CONSISTING of two conical parts with a short portion of uniform cross-section in between. This short portion has the minimum area and is known as the throat. The two conical portions have the same base diameter, but one is having a shorter length with a LARGER cone angle while the other is having a larger length with a smaller cone angle.Applying Bernoulli’s equation at section 1 and 2:\(\frac{{{P_1}}}{{\rho g}} + \frac{{V_1^2}}{{2G}} + {z_1} = \frac{{{P_2}}}{{\rho g}} + \frac{{V_2^2}}{{2g}} + {z_2}\)As the pipe is horizontal z1 = z2, we get\(h = \frac{{{P_1} - {P_2}}}{{\rho g}} = \frac{{(V_2^2 - V_1^2)}}{{2g}} = \frac{{V_2^2}}{{2g}}\left( {1 - \frac{{V_1^2}}{{V_2^2}}} \right)\)Where h = difference of pressure head at section 1 and 2From the continuity equation in sections 1 and 2,A1V1 = A2V2\(h = \frac{{V_2^2}}{{2g}}\left( {1 - \frac{{V_1^2}}{{V_2^2}}} \right) = \frac{{V_2^2}}{{2g}}\left( {1 - \frac{{A_2^2}}{{A_1^2}}} \right) = \frac{{V_2^2}}{{2g}}\frac{{\left( {A_1^2 - A_2^2} \right)}}{{A_1^2}}\)\(\Rightarrow {V_2} = \frac{{{A_1}}}{{\sqrt {A_1^2 - A_2^2} }}\;\sqrt {2gh} \)DischargeQ = A1V1 = A2V2\(Q = {A_2}{V_2} = \frac{{{A_1}{A_2}}}{{\sqrt {A_1^2 - A_2^2} }}\;\sqrt {2gh} \)So, Bernoulli and continuity EQUATIONS are used in DERIVING the relationship between the flow rate and the pressure difference between the straight section and the throat of a venturimeter.