What is Francis's formula, According to Francis's formula the discharge over a rectangular weir, Francis's formula for a rectangular weir for two end contraction is given by.

• Ther discharge over a rectangular weir is given by:-

     Q= 2/3 × Cd × L ×[ (2g)^1/2 ] × H^3/2.         ----i

       

        = 2/3 × Cd × L × [ (2g)^1/2 ] × [( H + ha )^3/2 -                     ha^3/2 ]                                     ------- ii

• Equation i and ii are applicable to ther weir or notch for which ther Crest length is equal to the width of the channel. 
• This type of weir is called Suppressed weir.
• But if the writer is not suppressed, ther effect of end of contraction will be taken into final. 

Francis's Formula:-

• Francis on the basis of his experiments established that one end contraction decreases the effective length of the Crest of weir and hence decreases the discharge. 

• Each end contraction reduces the Crest length by 0.1× H, where H is the head over the weir. 
• For a rectangular weir there are two end contraction only and hence effective length. 

                 L = ( L- 0.2H )

and,         Q = 2/3 × Cd × L ×[ (2g)^1/2 ] × H^3/2.

If,

                Cd = 0.623  ,  g = 9.81 m/s^2.

Then,

      Q  = 2/3 × 0.623 × L ×[ (2 × 9.81 )^1/2 ] × H^3/2.

           = 1.84 × ( L- 0.2H ) × H^3/2

If end contractions are suppressed then,

     Q = 1.84 × L × H^3/2.

If velocity of approach is considered then, 

 

     Q = 1.84 × L × [ ( H + ha )^3/2 - ha^3/2 ].