Water (density 1000 kg m ⁻³ ) flows steadily through a horizontal Venturi meter. The cross-sectional areas of the wide and narrow sections are 100 cm ^2 and 50 cm ^2 respectively. A U-tube manometer connected between the wide and narrow sections contains a liquid of density 13000 kg m ⁻³ . If the height difference of the manometer liquid in the two arms is 5 cm , the rate of flow of water is x 10⁻³ m ^3 s ⁻¹ . The va

Step-by-step solution

The pressure difference between the wide and narrow sections is given by the manometer reading: P = ( _m - _w)gh P = (13000 - 1000) 10 0.05 = 12000 0.5 = 6000 Pa Let v₁ and v₂ be the velocities at the wide and narrow sections respectively. By the equation of continuity: A₁ v₁ = A₂ v₂ v₁ = A₂ A₁ v₂ = 50 100 v₂ = v₂ 2 Applying Bernoulli's equation for a horizontal pipe: P₁ + 1 2 _w v₁^2 = P₂ + 1 2 _w v₂^2 P = 1 2 _w (v₂^2 - v₁^2) = 1 2 _w (v₂^2 - v₂^2 4 ) = 1 2 _w ( 3v₂^2 4 ) Substituting the values: 6000 = 1 2 1000