An interactive introduction to MATLAB

80 additional exercises

14. 3D plotting
    The van der Waals equation gives a relationship between the pressure
    P(atm), volumeV(L), and temperatureT(K)for a real gas:

P=

nRT

V−nb−

n^2 a

V^2 ,

wherenis the number of moles, R=0.08206(L atm)/(mole K)is

the gas constant, anda(L^2 atm/mole^2 )andb(L/mole)are material

constants. Consider 1.5 moles of nitrogen (a=1.39 L^2 atm/mole^2 , and

b=0.0391 L/mole). Make a 3dsurface plot that shows the variation of

pressure (dependent variable,zaxis) with volume (independent variable,

xaxis) and temperature (independent variable,yaxis). The domains for

volume and temperature are:0.3 6 V 6 1.2 Land 2736 T 6 473 K.

15. 3D plotting
    The normal stressσxxat point (y,z) in the cross section of a rectangular
    beam, due to the applied forceFat point (yF,zF) is given by:

σxx= F

A

+F zFz

Iyy

+F yFy

Izz

,

whereIzzandIyyare the area moments of inertia defined by:

Izz=^1

12

bh^3 and Iyy=^1

12

hb^3

Determine and make a 3dsurface plot of the normal stress in the cross-

x

y

z

F

yF zF

b

h

Figure 22: Cross section of a rectangular beam

sectional area shown in Figure 22, given that:h=40 mm,b=30 mm,

yF= −15 mm,zF= −10 mm, andF= −250000 N. Plot the coordinates