PLEASE ANSWER QUESTION 3 (4 as well if you want)

Upon graduation, you have been hired by the Department of Watershed Management of the newly incorporated city of Buzztown, GA, a thriving community located near lake Lanier. The US Army Corps of Engineers has just given the city permission to use the lake as its water supply, and your department is tasked with the design of the steel pipe that will deliver the water. Your specific assignment is to determine the diameter of the pipe, based on the present Buzztown demand for water, which requires a flow rate of 10,000 gallons per minute. Theoretical background Fully developed flow in a pipe is governed by an energy balance equation of the form 2 2 where point 1 represents one end of the pipe (in our case, the surface of the lake) and point 2 represents the other end (the city), p is the pressure, V is the average velocity of the fluid (water), z is the elevation, is the fluid density, g is the acceleration of gravity, and his the head loss, which represents the irreversible transfer of mechanical energy to thermal energy in the flow. 1Lake Buzztown Pipe 2 Referring to the figure above, the pressures at points 1 and 2 are the same, the average velocity at the surface of the lake is zero, the elevation z2 is the reference elevation defined as zero, and the velocity at point 2 is the average velocity in the pipe V. Thus, the energy balance simplifies to Copyright 2019 Francois M. Guillot. All Rights Reserved v2 2g The head loss is given by the following equation hi- f pipe length and The friction factor depends on the nature of the flow, and thus on the value of the Reynolds number, a dimensionless quantity defined as VD Re =--, where vis the kinematic viscosity of the fluid. For laminar flow, Re s 2100, and the friction factor is simply given by 64 For turbulent flow, Re > 2100, and the friction factor obeys the so-called Colebrook equation 1D 2.51 103.7 Ref - -2logio where is the pipe roughness. Note that in equation (6), fis an implicit variable, and the equation must therefore be solved numerically using root-finding techniques The goal of this project is to use this information to determine the minimum pipe diameter D required to deliver a flow rate Q of 10,000 gpm; the flow rate is defined as where A is the cross-sectional area of the pipe. The following data is available: Pipe length, L (km Pipe roughness, (mm) Lake elevation, z1 (m Kinematic viscosity of water, v (m2/s) Acceleration of gravit 2 0.2 30 1.12 x 10-6 9.807 1) Write a generic (that is, non-problem specific) MATLAB function that implements the Newton- Raphson method. The function should have the form function xr NewtonRaphson (F,dFdx , xi,Es, imax), - where F is a function handle that defines the root-finding problem F(x) 0, dFdx is a function handle for the derivative of F, xi is the initial guess, Es is the stopping criterion for the absolute value of the approximate relative error (NOT the % error), and imax is the maximum number of allowable iterations. The value of the root is returned in the output argument xr 2) Write a function to compute the friction factor for the pipe flow. The function should have the form function f - ffactor (Re,r), where f is the friction factor, Re is the Reynolds number and r is the pipe roughness ratio &/D. he acceptable ranges for the two input arguments are 0