Arrays have incompatible sizes for this operation.

I am trying to plot my graph for 4 given values in one graph for this matlab code.

format long
% Given Values
T   = 429.65; % K - Given Temperture
P = 99.6 ; % kPa - Pressure

% Specific Diameters given
Dp1 = 0.01:0.01:10;
Dp = Dp1 * 10^-6;

%Actual particle Density given.
Pp = 1260; % kg/m^3

% Standard Temperture and Mu at SATP
Ts0 = 298.15; % K
Ts  = 110.4; % K
Rair = 0.287; % kJ / kg * K
Mu_s = 1.849*10^-5; % kg/m*s
g = 9.81;

% Calculate Air Density
Pa = P / (Rair * T);
Mu = Mu_s * (T/Ts0)^(3/2) * (Ts0+Ts)/(T+Ts);


% lamda - Mean free path
lamda1 = (Mu/0.499) * sqrt(pi/(8*Pa*P*1000)); % Unit m
lamda = lamda1 *10^6; % Unit Mu*m

% Knudsen number
Kn = lamda1 ./ Dp;

% Cunningham Correction Factor
C = 1 + Kn .* (2.514+0.80.*exp(-0.55./Kn));
% -----------------------------------------------------------------
% Given
Df = [5, 10, 15, 20] *10^-6; % Given in microns change to m
U0 = 0.225; % m/s
e = 0.875; % fraction
L = 0.00335; % m

%intial
Kb = 1.381*10^-23

% Calvert & Englund
Stk = ((Pp-Pa).*Dp.^2.*(U0./e)) ./ (18.*Mu.*Df)

nfDpCE = ((Stk)./(Stk+0.425)).^2

%Cheng

Dap = (Kb.*T.*C)./ (3.*pi.*Mu.*Dp)

alpha = 1 - e;

Kk = -0.5.*log(alpha)+alpha-0.25.*alpha.^2-0.75

Pe = (Df.*U0)./(Dap)

nfDpCheng = 2.92 .* ((1-alpha)./Kk).^(1./3).*Pe.^(-2./3);

nfDp = nfDpCE + nfDpCheng

Lc = (pi./4).*(e./(1-e)).*(Df./nfDp)

nDp = (1 - exp(-L./Lc) )*100

% ========================================================================

Dp2= log(Dp1*10^1);
plot(Dp2,nDp)

This error shows up and I couldn't be able to fix it can you please assist me on this, thank you

Arrays have incompatible sizes for this operation.

Error in HW14Q2 (line 45)
Stk = ((Pp-Pa).*Dp.^2.*(U0./e)) ./ (18.*Mu.*Df)

Answer 1

[Walter Roberson]

format long
% Given Values
T   = 429.65; % K - Given Temperture
P = 99.6 ; % kPa - Pressure

% Specific Diameters given
Dp1 = 0.01:0.01:10;
Dp = Dp1 * 10^-6;

%Actual particle Density given.
Pp = 1260; % kg/m^3

% Standard Temperture and Mu at SATP
Ts0 = 298.15; % K
Ts  = 110.4; % K
Rair = 0.287; % kJ / kg * K
Mu_s = 1.849*10^-5; % kg/m*s
g = 9.81;

% Calculate Air Density
Pa = P / (Rair * T);
Mu = Mu_s * (T/Ts0)^(3/2) * (Ts0+Ts)/(T+Ts);


% lamda - Mean free path
lamda1 = (Mu/0.499) * sqrt(pi/(8*Pa*P*1000)); % Unit m
lamda = lamda1 *10^6; % Unit Mu*m

% Knudsen number
Kn = lamda1 ./ Dp;

% Cunningham Correction Factor
C = 1 + Kn .* (2.514+0.80.*exp(-0.55./Kn));
% -----------------------------------------------------------------
% Given
Df = [5, 10, 15, 20] *10^-6; % Given in microns change to m
U0 = 0.225; % m/s
e = 0.875; % fraction
L = 0.00335; % m

%intial
Kb = 1.381*10^-23

Kb = 
     1.381000000000000e-23

% Calvert & Englund
whos

  Name        Size              Bytes  Class     Attributes

  C           1x1000             8000  double              
  Df          1x4                  32  double              
  Dp          1x1000             8000  double              
  Dp1         1x1000             8000  double              
  Kb          1x1                   8  double              
  Kn          1x1000             8000  double              
  L           1x1                   8  double              
  Mu          1x1                   8  double              
  Mu_s        1x1                   8  double              
  P           1x1                   8  double              
  Pa          1x1                   8  double              
  Pp          1x1                   8  double              
  Rair        1x1                   8  double              
  T           1x1                   8  double              
  Ts          1x1                   8  double              
  Ts0         1x1                   8  double              
  U0          1x1                   8  double              
  cmdout      1x33                 66  char                
  e           1x1                   8  double              
  g           1x1                   8  double              
  lamda       1x1                   8  double              
  lamda1      1x1                   8  double              

Stk = ((Pp-Pa).*Dp.^2.*(U0./e)) ./ (18.*Mu.*Df)

Arrays have incompatible sizes for this operation.

Dp is 1 x 1000, but Df is 1 x 4, so you are dividing a 1 x 1000 element-wise by a 1 x 4.

[Walter Roberson]

If you want each Df in combination with each Dp then

format long
% Given Values
T   = 429.65; % K - Given Temperture
P = 99.6 ; % kPa - Pressure

% Specific Diameters given
Dp1 = 0.01:0.01:10;
Dp = Dp1 * 10^-6;

%Actual particle Density given.
Pp = 1260; % kg/m^3

% Standard Temperture and Mu at SATP
Ts0 = 298.15; % K
Ts  = 110.4; % K
Rair = 0.287; % kJ / kg * K
Mu_s = 1.849*10^-5; % kg/m*s
g = 9.81;

% Calculate Air Density
Pa = P / (Rair * T);
Mu = Mu_s * (T/Ts0)^(3/2) * (Ts0+Ts)/(T+Ts);


% lamda - Mean free path
lamda1 = (Mu/0.499) * sqrt(pi/(8*Pa*P*1000)); % Unit m
lamda = lamda1 *10^6; % Unit Mu*m

% Knudsen number
Kn = lamda1 ./ Dp;

% Cunningham Correction Factor
C = 1 + Kn .* (2.514+0.80.*exp(-0.55./Kn));
% -----------------------------------------------------------------
% Given
Df = [5, 10, 15, 20].' *10^-6; % Given in microns change to m
U0 = 0.225; % m/s
e = 0.875; % fraction
L = 0.00335; % m

%intial
Kb = 1.381*10^-23;

% Calvert & Englund
Stk = ((Pp-Pa).*Dp.^2.*(U0./e)) ./ (18.*Mu.*Df);

nfDpCE = ((Stk)./(Stk+0.425)).^2;

%Cheng

Dap = (Kb.*T.*C)./ (3.*pi.*Mu.*Dp);

alpha = 1 - e;

Kk = -0.5.*log(alpha)+alpha-0.25.*alpha.^2-0.75;

Pe = (Df.*U0)./(Dap);

nfDpCheng = 2.92 .* ((1-alpha)./Kk).^(1./3).*Pe.^(-2./3);

nfDp = nfDpCE + nfDpCheng;

Lc = (pi./4).*(e./(1-e)).*(Df./nfDp);

nDp = (1 - exp(-L./Lc) )*100;

% ========================================================================

Dp2= log(Dp1*10^1);
plot(Dp2,nDp)
legend(string(Df))