A horizontal venturimeter is used to measure the flow speed of water (density = 1000 kg m ⁻³ ). The cross-sectional areas of the wide and narrow sections of the pipe are 30 cm ^2 and 10 cm ^2 , respectively. A U-tube manometer connected between these two sections contains a liquid of density 5000 kg m ⁻³ . If the height difference of the manometer liquid in the two arms is 40 cm , what is the flow speed of water at t

Step-by-step solution

Let the flow speed at the wide section be v₁ and at the narrow section be v₂ . From the equation of continuity: A₁ v₁ = A₂ v₂ 30 v₁ = 10 v₂ v₂ = 3 v₁ The pressure difference P between the two sections is given by the manometer reading: P = ( _m - _w) g h Substitute the given values ( _m = 5000 kg m ⁻³ , _w = 1000 kg m ⁻³ , h = 0.4 m ): P = (5000 - 1000) 10 0.4 = 4000 4 = 16000 Pa Applying Bernoulli's equation for a horizontal pipe: P = 1 2 _w (v₂^2 - v₁^2) 16000 = 1 2 1000 ((3 v₁)^2 - v₁^2) 16000 = 500 (9 v₁^2 - v₁