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## Background

The MATLAB m-files below incorporate the theory of Louge and Keast (2001) predicting flows of grains down flat, frictional inclines; in particular, they calculate the effective friction in terms of parameters (restitution, friction, angle of inclination, etc) that can be measured independently.

The first step is to download all programs listed below.  There are two principal programs:

plot_flat_chute_mueff(Frmin,Frmax,num,holdupin,nu0in,ewi,muwi,b0wi,eei,muui,b00i,muEi,flagres,rguessi)

and

[Fres] = SFD_flat_chute(tanalphai,holdupi,ewi,muwi,b0wi,eei,muui,b00i,muEi,guess)

You can enter

help plot_flat_chute_mueff
help SFD_flat_chute

to read specifications for each file.  Here are two examples you can try:

plot_flat_chute_mueff(.2,10,50,[3],[.2 .4 .6],.8,.141,.35,.972,.177,.25,.593,1,.4) ;
[Fres] = SFD_flat_chute([.278:.001:.364],5,.8,.141,.35,.972,.177,.25,.593,[2 .5]) ;

The first program, plot_flat_chute_mueff, allows you to calculate the effective friction in terms of Fr for a given value of the solid volume fraction at the base.  (It plots the thin lines in Fig. 8 of Louge and Keast).  It does not assume that the flow is steady and fully-developed (SFD).  Therefore, its curves decrease with Fr at constant solid volume fraction.

Instead, the second program, SFD_flat_chute, assumes that the flow is SFD and uses the steady angular momentum balance to find the solid volume fraction in the shear layer.  This program also graph predictions and compares with our own measurements.