River basins by slope of triangle

 

 

                               

 

 

 

 

 

 

 

 

 

 

 


                                                                VI

 

 


                                SA

 

                                                                SB

 

 

 

                VJ           SC                           VK

 

Tipping toward SA           VK > (VI+ VJ) / 2

Tipping toward SB            VK < (VI + VJ) / 2 and VI < VJ

Tipping toward SC            VK < (VI + VJ) / 2 and VI > VJ

 

                                               

VA                                          VB

 

VA = 100

VB = 120                                     VE

VC = 150

VD = 140

 

VC                                          VD

 

 

Therefore VE < (VB+VD)/2   and   VB > VD (not possible)

 


 

 

                               VA                                          VB

VA = 100                                          VE

VB = 120

VC = 150

VD = 140

                                VC                                                VD

 

Therefore VE < (VB+VD)/2   and   VD < VB

                VE < 130

VE < (VC+VD)/2    and    VC > VD

VE < 145

VE < (VC+VA)/2   and VA > VC (not possible)

 

 

                               VA                                          VB

VA = 100                                          VE

VB = 120

VC = 150

VD = 140

                                VC                                                VD

 

 

Therefore VE < (VB+VD)/2   and   VD < VB

                VE < 130

VE < (VC+VD)/2    and    VC > VD

VE < 145

VE < (VC+VA)/2   and VC > VA

                VE < 125

VE > (VA+VB)/2

                VE > 110

 

Valid configuration for 110 < VE < 125


 

                               VA                                          VB

 

VA = 100                                          VE

VB = 120

VC = 150

VD = 140

                                VC                                                VD

 

 

Therefore VE < (VB+VD)/2   and   VD < VB

                VE < 130

VE < (VC+VD)/2    and    VC > VD

VE < 145

VE > (VC+VA)/2

                VE > 125

VE > (VA+VB)/2

                VE > 110

 

Valid configuration for 125 < VE < 130