By Chyan-Deng Jan
Gradually-varied circulation (GVF) is a gentle non-uniform stream in an open channel with sluggish alterations in its water floor elevation. The evaluate of GVF profiles less than a selected movement discharge is essential in hydraulic engineering. This booklet proposes a unique method of analytically remedy the GVF profiles by utilizing the direct integration and Gaussian hypergeometric functionality. either normal-depth- and critical-depth-based dimensionless GVF profiles are awarded. the unconventional process has laid the root to compute at one sweep the GVF profiles in a chain of maintaining and adversarial channels, that could have horizontal slopes sandwiched in among them.
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Extra info for Gradually-varied Flow Profiles in Open Channels: Analytical Solutions by Using Gaussian Hypergeometric Function
Wiley, New York Zaghloul NA (1990) A computer model to calculate varied flow functions for circular channels. Adv Eng Softw 12(3):106–122 Zaghloul NA (1992) Gradually varied flow in circular channels with variable roughness. Adv Eng Softw 15(1):33–42 Zaghloul NA (1998) Hydraulic exponents M and N for gravity flow pipes. Adv Water Resour 21(3):185–191 Zaghloul NA, Anwar MN (1991) Numerical integration of gradually varied flow in trapezoidal channel. 1 Introduction The literature survey as shown in Chap.
The assumption of constant hydraulic exponents is satisfactory in the evaluation the GVF profiles in most rectangular and trapezoidal channels. However, the hydraulic exponents may vary appreciably with respective to the flow depth when the channel section has abrupt changes in geometry of cross section or is topped with a gradually closing crown, such as circular channels. An innovative method to get analytical solution of the GVF equation by using the direct integration method and the Gaussian hypergeometric functions will be introduced in the next chapters.
Evaluated the two indefinite integrals in two steps. 5, 4 and 5 for each case of sustaining and adverse slopes, thereby obtaining the ETF-based solution of the first integral for each N -value studied. Upon acquiring all the ETF-based solutions of the first integrals for such N -values studied, Gill proceeded to evaluate the second integral by transposition to a form of the VFF of a composite variable with a modified parameter expressed in terms of M and N , by which he was able to express the second integral in the form of the first integral.
Gradually-varied Flow Profiles in Open Channels: Analytical Solutions by Using Gaussian Hypergeometric Function by Chyan-Deng Jan