Venturimeter

It is a device based on the horizontal extension of the Bernoulli’s theorem. It is a device used to measure the rate of flow of liquid through the pipe.

According to Bernoulli’s theorem –

P1 + ½ ρv12 + ρgh1 = P2 + ½ ρv22 + ρgh2

 P1 + ½ ρv12 + ρgh =  P2 + ½ ρv22 + ρgh

since h1 = h2 , so

P1 – P2 = ½ ρ ( v22 – v12 )

Divide and multiply by v12 -----

∆P = ½ ρv12 ( v22 – v12 ) / v12

∆P = ½ ρv12 (v22 /v12  - 1)

          According to equation of continuity-----

          A1 v1 = A2 v2 ,   v2 /v1 = A1 /A2

          ∆P = ½ ρv12 { (A1 /A2 )2 – 1 }

          ∆P = ½ ρv12 (A12 – A22 ) /A22

          hρHg g = ½ ρv12 (A12 – A22 ) /A22    {ρHg  = density of mercury}

          v12 = 2 hρHggA22 / ρ(A12 – A22)

                         v1 = A2 {2 hρHgg / ρ(A12 – A22)}1/2

                                           https://youtu.be/UCHIvvAvekA