520 ADV FLUID MECH I  
                      Fall Term 2003
                  
Hwk 1 (Due Sep 18)



1. In two or maximum three pages, present a brief summary of your experimental investigation of autorotation of paper strips.  Present at least one graph and use nondimensionalization.




2. Briefly describe how and why a paper strip (or card) begins to spin when it is dropped lengthwise, but flutters when dropped broadside.




3. Water bottle rocket algorithm...


A plastic toy rocket is propelled by a
water jet  forced out the nozzle
by compressed air. Your assignment is to create a model of a rocket and
determine the optimum initial water mass in the rocket. This will require
using the conservation of mass and momentum in an unsteady manner. 

Conservation of mass. The mass of the rocket changes continuously
with time as water leaves. Neglect the mass of the air.

Velocity at the nozzle exit can be calculated from the
Bernoulli equation.  For simplicity, use the steady Bernoulli equation and
ignore gravitational effects and the velocity of the air-water interface
inside the rocket. The air pressure will change continuously as the water leaves
and the air expands. We can assume that the expansion is isentropic (i.e.,
adiabatic and reversible). 

Conservation of momentum. The rocket acceleration, as a function
of time, is determined from a momentum study in the vertical direction. For simplicity
assume all the water inside the rocket has the same velocity as the rocket
itself. The momentum flux from the water is the driving force and the acceleration
of gravity opposes it.  Neglect air drag on the outside. 
The minimum information you will need is given below:



    mass of rocket = .0184 kg                                    initial gauge pressure= 5 atm


    internal volume of rocket = 75e-6 cubic meters     nozzle diameter=5.5mm



Your writeup should be approximately 3 pages long (excluding figures
and program listing or output) and contain the following items in an appropriate
order:
  1.  Problem statement--including sketch, governing equations and list of assumptions
  2.   Brief discuss solution procedure
  3.  Find the optimum original mass of water (by ``trial and error", a figure would be nice)
  4.  Conclusions and Recommendations
  5.  appendix-computer program listing (Fortran, Basic, Pascal, ...)
  6.  appendix-sample computer output
    


Consider the following additions:
  1.  Use the unsteady Bernoulli equation
  2.  Include the air-water interface velocity and gravity in the Bernoulli equation.
  3.  Add head loss to the Bernoulli equation
  4.  Add 
  air drag  to the rocket