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Dietrich.m
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%==============================================================================
% FluEgg -Fluvial Egg Drift Simulator
%==============================================================================
% Copyright (c) 2013 Tatiana Garcia
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License version 3 as published by
% the Free Software Foundation (currently at http://www.gnu.org/licenses/agpl.html)
% with a permitted obligation to maintain Appropriate Legal Notices.
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::%
%% Calculate settling velocity using Dietrich equation %
%:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::%
%-------------------------------------------------------------------------%
% This function is used calculate settling velocity using Dietrich
% equation %
%-------------------------------------------------------------------------%
% %
%-------------------------------------------------------------------------%
% Created by : Tatiana Garcia %
% Last Modified : May 27, 2016 %
%-------------------------------------------------------------------------%
% Reference: Garcia, M. H. (2008). Sedimentation engineering: processes,
% measurements, modeling and practice. ASCE Manuals and Reports
% on Engineering Practice No. 110. Page 41 %
% Inputs:
% D = egg diameter in mm
% T = temperature in Celsius degrees
% SG =egg specific gravity (dimensionless)= density of egg/density
% of water.
% Outputs:
%
%:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::%
function [vs] = Dietrich(D,SG,T)
D = D/10; % convert to cm from mm
g = 981; %gravity cm/s^2
viscosity = (1.79e-6*100^2)/(1+(0.03368*T)+(0.00021*(T^2)));%cm^2/s
% constants
b1 = 2.891394;
b2 = 0.95296;
b3 = 0.056835;
b4 = 0.002892;
b5 = 0.000245;
Rep = (D*sqrt((SG-1)*g*D))/viscosity; %Reynolds particle number.
Rf = exp(-b1+(b2*(log(Rep)))-(b3*((log(Rep))^2))...
-(b4*((log(Rep))^3))+(b5*((log(Rep))^4)));
vs = Rf*sqrt((SG-1)*g*D); %Settling velocity in cm/s