of depth to disclose the exact amount of cross-sectional area and the depth of erosion, as shown in Figure 5. This figure presents a three-dimensional map of the eroded surface, a diagram of the depth versus width of the damaged surface along the horizontal line, and a diagram of the depth versus width of the damaged surface along the vertical line induced by 500 single cavitation bubbles with a wall distance of \(\gamma=1.8\) in parts I, II, and III, respectively. Figure 5a illustrates the average depth of erosion of 432.281 \(\upmu\)m and an average radius of the cross-section of erosion of 162.5 \(\upmu\)m for Al with a flat surface. Intercomparison of these values with the average depth (346.115 \(\upmu\)m) and radius (157.5 \(\upmu\)m) of the cross-section of erosion for brass with a flat surface in Figure 5b reveals that both the depth and area of erosion in brass are smaller than those in Al by 19.9% and 3.0%, respectively. These results originate from the nature of the physical properties of Al and brass. Brass exhibits a Young's modulus of 97 gigapascals (GPa), a shear modulus of 37 GPa, and a Poisson's ratio of 0.34 (dimensionless) [40]. In comparison, Al has a Young's modulus of 68 GPa, a shear modulus of 25 GPa, and a Poisson's ratio of 0.33 [40]. Intercomparison of these values proves that brass offers greater mechanical stability than Al, with the ability able to tolerate the impulse of the water hammer more effectively than Al and resulting in a lower erosion depth and area in comparison to those of Al. Based on the obtained results for the exact amount of cross-sectional area and depth of erosion in the case of Al and brass with flat surface morphology, it can be expected that in the presence of riblets, the erosion area and depth for brass will be lower than for Al. Intercomparison of the average depth and radius of the cross-section of erosion for Al and brass with riblets in Figures 5c and 5d, respectively, confirms this prediction. According to these figures, the average depth of erosion for Al and brass with riblets are 415.541 and 318.553 \(\upmu\)m, respectively. These outcomes clearly indicate that brass with riblets exhibits 23.3% less erosion compared to that of Al with riblets. Moreover, in the presence of riblets, the erosion depth of Al and brass is reduced by 3.8% and 7.9%, respectively, in comparison with that for flat surfaces. Furthermore, the erosion depth of brass is lower than that of Al when both have surfaces with riblets. Figure 5: Three-dimensional map of the eroded surface and diagram of depth. (**I**) Three-dimensional map of the damaged surface, (**II**) diagram of depth versus width of the damaged surface along horizontal line, and (**III**) diagram of depth versus width of the damaged surface along vertical line induced by 500 single cavitation bubble with wall distance of \(\gamma=1.8\). (**a**) Flat Al surface without riblets, (**b**) flat brass surface without riblets, (**c**) Al surface with riblets, and (**d**) brass surface with riblets. All experiments (cavitation bubble) were performed at a temperature of 20 degrees Celsius and a pressure of 101 kilopascals (kPa), which are well-known atmospheric conditions. Intercomparison of the erosion width along horizontal and vertical axes for surfaces with and without riblets in Figure 5 indicates that the width of erosion perpendicular to the riblet lines decreases, while this value parallel to the riblet lines remains similar to those observed for flat surfaces.