--- title: "Sewer at 2/3 depth, 0.70 m³/s" subject: "Sanitary Engineering" chapter: 3 key: "semester_6/sanitary_engineering:sewer-2-3-depth-0p70" source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sewer-2-3-depth-0p70 site: BCT Engineering --- # Sewer at 2/3 depth, 0.70 m³/s Sanitary Engineering · Chapter 3: Design and Construction of Sewers - Asked in: 2073 Bhadra, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sewer-2-3-depth-0p70 - Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-3 ## Question What will be the diameter of a circular concrete sewer carrying 2/3rd depth at the peak discharge of 0.70 m³/s laid in a gradient of 1 in 1000? Also check whether it is safe for non-scouring velocity or not. Assume Manning's 'n' as 0.012. ## Short answer Full-flow discharge Q_f = 0.70/0.7839 = 0.893 m³/s, giving D = 1.032 m (adopt 1050 mm). At peak flow, velocity is 1.20 m/s, which is below the non-scouring limit of 3 m/s, so safe. ## Answer #### Given Peak discharge $Q=0.70$ m³/s, $S=1/1000$, $n=0.012$, depth of flow $d/D=2/3=0.667$. For $d/D=0.6667$: $\theta = 2\cos^{-1}(1-2d/D)=218.94^\circ$, $A/A_f=\dfrac{\theta-\sin\theta}{2\pi}=0.7082$, $R/R_f=1-\dfrac{\sin\theta}{\theta}=1.1645$, so $v/v_f=(R/R_f)^{2/3}=1.1069$ and $Q/Q_f=(A/A_f)(v/v_f)=0.7839$ (n taken constant). #### Size of the sewer Discharge when running full: $$ Q_f=\frac{Q}{Q/Q_f}=\frac{0.7000}{0.7839}=0.8930\ \text{m}^3/\text{s} $$ Manning's formula for a full circular pipe, $Q_f=\dfrac{0.3117}{n}D^{8/3}S^{1/2}$, with $S=0.00100$ and $n=0.012$: $$ D=\left(\frac{Q_f\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{0.8930\times0.012}{0.3117\times0.03162}\right)^{3/8}=1.032\ \text{m} $$ Adopt the next standard size, **D = 1050 mm**. #### Check of velocity and capacity For the adopted pipe: $v_f=\dfrac{0.3969}{n}D^{2/3}S^{1/2}=1.081$ m/s and $Q_f=0.9355$ m³/s. $$ \begin{aligned} v&=v_f\times(v/v_f)=1.081\times1.1069=1.20\ \text{m/s}\\ Q_{capacity}&=Q_f\times(Q/Q_f)=0.9355\times0.7839=0.7333\ \text{m}^3/\text{s}\ (\ge 0.7000) \end{aligned} $$ The velocity at maximum flow, 1.20 m/s, lies between the minimum (0.6 m/s) and the maximum non-scouring limit (3.0 m/s), so it is satisfactory. For non-scouring, the velocity must not exceed the maximum permissible value (about 3 m/s for concrete sewers), and for self-cleansing it should be at least 0.6 m/s. The velocity is 1.20 m/s at peak flow, which is within 0.6-3.0 m/s, so the sewer is **safe against scouring** and also self-cleansing at peak flow. (At lower flows the velocity falls, so flows below about 0.058 m³/s give less than 0.6 m/s, and the minimum flow should be checked separately.) **Answer: D = 1050 mm (computed 1.032 m); v = 1.20 m/s < 3 m/s, so safe.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. At d/D = 2/3 (constant n), Q/Q_f is A. 0.7839 B. 0.667 C. 0.7082 D. 1.1069 Answer: A. Q/Q_f = 0.7082 x 1.1069 = 0.7839. (Key point: Discharge ratio at 2/3 depth) 2. How is the diameter obtained for peak flow 0.70 m3/s? A. Put Q = 0.70 directly into the full-pipe formula only B. Q_f = 0.70/0.7839 = 0.893 m3/s, then Manning's full-pipe formula gives D = 1.032 m C. Q_f = 0.70 x 0.7839 then D from the formula D. D = 2/3 x 0.70 m Answer: B. The peak flow occurs at 2/3 depth, so the full capacity must be larger than 0.70. (Key point: Sizing steps) 3. What is the maximum permissible velocity for non-scouring in concrete sewers (as used here)? A. About 0.6 m/s B. About 1 m/s C. About 3 m/s D. About 10 m/s Answer: C. Velocities above about 3 m/s scour the sewer invert; 0.6 m/s is the self-cleansing minimum. (Key point: Non-scouring limit) 4. The velocity at peak flow is 1.20 m/s. Conclusion? A. Unsafe, since it exceeds 0.6 m/s B. Unsafe, since it is below 3 m/s C. Cannot decide without minimum flow D. Safe against scouring and also self-cleansing at peak flow Answer: D. 1.20 m/s lies between 0.6 and 3.0 m/s; minimum flows should still be checked separately. 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