References
- Abdulrahman, A. 2008. “Direct solution to problems of open-channel transitions: Rectangular channels.” J. Irrig. Drain. Eng., 134(4), 533–537. doi:https://doi.org/10.1061/(ASCE)0733-9437 (2008)134:4(533).
- Abramowitz, M., and Stegun, I.A. (1972). Handbook of mathematical functions, Dover Publications Inc, New York. Google Scholar.
- Allen, R.F. 1980. “Steady solution for river flow.” J. Hydraulics Div., 106(4), 608–611.
- Chow, V.T. 1959. Open-channel hydraulics. Vol. 1, McGraw-Hill, New York.
- Dey, S. 1994. “No-choke flow in trapezoidal channels.” J. Eng. Mech., 120(10), 2224–2231. doi:https://doi.org/10.1061/(ASCE)0733-9399 (1994)120:10(2224).
- Dey, S. 1998. “Choke-free flow in circular channels with increase in bed elevations.” J. Irrig. Drain. Eng., 124(6), 317–320. doi:https://doi.org/10.1061/(ASCE)0733-9437 (1998)124:6(317).
- Dey, S., and Sil, S. 1998. “Choke-free flow in trapezoidal channels with change in bed elevation.” Sadhana, 23(3), 259–267. doi:https://doi.org/10.1007/BF02745741.
- Jain, S.C. 2001. Open-channel flow, John Wiley & Sons, New York.
- Liong, S.-Y. 1984. “Channel design and flow operation without choke.” J. Irrig. Drain. Eng., 110(4), 403–407. doi:https://doi.org/10.1061/(ASCE)0733-9437 (1984)110:4(403).
- Nickalls, R.W.D. 2006. “Viete, Descartes and the cubic equation.” Math. Gaz., 90(518), 203–208. doi:https://doi.org/10.1017/S0025557200179598.
- Pandey, K.K., Subramanya, K., and Kumar, N. 2018. “Exact solutions of alternate depth ratio for three exponential channels.” ISH J. Hydraulic Eng., 1–9. https://doi.org/https://doi.org/10.1080/09715010.2018.1487805
- Ranga Raju, K.G. 1993. Flow through open channels. 2nd ed, Tata McGraw-Hill, New Delhi.
- Subramanya, K. 2019. Flow in Open Channels, 5.
- Vittal, N. 1978. “Direct solution to problems of open channel transitions.” J. Hydraulics Div., 104(11), 1485–1494.
- Zucker, I.J. 2008. “92.34 The cubic equation-a new look at the irreducible case.” Math. Gaz., 92(524), 264–268. doi:https://doi.org/10.1017/S0025557200183135.