script to compare various boat placement strategies

boat_placement.py

t_flow = 4000.#m^3/s total chaopraya flow
t_area = 4000.#m^2 total crossection of chaopraya
rho = 1000.#kg/m^3 water density
P_smallboat = 1000
A_smallboat = 0.1
#non interference
#P is power per boat  (watts)
#A is effective area (m^3)
#n is number of boats in parallel
#return the addition in flow 
def flowdiff(P,A,n,t_flow):
    a_area = A #affected Area
    a_flow = t_flow/t_area*A #flow in affected area
    f_new = newflow_columate(P,A,a_flow) #new flow in affected area
    #print 'f_new-a_flow',(f_new-a_flow) #flow generated per boat
    un_flow = t_flow/t_area*(t_area-n*A)#unaffected flow
    new_total = f_new*n+un_flow #new total flow
    flow_diff = new_total - t_flow
    return flow_diff

#calculate new flow given power area and initial flow
#in columated area
#f_old initial flow
#A effective area
#P power
def newflow_columate(P,A,f_old):
    f_new = pow(f_old**3 + 2*P*A**2/rho,1./3.)
    return f_new

#calculate new flow assuming faraway assumption
#(flow are distributed throughout when it gets through the second row)
def newflow_faraway(nboat,npara,P,A):
    #assume nboat is divisible by nboat
    nseries = nboat/npara #yep integer division
    new_flow = t_flow
    for i in xrange(nseries):
        new_flow = new_flow + flowdiff(P,A,npara,new_flow)
    return new_flow


#calculate new flow assuming short distance assumption
#(new flow is still columated when it gets to the second row)
def newflow_shortdistance(nboat,npara,P,A):
    #assume nboat is divisible by npara
    nseries = nboat/npara
    unaffected_area = t_area-npara*A
    initial_flow = t_flow*A/t_area#initial flow per column
    #find new flow for each column
    new_flow = initial_flow
    for i in xrange(nseries):
        new_flow = newflow_columate(P,A,new_flow)
    total_new_flow = npara*new_flow #total new flow in all the affected area
    return total_new_flow + unaffected_area/t_area*t_flow #add it back to unaffected area
    
def faraway_analysis(nboat,P,A):
    print 'For faraway assumption'
    print 'npara','nseries','totalnewflow'
    for npara in xrange(1,nboat+1):
        if nboat%npara==0:
            totalflow = newflow_faraway(nboat,npara,P,A)
            print (npara,nboat/npara,totalflow)
        else:
            pass

def shortdistance_analysis(nboat,P,A):
    print 'For short distance assumption'
    print 'npara','nseries','totalnewflow'
    for npara in xrange(1,nboat+1):
        if nboat%npara==0:
            totalflow = newflow_shortdistance(nboat,npara,P,A)
            print (npara,nboat/npara,totalflow)
        else:
            pass

def main():
    faraway_analysis(1000,P_smallboat,A_smallboat)
    shortdistance_analysis(1000,P_smallboat,A_smallboat)

if __name__ == '__main__':
    main()
#using estimated power and effective from K.Matipon
#print '1000 small boats non interference'
#print flowdiff(P=1000.,A=0.1,n=1000.,t_flow=t_flow)
#print '10 big ones non interference'
#print flowdiff(P=2000000.,A=1.,n=10.,t_flow=t_flow)

The result

For faraway assumption
npara nseries totalnewflow
(1, 1000, 4174.006179381851)
(2, 500, 4174.008036625053)
(4, 250, 4174.011751293362)
(5, 200, 4174.013608718646)
(8, 125, 4174.019181358588)
(10, 100, 4174.022896755448)
(20, 50, 4174.04147738306)
(25, 40, 4174.05076997475)
(40, 25, 4174.078656866721)
(50, 20, 4174.097255729882)
(100, 10, 4174.190341401425)
(125, 8, 4174.23694142936)
(200, 5, 4174.376970953434)
(250, 4, 4174.470515731825)
(500, 2, 4174.940557782721)
(1000, 1, 4175.892417638112)
For short distance assumption
npara nseries totalnewflow
(1, 1000, 4002.6144628561347)
(2, 500, 4004.1090130042558)
(4, 250, 4006.4403597498963)
(5, 200, 4007.4376666218354)
(8, 125, 4010.0591179627927)
(10, 100, 4011.601310017484)
(20, 50, 4018.0066644456783)
(25, 40, 4020.7176101184396)
(40, 25, 4027.769172292149)
(50, 20, 4031.870989700814)
(100, 10, 4048.5776600265067)
(125, 8, 4055.501522817685)
(200, 5, 4073.1401901560766)
(250, 4, 4083.1687177730555)
(500, 2, 4122.410862019136)
(1000, 1, 4175.892417638112)