ABE 325 2021 HWK Channel Stability Restoration and Water Supply - KEY1

ABE 32500 Soil and Water Resources Engineering 3 4. (3 pts) Channel Restoration - Compute the required diameter of rock material to form a riffle in a stream with a width to depth ratio of 8:3. The bankfull depth is 1.3 m and the slope of the stream is 0.01 m/m. What would be the diameter required if the channel slope was 0.001 m/m? Width to depth ratio should be based on a stable riffle, so it reflects the conditions of the channel where we have been asked to make our calculations. Start by calculating the width of the channel for the given bank full depth: t = 8 / 3 × 1.3 m = 3.47 m Calculate the hydraulic radius for a parabolic stream channel: ࠵? = 2࠵?࠵? 3 = 2(3.47 ࠵?)(1.3࠵?) 3 = 3.01 ࠵? 4 ࠵? = ࠵? + 8࠵? 4 3࠵? = 3.47 ࠵? + 8(1.3 ࠵?) 4 3(3.47 ࠵?) = 4.77 ࠵? Note: The equation for P for a parabolic cross-section is wrong in the 5 th Edition textbook. ࠵? = ࠵? ࠵? = ࠵?. ࠵?࠵? ࠵? ࠵? ࠵?. ࠵?࠵? ࠵? = ࠵?. ࠵?࠵?࠵? m R can also be approximated using ࠵? = ࠵?࠵? ࠵? = ࠵?(࠵?.࠵?࠵?) ࠵? = ࠵?. ࠵?࠵?࠵? ࠵? Use equation 10.10 to estimate the shear stress from the defined flow: ࠵? ࠵? = ࠵?࠵?࠵? = (࠵?࠵?࠵?࠵?)(࠵?. ࠵?࠵?࠵? ࠵?)(࠵?. ࠵?࠵?) = ࠵?࠵?. ࠵? N/m 2 ( exact ) or = ࠵?࠵?. ࠵? N/m 2 (approx) At incipient motion, the critical shear stress must be equal to the hydraulic shear stress of the stream. Assuming a particle density of 2650 kg/m 3 , solve for the minimum diameter from Equation 10.11 as: ࠵? = ࠵? ࠵? ࠵?࠵?(࠵? ࠵? − ࠵?) = ࠵?࠵?. ࠵? (࠵?. ࠵?࠵?࠵?)(࠵?. ࠵?࠵?)(࠵?࠵?࠵?࠵? − ࠵?࠵?࠵?࠵?) = ࠵?. ࠵?࠵?࠵? m = ࠵?࠵? mm ( exact ) or = ࠵?. ࠵?࠵?࠵? ࠵? = ࠵?࠵?࠵? ࠵?࠵? (approx) If the slope is reduced to 0.001 m/m then the size of the particle can be reduced to: D s=0.001 = ࠵?. ࠵?࠵?࠵?࠵? m = ࠵?. ࠵? mm ( exact ) or = ࠵?. ࠵?࠵?࠵?࠵? ࠵? = ࠵?࠵?. ࠵? ࠵?࠵? (approx)