def find_R_Formula2(P1,W,M,A1):
A=find_A(A1,W)
C=find_C(M,W,A)
D=find_D(C,P1,W,A)
condition_for_K=find_condition_for_K(P1,W,A)
if square(C)<=cube(condition_for_K):
K=find_K(D)
lamba=math.pi
condition_1=find_condition_1(P1,A,W)
condition_2=find_condition_2(A,W,lamba)
if M<=condition_1:
R=value_from_equation_1(C, K)
equation_no=1
elif M>condition_1 and M<=condition_2:
R=value_from_equation_2(C, D)
equation_no=2
else:
lamba=math.pi
while(lamba>0):
if(check_condition(P1, M, A, lamba, W)==1.0):
break
else:
lamba=lamba-0.005
R=value_from_equation_3(M, A, lamba)
equation_no=3
result={
'R':round(R,3),
'equation':equation_no,
'lambda':round(lamba,3)
}
return result
def find_condition_2(A,W,lamba):
part_1=math.sqrt(A)*math.pow((1-(math.pi*W/A*square(find_small_f(lamba)))), 1.5)
part_2=cube(find_small_f(lamba)/find_capital_F(lamba))
return inverse(part_1)*part_2
def find_capital_F(lamba):
numerator=1.0-math.cos(lamba)
deno_1=-(2.0/3.0)*cube(math.sin(lamba))*math.cos(lamba)
deno_2=-(quad(math.sin(lamba))/16.0)
deno_3=lamba/4
return math.pow((numerator/(deno_1+deno_2+deno_3)), (1.0/3.0))
def find_small_f(lamba):
numerator=1.0-math.cos(lamba)
deno_1=(2.0/3.0)*cube(math.sin(lamba))
deno_2=(math.sin(2*lamba)*math.cos(lamba))/2.0
deno_3=-(lamba*math.cos(lamba))
return math.sqrt(numerator/(deno_1+deno_2+deno_3))
def find_condition_for_K(P1,W,A):
return cube((P1/3.0)/((A-W)*math.pi))
def find_D(C,P1,W,A):
part1=square(C)
part2=cube((P1/3.0)/((A-W)*math.pi))
return part1-part2