Water flows through a horizontal pipe of variable cross-section at the rate of 20 ~L ~min ⁻¹ . What will be the velocity of water at a point where diameter is 4 cm ?

Step-by-step solution

Volume of the water flowing per second, V =20 Lmin ⁻¹= 20 1000 60 (100)^3 ~m ^3 ~s ⁻¹= 1 3 10⁻³ ~m ^3 ~s ⁻¹ Radius of the pipe, r = 4 2 =2 ~cm =0.02 ~m Area of cross-section, r = r ^2= 22 7 (0.02)^2 ~m ^2 Let v be the velocity of the flow of water at the given point. Clearly, V = Av or 1 3 10⁻³= 22 7 (0.02)^2 v or v = 7 10⁻³ 3 22 (0.02)^2 =0.2639 ~ms ⁻¹