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please solve with matlab or explain process thank you ! There exist several formulas that have been devised to calculate velocities in open-channel flows under
please solve with matlab or explain process thank you !
There exist several formulas that have been devised to calculate velocities in open-channel flows under uniform conditions, such as Chezy's, and Manning's, among others. These formulas express the flow velocity in terms of the slope of energy grade line, properties of the cross section (wetted area and perimeter), and resistance/conveyance coefficients. In particular, Manning's equation reads: v=nKnRh2/3sf1/2 where v is the cross-sectionally-averaged velocity, Kn is a unit-conversion factor, Rh is the hydraulic radius (the ratio of the area and the wetted perimeter), Sf is the slope of the energy grade line, and n is a resistance coefficient - Manning's n. The discharge (volumetric flow rate) can be computed as the product of the wetted area and the velocity; thus, Manning's equation is used for the design of open channels. When the unknown is the water depth, the above equation becomes in general implicit. For a trapezoidal cross section, for example, the wetted area and perimeter can be expressed as functions of the water depth, and the water depth for uniform flow conditions (the "normal depth") is obtained via an iterative procedure. a) Please develop a flow chart for the bisection method used to calculate the normal depth for a trapezoidal channel. b) Compute the normal depth for a trapezoidal channel, using the methods of bisection, Newton-Raphson, and fixed point, given the following information for an asphalt channel: Q=300ft3/s;S=0.0015; lateral sides angle =50 degrees; bottom width =6ft. Please discuss suitable values of the normal depth to start the computations, and select three valuesStep by Step Solution
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