Revision history [back]
 | 1 | initial version |
I did not check further, but apparently sympy is able to solve it:
sage: Rl,Rp,W,Vb,Rho,L,r,pi,F = var('Rl,Rp,W,Vb,Rho,L,r,pi,F')
sage: eq = 1/2*(Vb^2 - 2*Rp*W + sqrt(Vb^2 - 4*Rp*W)*Vb)*pi*r^2/(Rho*W) - W/(F * 2 * pi * r)
sage: seq = eq._sympy_() ; seq
pi*r**2*(-2*Rp*W + Vb**2 + Vb*sqrt(-4*Rp*W + Vb**2))/(2*Rho*W) - W/(2*F*pi*r)
sage: import sympy
sage: sympy.solve(seq,W)
[pi*(-2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))/Rho**2,
-pi*(2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))/Rho**2]
| | 2 | No.2 Revision |
I did not check further, but apparently sympy is able to solve it:
sage: Rl,Rp,W,Vb,Rho,L,r,pi,F = var('Rl,Rp,W,Vb,Rho,L,r,pi,F')
sage: eq = 1/2*(Vb^2 - 2*Rp*W + sqrt(Vb^2 - 4*Rp*W)*Vb)*pi*r^2/(Rho*W) - W/(F * 2 * pi * r)
sage: seq = eq._sympy_() ; seq
pi*r**2*(-2*Rp*W + Vb**2 + Vb*sqrt(-4*Rp*W + Vb**2))/(2*Rho*W) - W/(2*F*pi*r)
sage: import sympy
sage: sympy.solve(seq,W)
[pi*(-2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))/Rho**2,
-pi*(2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))/Rho**2]
However i am not sure this leads to a correct solution (to be hand-checked):
sage: s = _[0]
sage: seq.subs({W:s})
Rho*r**2*(Vb**2 + Vb*sqrt(Vb**2 - 4*Rp*pi*(-2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))/Rho**2) - 2*Rp*pi*(-2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))/Rho**2)/(2*(-2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))) - (-2*F*Rho*Rp*pi*r**3 + sqrt(2)*Vb*sqrt(F*Rho**3*r**3))/(2*F*Rho**2*r)
sage: seq.subs({W:s}) == 0
False
