Please solve using math lab
The terminal velocity of a spherical particle falling through a fluid is given by the equation:
4g(p,-p)D 3CpP
Where The coal particle density Pp = 1800 kg/m3 Density of water p = 994.6 kg/m3 Gravitational constant g = 9.80665 m/s2 Cp = the coefficient of drag D, = the diameter of the coal particle (m) The viscosity = 8.931 x 10-4 kg/m-s
The coefficient of drag is a function of the particle Reynolds number and is given by
D,vtP Re=-
1+0.14Re0.7
For a given particle of coal falling through water, find the terminal velocity vt (m/s) using the Matlab fzero function for 4 separate particle diameters. Set up a while loop in which the particle diameter is varied as follows: 0.15 mm, 0.20 mm, 0.25 mm & 0.30 mm. (Hint you must convert from mm to m)
Use the fzero function within the loop to find v by passing the particle diameter and an initial guess (use vt = 0.03 m/s) to the function file for each iteration. Define and save the function file as terminal.m to solve the problem
Within the loop save the values of terminal velocity vt,and particle diameter Dp in a new array and plot the terminal velocity as a function of particle diameter for each value of the diameter without using the hold on command. Also print out the terminal velocity using an fprintf statement in the following format:
The terminal velocity is * ***** for a * ** mm particle.
