BERNOULLI’S EQUATION Fluid Flow Bernoulli’s equation states that the total head of the flow must be constant.   Since the elevation does  not  change  significantly,  if  at  all,  between  points  1  and  2,  the  elevation  head  at  the  two points will be essentially the same and will cancel out of the equation.   So Bernoulli’s equation simplifies to Equation 3-13 for a venturi. (3-13) v² 1 2g P_1n1 g_c g v² 2 2g P_2n2 g_c g Applying the continuity equation to points 1 and 2 allows us to express the flow velocity at point 1 as a function of the flow velocity at point 2 and the ratio of the two flow areas. r1A1v1 r2A2v2 v₁ r2A2v2 r1A1 v₁ v₂ A₂ A₁ Using algebra to rearrange Equation 3-13 and substituting the above result for v₁  allows us to solve for v₂. v² 2 v² 1 2g (P₁ P₂)  n g_c g v² 2 æ ç ç è ö ÷ ÷ ø v₂ A₂ A₁ 2 (P₁ P₂)  2ng_c v² 2 æ ç ç ç è ö ÷ ÷ ÷ ø 1 æ ç ç è ö ÷ ÷ ø A₂ A₁ 2 (P₁ P₂)  2ng_c HT-03 Page 28 Rev. 0