Water flows through a horizontal cylindrical pipe of diameter 2 cm . The density of water is 1000 kg/m ^3 and its coefficient of viscosity is 10⁻³ Pa s . If the critical Reynolds number for the onset of turbulent flow is 2000 , what is the maximum average velocity of water for which the flow remains streamline?

Step-by-step solution

The Reynolds number is given by the formula: R_e = v d where is the density, v is the flow velocity, d is the diameter of the pipe, and is the coefficient of viscosity. To find the maximum velocity for streamline flow (critical velocity), we rearrange the formula to solve for v : v = R_e d Given values are: R_e = 2000 = 10⁻³ Pa s = 1000 kg/m ^3 d = 2 cm = 0.02 m Substituting these values into the equation: v = 2000 10⁻³ 1000 0.02 v = 2 20 = 0.1 m/s Thus, the maximum average velocity for which the flow remains strea