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Example 11-17 Viscous Laminar Flow in a Long, Narrow Pipe Water at 20°C moves in laminar flow at an average flow speed of 0.800 m>s through a pipe of radius 0.500 mm = 5.00 * 1024 m. The pipe is 2.00 m long. Determine what the pressure difference must be between the two ends of the pipe. Set Up We saw in part (a) of Example 11-16 that the flow is laminar for water at this temperature moving through such a pipe at this speed. Because the pipe is long and narrow, viscosity is important and laminar flow is an example of Hagen-Poiseuille flow. (The density and viscosity are given in Example 11-16.) Our goal is to find the pressure difference p between the ends of the pipe, and we use the Hagen-Poiseuille equation, Equation 11-30. Solve In Example 11-16 we calculated the volume flow rate. Solve the Hagen-Poiseuille equation for the pressure ­difference p and substitute values. Hagen-Poiseuille equation for laminar flow of a R viscous fluid: Q = pR4 p 8hL (11-30) L ∆p = ? Volume flow rate: Q = 6.28 * 10-7 m3 >s p = = 8hLQ pR4 811.002 * 10-3 Pas2 12.00 m2 16.28 * 10-7 m3 >s2 = 5.13 * 104 Pa p 15.00 * 10-4 m2 4 Reflect Even though the viscosity of water is low, the pressure required to sustain the flow is substantial (about half an atmosphere) because the pipe is so narrow and long. p = 15.13 * 104 Pa2 a = 0.506 atm 1 atm b 1.01325 * 105 Pa