SW_Viscosity Dynamic viscosity of seawater ========================================================================= USAGE: mu = SW_Viscosity(T,S) DESCRIPTION: Dynamic viscosity of seawater at atmospheric pressure (0.1 MPa) using Eq. (22) given in [1] which best fit the data of [2], [3] and [4]. The pure water viscosity equation is a best fit to the data of [5]. Values at temperature higher than the normal boiling temperature are calculated at the saturation pressure. INPUT: (all must have same dimensions) T = temperature [degree C] (ITS-90) S = salinity [g/kg] (reference-composition salinity) OUTPUT: mu = dynamic viscosity [kg/m s] AUTHOR: Mostafa H. Sharqawy 12-18-2009, MIT (mhamed@mit.edu) DISCLAIMER: This software is provided "as is" without warranty of any kind. See the file sw_copy.m for conditions of use and licence. VALIDITY: 0 < T < 180 C and 0 < S < 150 g/kg; ACCURACY: 1.5% REFERENCES: [1] Sharqawy M. H., Lienhard J. H., and Zubair, S. M., Desalination and Water Treatment, 2009 [2] B. M. Fabuss, A. Korosi, and D. F. Othmer, J., Chem. Eng. Data 14(2), 192, 1969. [3] J. D. Isdale, C. M. Spence, and J. S. Tudhope, Desalination, 10(4), 319 - 328, 1972 [4] F. J. Millero, The Sea, Vol. 5, 3 � 80, John Wiley, New York, 1974 [5] IAPWS release on the viscosity of ordinary water substance 2008 =========================================================================
0001 function mu = SW_Viscosity(T,S) 0002 % SW_Viscosity Dynamic viscosity of seawater 0003 %========================================================================= 0004 % USAGE: mu = SW_Viscosity(T,S) 0005 % 0006 % DESCRIPTION: 0007 % Dynamic viscosity of seawater at atmospheric pressure (0.1 MPa) using 0008 % Eq. (22) given in [1] which best fit the data of [2], [3] and [4]. 0009 % The pure water viscosity equation is a best fit to the data of [5]. 0010 % Values at temperature higher than the normal boiling temperature 0011 % are calculated at the saturation pressure. 0012 % 0013 % INPUT: (all must have same dimensions) 0014 % T = temperature [degree C] (ITS-90) 0015 % S = salinity [g/kg] (reference-composition salinity) 0016 % 0017 % OUTPUT: 0018 % mu = dynamic viscosity [kg/m s] 0019 % 0020 % AUTHOR: 0021 % Mostafa H. Sharqawy 12-18-2009, MIT (mhamed@mit.edu) 0022 % 0023 % DISCLAIMER: 0024 % This software is provided "as is" without warranty of any kind. 0025 % See the file sw_copy.m for conditions of use and licence. 0026 % 0027 % VALIDITY: 0 < T < 180 C and 0 < S < 150 g/kg; 0028 % 0029 % ACCURACY: 1.5% 0030 % 0031 % REFERENCES: 0032 % [1] Sharqawy M. H., Lienhard J. H., and Zubair, S. M., Desalination and Water Treatment, 2009 0033 % [2] B. M. Fabuss, A. Korosi, and D. F. Othmer, J., Chem. Eng. Data 14(2), 192, 1969. 0034 % [3] J. D. Isdale, C. M. Spence, and J. S. Tudhope, Desalination, 10(4), 319 - 328, 1972 0035 % [4] F. J. Millero, The Sea, Vol. 5, 3 � 80, John Wiley, New York, 1974 0036 % [5] IAPWS release on the viscosity of ordinary water substance 2008 0037 %========================================================================= 0038 0039 %---------------------- 0040 % CHECK INPUT ARGUMENTS 0041 %---------------------- 0042 if nargin ~=2 0043 error('SW_Viscosity.m: Must pass 2 parameters') 0044 end 0045 0046 % CHECK S,T dimensions and verify consistent 0047 [ms,ns] = size(S); 0048 [mt,nt] = size(T); 0049 0050 % CHECK THAT S & T HAVE SAME SHAPE 0051 if (ms~=mt) | (ns~=nt) 0052 error('check_stp: S & T must have same dimensions') 0053 end 0054 0055 % CHECK THAT S & T ARE WITHIN THE FUNCTION RANGE 0056 vectorsize=size(S); 0057 for i = 1:vectorsize(1,1) 0058 for j = 1:vectorsize(1,2) 0059 if T(i,j)<0 | T(i,j)>180 0060 disp('Temperature is out of range for Viscosity function 10<T<180 C'); 0061 end 0062 if S(i,j)<0 | S(i,j)>150 0063 disp('Salinity is out of range for Viscosity function 0<S<150 g/kg'); 0064 end 0065 0066 %------ 0067 % BEGIN 0068 %------ 0069 S(i,j)=S(i,j)/1000; 0070 a1 = 1.5700386464E-01;a2 = 6.4992620050E+01;a3 = -9.1296496657E+01;a4 = 4.2844324477E-05; 0071 mu_w(i,j) = a4 + 1/(a1*(T(i,j)+a2)^2+a3); 0072 a5 = 1.5409136040E+00;a6 = 1.9981117208E-02;a7 = -9.5203865864E-05; 0073 a8 = 7.9739318223E+00;a9 = -7.5614568881E-02;a10 = 4.7237011074E-04; 0074 A = a5 + a6 * T(i,j) + a7 * T(i,j)^2; 0075 B = a8 + a9 * T(i,j) + a10* T(i,j)^2; 0076 mu(i,j) = mu_w(i,j)*(1 + A*S(i,j) + B*S(i,j)^2); 0077 end 0078 end 0079 end