Title 11 Flow in Open Channels.pdf ✅

• Chezy Coefficient in S.I. Units • Kutter’s Formula C = 23 + 1 n + 0.00155 S 1+ n √R (23 + 0.00155 S ) • Bazin’s Formula C = 87 1 + m √R • Manning’s Formula C = R 1 6 n • Darcy-Weisbach Formula C = √ 8g f Specifically for Manning’s formula, v = C√RS v = R 1 6 n (RS) 1 2 v = 1 n R 2 3S 1 2 For the discharge of the channel, Q = A n R 2 3S 1 2 3. Boundary Shear Stress. The shearing stress on the channel caused by the flow can be computed by: τ = γRS Where: V = velocity of flow C =Chezy coefficient R = hydraulic radius S = slope of energy gradient 4. Seepage along Sides. J = Area of seepage diagram Where: J = seepage in m3 /s per m C = seepage coefficient For minimum seepage, the base width is: b = 4d tan θ 2 where: d = depth of flow θ = side slope (symmetrical)
5. Most Efficient Sections. The most efficient cross-sections cover the most area with the smallest wetted perimeter. The proportions can be derived from differential calculus. • Rectangular Section (b = 2d) b = 2d R = d 2 • Trapezoidal Section (half-hexagon) θ = 30° R = d 2 • Triangular Section (right triangle) θ = 90° R = d√2 4 • Circular Section (semicircle) R = D 4 h = 0. 810D (maximum velocity) h = 0. 938D (maximum discharge)
6. Stages of Flow. Type of Flow Subcritical Critical Supercritical Depth > dc dc < dc Velocity < vc vc > vc Slope < Sc Sc > Sc Specific Energy < 3 2 dc 3 2 dc > 3 2 dc Froude Number < 1 1 > 1 • Critical Velocity vc = √gm • Froude Number Froude number is the ratio of the actual velocity to the critical velocity. FN = v √gm • Critical Slope From Manning’s formula, vc = 1 n R 2 3Sc 1 2 Sc 1 2 = nvc R 2 3 Sc = n 2vc 2 R 4 3 • Area and Flow at Critical Level From the Froude number, FN = v √gm 1 = Q A √ Ag B √ Ag B = Q A Ag B = Q 2 A2 Q 2 g = A 3 B 7. Non-Uniform Flow. Hydraulic jump is a sudden change in depth due to a change in stage of flow. Apron is the distance covered by the sections in which the jump occurs.