Water Rocket
Computer Model Problems
Here is the first Water
Rocket Computer Model Problem.
The screen shot below is from the 3D optimisation of a
250 ml water rocket with launch
tube and T nozzle.
I have included the file details so that you can
reproduce it yourself to investigate the peculiar maxima
displayed in the screen shot on the right.
It is a plot of speed (velocity along the axis of the
rocket  in this case, the launch angle is 90 degrees so
effectively, it is vertical velocity) as the output
variable with Mass of Water (20g to 140g) on the Y axis
and Mass of Rocket Empty (10g to 150g) on the X axis.
It is clear that the highest speeds will be gained
from the lowest combined weight of water and rocket, as
indeed they are as displayed in the bottom left of the
screen shot.
Variables 
Water Rocket Computer Model Problem
01 

Rocket 
Mass of Rocket Empty 
25 

g 
Capacity of Pressure Vessel 
269 

cm^{3} 
Rocket Diameter 
5.7 

cm 
Rocket Coeff of Drag 
0.56 


Nozzle Diameter 
21.75 

mm 
Constant K for nozzle 
0.16 


[X] Launch Tube in use 
Used 


Duration of air impulse 
1000 

ms 
[ ] Parachute in use 
Not Used 


Launch
Tube 
Length 
8 

cm 
External Diameter 
21.5 

mm 
[X] Hollow Launch Tube 
Used 


Wall Thickness 
2 

mm 
Length of Tube Empty 
8 

cm 
Distance of Vent from End 
0 

cm 
[X] TNozzle in use 
Used 


TNozzle Diameter 
1.3 

mm 
Parachute 
Diameter
opened out flat 
3 

m 
Parachute
Coeff of Drag 
0.9 


Deploy ()
Apogee.( ) Timer 
4 

s 
Delay in
opening 
2 

m 
Initial 
Mass of Water 
64 

g 
Pressure in Vessel 
94.3 

psi 
Height 
1.3 

feet 
Angle of Elevation 
90 

° 
Speed at Angle of Elevation 
0 

m/s 
Temperature 
20 

C 
Environmental 
Gamma of Gas in Rocket 
1.402 


Density of Gas in Rocket 
1.293 

kg/m^{3} 
Density of Liquid in Rocket 
998 

kg/m^{3} 
Acceleration due to Gravity 
9.81 

m/s^{2} 
Atmospheric Pressure 
1013 

mBar 
Density of Air at STP 
1.293 

kg/m^{3} 
The problem here
is . . . 
1. 
to
find an explanation for the large central
maximum; and, 
2. 
the
maximum at the top edge towards the left. 
If you give up or you think you know what is going on,
look at the answers.
