Water is conveyed through a uniform tube of 8 cm in diameter and 3140 ~m in length at the rate 2 10⁻³ ~m ^3 per second. The pressure required in maintain the flow is (Viscosity of water =10⁻³ SI units)

Step-by-step solution

Radius r= 8 2 ~cm =4 ~cm =4 10⁻² ~m , Rate of flow of water aligned & Q=2 10⁻³ ~m ^3 / s & Q= P r^2 8 l aligned P= Q(8 l) r^4 = coefficient of viscosity of water =10⁻³ SI units aligned P & = 2 10⁻³ 8 10⁻³ 3140 3.14 (4 10⁻² )^4 & = 2 8 3140 10⁻⁶ 3.14 256 10⁻⁸ & = 3140 10^2 3.14 16 & .= 100 10^3 16 ] & =6.25 10^3 ~N / m ^2 aligned