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52 1 0.8 = 0.30 0.40 0.49 0.6 0.59 0.69 0.88 Y/B 1.17 0.78 0.4 0.2 Flow 0 -0.5 0 0.5 X/B Figure 6.13. Initial bed shear stress distribution (N/m2) around the pier (S/B = 6, H = 0.38m, V = 0.33m/s). 1.7 Flow 1.6 1.5 S 1.4 1.3 B k sp 1.2 1.1 1 0.9 0.8 0 1 2 3 4 5 6 7 S/B Figure 6.14. Relationship between ksp (= max/max(single)) and S/B for deep water H/B > 2). on Figure 6.21 correspond to the results of the seven numer- 6.11 ATTACK ANGLE EFFECT: ical simulations. NUMERICAL SIMULATION RESULTS The correction factor for shape effect ksh is given by the following equation, which was obtained by regression of the The objective of this parametric study was to obtain the data points on Figure 6.21: relationship between the maximum bed shear stress max and the angle of attack defined as the angle between the flow -4 L direction and the pier direction (Figure 6.22). One of the ksh = 1.15 + 7e B (6.4) flume experiments was chosen to perform the numerical sim- ulation. A rectangular pier with a width of 0.061 m was placed vertically in a 1.5-m-wide flume. The velocity was 0.33 m/s, the aspect ratio of the pier was L/ B = 4, and the water depth was 0.375 m. Four different attack angles were investigated: = 15, 30, 45, and 90 degrees. Based on this data, the value of the Reynolds Number based on the width B of the rectangular pier was Re = 20130 and the Froude Num- Flow L ber based on the width of the rectangular pier was Fr = 0.4267. The bed shear stress distributions for attack angles of 15, 30, and 45 degrees are shown in Figures 6.23 to 6.25. These Figure 6.15. Problem definition for the shape effect. figures indicate that the value of the maximum bed shear