Water from a tap of cross-sectional area 1 ~cm ^2 , falls vertically downwards at 2 ~m / s . The cross sectional area of the stream, 20 ~cm below the tap is (assume that pressure is constant throughout and the flow is streamlined; ( g =10 ~ms ⁻² )

Step-by-step solution

Let A₁ = 1 cm ^2 be the cross-sectional area at the tap and v₁ = 2 m/s be the velocity at the tap. Let A₂ be the cross-sectional area at a depth h = 20 cm = 0.2 m below the tap, and v₂ be the velocity at that point. Using the equation of continuity, A₁ v₁ = A₂ v₂ . Using the principle of conservation of energy (Bernoulli's equation) for a streamline, v₂^2 = v₁^2 + 2gh . Substituting the given values, v₂^2 = (2)^2 + 2 10 0.2 = 4 + 4 = 8 . Thus, v₂ = 8 = 2 2 m/s 2 1.414 = 2.828 m/s . From the continuity equation, A₂