L4-1

Do the rain-drop problem from Lecture 4. (It follows)

A small raindrop falls through a cloud. It has a 1 mm radius. The viscosity of air is 180 mPoise. The density of air is 1.3 g/liter at STP.

a)What is the Reynolds number of this raindrop? (assume 10 m/s fall velocity)

b)Based on “a”, which type of drag should be more important?

c)What should be the terminal velocity of the raindrop, using quadratic drag?

d)What should be the terminal velocity of the raindrop, using linear drag?

e)Which of the previous of two answers should we use and why?

M3-1

Write a Matlab function to solve Taylor Problem 2.10 by the Euler method (Extra credit for Runge-Kutta, if you know it). Generate plots of velocity vs. time and position vs. time for the conditions of problem 2.10.

Submit your script and your plots.

IMPORTANT: The goal of this exercise is to introduce you to numerical methods. You could get an answer by using the closed form solutions for problem 2.10 and simply plot the function obtained. However, that is NOT what is being asked for here. Instead, use the Euler method to solve the differential equation numerically. This will be useful to you on future problems that do not have closed-form solutions.