--- title: "Khosla (analytical): uplift and d/s floor thickness" subject: "Irrigation and Drainage Engineering" chapter: 5 key: "semester_6/irrigation_and_drainage_engineering:khosla-analytical-head-regulator-floor-thickness" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-analytical-head-regulator-floor-thickness site: BCT Engineering --- # Khosla (analytical): uplift and d/s floor thickness Irrigation and Drainage Engineering · Chapter 5: Diversion Headworks - Asked in: 2065 Kartik (old course), 16 marks - Video: [Problem on Khosla Theory.](https://www.youtube.com/watch?v=2NEHgwXCa-U) — Civil Giri - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-analytical-head-regulator-floor-thickness - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-5 ## Question Using Khosla's theory (analytically), calculate the uplift pressure percentage at key points and also mention the floor thickness required at the d/s floor of canal head regulator as shown in figure below. [Figure: water level 291 m; upstream floor level 289 m with upstream pile bottom 285 m; intermediate pile bottom 282 m; downstream floor level 288 m with downstream pile bottom 281.5 m; horizontal distances 7 m, 3 m and 12 m] ## Short answer Uplift pressures at key points: C1 70.8%, C2 44.3%, E3 38.6% of head. Required floor thickness on the d/s floor is 0.95 m at start, 0.89 m at mid, and 0.83 m at end. ## Answer #### Data and assumptions Reading of the figure: u/s water level 291 m; no tail water, so the d/s water level is taken at the d/s floor level 288 m and $H = 3$ m. U/s pile at 0 m: floor 289 m, bottom 285 m ($d = 4$ m). Intermediate pile at 10 m ($7 + 3$): floor 289 m, bottom 282 m ($d = 7$ m); the d/s floor at 288 m starts just downstream of it. D/s pile at 22 m: floor 288 m, bottom 281.5 m ($d = 6.5$ m). Floor length $b = 22$ m. Floor thickness is not known, so the thickness correction is neglected. $G = 2.4$. #### Khosla's constants End piles: $\alpha = b/d$, $\lambda = \dfrac{1+\sqrt{1+\alpha^2}}{2}$, $\phi_E = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda-2}{\lambda}$, $\phi_D = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda-1}{\lambda}$ (in percent), $b = 22$ m; for the u/s pile $\phi_{D1} = 100-\phi_D$, $\phi_{C1} = 100-\phi_E$. Intermediate pile ($b_1$ from the u/s end, $b_2$ from the d/s end): $\lambda_1 = \dfrac{\sqrt{1+\alpha_1^2}-\sqrt{1+\alpha_2^2}}{2}$, $\lambda = \dfrac{\sqrt{1+\alpha_1^2}+\sqrt{1+\alpha_2^2}}{2}$, $\phi_E = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda_1-1}{\lambda}$, $\phi_D = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda_1}{\lambda}$, $\phi_C = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda_1+1}{\lambda}$. | Pile | d (m) | α | λ | φE (%) | φD (%) | |---|---|---|---|---|---| | U/s pile | 4.00 | 5.500 | 3.295 | 37.14 | 25.47 | | D/s pile | 6.50 | 3.385 | 2.265 | 46.27 | 31.14 | | Intermediate pile | d (m) | α1 | α2 | λ1 | λ | φE (%) | φD (%) | φC (%) | |---|---|---|---|---|---|---|---|---| | at 10 m | 7.00 | 1.429 | 1.714 | -0.120 | 1.864 | 70.52 | 52.06 | 34.36 | #### Pressures at the key points Pressure is expressed as a percentage of the head $H = 3.00$ m (no flow). | Point | Simple φ (%) | Corrections (%) | Corrected φ (%) | Pressure head (m) | |---|---|---|---|---| | E1 (top of u/s pile) | 100.00 | 0 | 100.00 | 3.00 | | D1 | 74.53 | - | 74.53 | 2.24 | | C1 | 62.86 | int +7.95 | 70.81 | 2.12 | | E2 | 70.52 | int -6.01 | 64.52 | 1.94 | | D2 | 52.06 | - | 52.06 | 1.56 | | C2 | 34.36 | int +9.90 | 44.26 | 1.33 | | E3 | 46.27 | int -7.63 | 38.64 | 1.16 | | D3 | 31.14 | - | 31.14 | 0.93 | | C3 (d/s end) | 0 | 0 | 0 | 0 | Corrections: int = mutual interference, $19\sqrt{D/b'}\,\dfrac{d+D}{b}$, positive at C of the u/s pile and negative at E of the d/s pile of each pair ($D$ = depth of the neighbouring pile below the floor level at the pile being corrected, $b'$ = distance between the two piles; e.g. at $C_2$: $D = 289-281.5 = 7.5$ m, $d = 7$ m, $b' = 12$ m). The D points are not corrected. #### Floor thickness Unbalanced head $h$ = hydraulic-gradient level at the floor $-$ floor top level; required thickness $t = \dfrac{h}{G-1}$ with $G = 2.40$ (on the d/s floor the HGL is taken as a straight line from $C_2$ to $E_3$). | Location | x (m) | φ (%) | HG level (m) | Floor top (m) | Unbalanced head (m) | Required t (m) | Provided t (m) | Check | |---|---|---|---|---|---|---|---|---| | Start of d/s floor (C2) | 10 | 44.26 | 289.33 | 288.00 | 1.33 | 0.95 | - | provide at least 0.95 | | Mid d/s floor | 16 | 41.45 | 289.24 | 288.00 | 1.24 | 0.89 | - | provide at least 0.89 | | E3 (d/s end) | 22 | 38.64 | 289.16 | 288.00 | 1.16 | 0.83 | - | provide at least 0.83 | #### Exit gradient $$ G_E = \frac{H}{d}\cdot\frac{1}{\pi\sqrt{\lambda}} = \frac{3.00}{6.50}\times\frac{1}{\pi\sqrt{2.265}} = 0.0976\ (\approx 1/10.2) $$ Permissible (assumed) $= 0.2000$. Safe (less than the permissible value). **Answer:** Uplift pressures at the key points are in the table above (percent of $H$ = 3 m). The d/s floor of the regulator needs about 0.95 m thickness at its start (just d/s of the intermediate pile), reducing to about 0.9 m at mid-length and 0.83 m at the d/s end; provide at least these values. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Water level 291 m with no tail water and d/s floor at 288 m. What is H? A. 1 m B. 5 m C. 3 m D. 2 m Answer: C. The d/s water level is taken at the d/s floor level 288 m, so H = 291 - 288 = 3 m. (Key point: Head with no tail water) 2. Distances are 7 m, 3 m and 12 m. Where is the d/s pile measured from the u/s pile, giving floor length b? A. 12 m B. 15 m C. 22 m D. 10 m Answer: C. b = 7 + 3 + 12 = 22 m, with the intermediate pile at 10 m. (Key point: Intermediate pile position) 3. Why is the floor thickness correction neglected here? A. It is always zero for regulators B. Only slope corrections are valid in analytical solutions C. Thickness has no effect on pressures D. Floor thickness is not given Answer: D. With the thickness unknown, the correction cannot be applied, so only interference is included. (Key point: Thickness correction omitted) 4. Required thickness is 0.55 m, 0.95 m and 0.80 m at three locations. What should the d/s floor satisfy? A. At least the largest, about 0.95 m B. At least the smallest, 0.55 m C. The average, 0.77 m only D. 0.80 m at the mid point Answer: A. The floor must resist uplift everywhere, so the governing (maximum) requirement of about 0.95 m controls. 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