Matlab: User Defined Functions

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Matlab User Defined Functions

• The objectives for this tutorial are to review
  what has been covered to this point and to
  introduce the use of user defined functions.
  Again, please do not treat the code examples as a
  typing exercise. Be certain that you understand
  the syntax and purpose of each program line. The
  code examples and assignment for this tutorial
  are very similar to what you will be expected to
  do in next weeks exam.

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• We will start the tutorial by illustrating the
  process for developing a solution to last weeks
  assignment
• For the assignment, you were given the formula
  for calculating the pressure drop in a pipe flow
  and a set of sample calculations

• Steps for program creation
• Workspace and console initialization
• Program constants
• Sample calculation
• Implement array calculations with a for or
  while loop
• Add plotting functions
• In the program creation process, it is important
  to develop the program incrementally and to fully
  debug and verify each addition before going
  further

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clear clc format compact close all

• Steps for program creation
• Workspace and console initialization
• create a new m-file with this code
• save the file as pipe1.m execute it
• verify that it runs without errors
• Program constants
• add this program segment save changes
• verify that the program runs with the
  modifications without errors and that the
  variables and correct values show up in the
  workspace
• Sample calculation
• add this program segment save changes
• verify that the program segment executes without
  errors and generates the correct result, dp
  1.87 x 105

f 0.020 rho 998 L 1000 D 0.5 mdot
600
A piD2/4 V mdot/(rhoA) dp
f(L/D)rhoV2/2 disp(dp)
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clear clc format compact close all f
0.020 rho 998 L 1000 D 0.5 mdot 600

• Steps for program creation
• This code has been entered and validated
• Delete the sample calculation and add the code to
  determine the number of passes through the for
  loop and the increment in mass flow rate between
  loops
• enter and save the changes
• execute the code and verify the results
• Now add the code for the for loop
• enter and save the changes
• execute the code and verify the array results are
  created as expected
• Add the code for the plot
• enter and save the changes
• execute the code and verify that the plot is
  created as expected
• be certain that you understand the syntax and
  purpose of each program statement

A piD2/4 V mdot/(rhoA) dp
f(L/D)rhoV2/2 disp(dp)
A piD2/4 n 1000 mdotMin 0 mdotMax
800 dMdot (mdotMax - mdotMin)/(n-1)
for i 11n mdot(i) (i-1)dMdot V
mdot(i)/(rhoA) dp(i) f(L/D)rhoV2/2 en
d
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clear clc format compact close all f
0.020 rho 998 L 1000 D 0.5 A
piD2/4 dPmax 500000 dMdot 10 i
1 mdot(i) 0 dp(1) 0 while (dp(i) lt
dPmax) i i1 mdot(i) (i-1)dMdot
V mdot(i)/(rhoA) dp(i)
f(L/D)rhoV2/2 end plot(mdot,dp) title('Pipe
Flow Pressure Drop') xlabel('mass flow rate
(kg/s)') ylabel('pressure drop (Pa)')
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clear clc format compact close all f
0.020 rho 998 L 1000 D 0.5 A
piD2/4 dPmax 500000 dMdot 10 i
1 mdot(i) 0 dp(1) 0 while (dp(i) lt
dPmax) i i1 mdot(i) (i-1)dMdot
V mdot(i)/(rhoA) dp(i)
f(L/D)rhoV2/2 end plot(mdot,dp) title('Pipe
Flow Pressure Drop') xlabel('mass flow rate
(kg/s)') ylabel('pressure drop (Pa)')

• This is the second version of the program which
  uses a while loop save it as pipe2.m
• Create and test this program incrementally as you
  did for the first program
• workspace initialization
• variable initialization
• initialization required for the first pass
  through the while loop
• while loop calculations
• plot the results
• Be certain that you understand the syntax and
  function of each program statement before going
  further in the turial

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function dp PressureDrop (mdot) dp
PressureDrop (mdot) dp - pressure drop (Pa)
mdot - mass flow rate (kg/s) f 0.020 rho
998 L 1000 D 0.5 A piD2/4 V
mdot/(rhoA) dp f(L/D)rhoV2/2

• Notes
• the first word on the first line (function header
  line) must be function this is a keyword for
  matlab
• next on the header line
• return variable (dp)
• equals sign ()
• function name (PressureDrop)
• parameter list (mdot) contained in parentheses
• the lines beginning with are comments used for
  documentation
• when the function executes, it will have its own
  private workspace for variable storage required
  variables must be defined in the function file
• calculations ending with the evaluation of the
  function return value that was specified in the
  header line (dp)

• Now we are going to modify the two programs to
  use a user-defined function to calculate the
  pressure drop rather than including the
  calculations directly within the program
• Create a new m-file which contains the code shown
  above
• Save the file as PressureDrop.m (this will be the
  default choice)

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clear clc format compact close all n
1000 mdotMin 0 mdotMax 800 dMdot
(mdotMax - mdotMin)/(n-1) for i 11n
mdot(i) (i-1)dMdot dp(i)
PressureDrop(mdot(i)) end plot(mdot,dp) title('
Pipe Flow Pressure Drop') xlabel('mass flow rate
(kg/s)') ylabel('pressure drop (Pa)')

• Modify pipe1.m as shown to use the new function
  file PressureDrop.m
• Notes
• most of the variable initialization has been
  deleted since the variables are only needed with
  the function
• the function is called with the syntax that was
  defined in the function header line
• the function name is PressureDrop
• it requires one parameter, the mass flow rate
  mdot
• it returns a single result dp
• Save and execute the modified program
• Verify that the results are the same as before
• Be certain that you understand the syntax and
  function of each program line

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clear clc format compact close all dMdot
10 dPmax 50000 i 1 mdot(i) 0 dp(1)
0 while (dp(i) lt dPmax) i i1
mdot(i) (i-1)dMdot dp(i)
PressureDrop(mdot(i)) end plot(mdot,dp) title('
Pipe Flow Pressure Drop') xlabel('mass flow rate
(kg/s)') ylabel('pressure drop (Pa)')

• Modify pipe2.m to use the function PressureDrop.m
  as shown
• Save the changes, execute the program, and verify
  the same results are produced

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• The aerodynamic drag on an aircraft may be
  calculated from

• Sample calculations at a speed of 65 m/s from
  Mathcad and Matlab are shown at left
• Create 2 programs to calculate and plot the
  variation of drag with flight speed with the
  following requirements
• both programs should use a function drag.m which
  takes velocity as an input parameter and returns
  the drag
• drag1.m use for loop to calculate and plot
  drag for 100 values of velocity with 20 m/s lt V lt
  100 m/s
• drag2.m use a while loop to calculate and
  plot drag for V gt 20 m/s and D lt 2.5 kN with
  velocity increments of 2 m/s
• Sample results are on the next slide

clear clc format compact close all CD0
0.025 AR 8 S 16 W 13000 rho 1.225 V
65 CL W/(0.5rhoV2S) CD CD0
CL2/(piAR) D 0.5rhoV2CDS
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