Question Sailboat Mast
The following equation be used to model the deflection sailboat mast subject b
wind force:
dy-56-(2-2)
2EI
where Eis the modulus of clasticity. Lthe mast length, Ithe second moment of area and
f(z) is the wind force depending the height andi given by:
f(z)=
Calculate the deflection of the mast using the 4th order Runge Kutta method with y=0
and "=0 ==0 Perform the first analysis with divisions of the length Ltc define the
step (see the table below for your assigned value f n). Repeat the analysis with twice the
number of divisions (i.e. 2n divisions) and produce graph of the deflection and
curvature the height for the two cases.
Number of
Data Set
E(N/m²)
((m)
L(m)
Divisions, n
1.08E+OS
0.05
29
1.34E+OS
0.03
42
1.18E+OS
0.04
41
1.01E+OS
005
1.25E+OS
0.06
10
6
1.32E+OS
0.07
41
1.50E+OS
0.08
19
1.05E+OS
0.04
39
1.10E+O8
0.05
14
10
1.44E+O8
0.06
35
10
1.05E+OS
0.04
40
12
1.10E+OS
0.06
36
1.05E+OS
0.07
28
14
1.25E+OS
0.05
30
Source Numerica Mcthods for Engineers Chapra
Question Hanging Cable
It can be shown that the curve y(x) an inextensible flexible homogeneous cable
hanging between two fixed points obtained by solving the following equation:
where the constant depends on the weight This curve called a "catenary ("chain in
Latin) Find and plot y(x). assuming given value for k and those fixed points are (-1,0)
and (1,0) in a vertical ry-plane. using the 4th order Runge Kutta method with step of
0.025.
N.B. you should use reasonable estimate for the initial slope and modify the
spreadsheet until the solution is correcti.c the slope the midpoint zero.
Data Set
10
0.6
os
1.3
1.3
15
07
1.2
11
1.45
12
1.25
1.15
14
09
Source Numerica Methods for Engineers Chapra
Question Carbon Monoxide Concentrations in a Restaurant
Qins Cine
Cing
Qouts
Qinx
+ Kitchen
Eating Area
- Qouta
Grill Load
EL
Wagill
Overhead view oftwo a restaurant Th volumetric
mising The gillloads add carbon
momoride
airflow
Indoor pollution deals with air contamination in closed spaces such a the restaurant
shown here. Suppose you are designing ventilation system for the restaurant which
consists of kitchen larger cating areal The kitchen has source of carbon monoxide
from faulty grill The differential equation describing the variation of carbon
monoxide with time in the kitcheni performing mass balance
where Cx deating area respectively
the diffusive between the two while Qouts and Qoute are determined by
calculation
You should for the area and then solve both equations
with the Runge method should produce plot of the temporal variation
of
carbon monoxide You should assume the initial values of
Cgand C,
Cing
Cing
Data St
Wgrill
500
100
600
120
550.0
100
400.0
800.0
20
1000.0
25
750.0
20
500.0
25
600.0
120
30
650.0
400.0
550.0
580.0
14
680.0
125
30
Vkinches V1=10x 8, 3.5 280m
V¿=10x 24x3.5=840m
25m'/h
Source Numerical Methods for Engineers Chapra

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h = 1; % time step
T = 0:h:50; % timespan
n = length(T);

C = [0, 0]; % initial conditions

Ck = zeros(n,1);
Ce = zeros(n,1);

for i=1:n-1
t = T(i);
k1 = h*f(t,C);
k2 = h*f(t+h/2, C+k1/2);
k3 = h*f(t+h/2, C+k2/2);
k4 = h*f(t+h, C+k3);
C = C + (k1+2*k2+2*k3+k4)/6;
Ck(i+1) = C(1);
Ce(i+1) =...

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