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24.54 The pressure gradient for laminar flow through a constant radius tube is given by dp dx 8µ Q where p = pressure (N/m), x = distance along the tube's centerline (m), u = dynamic viscosity (N s/m²), Q = flow (m³/s), and r = radius (m). (a) Determine the pressure drop for a 10-cm length tube for a vis- cous liquid (u = 0.005 N s/m, density = p = 1 x 10 kg/m³) with a flow of 10 × 10 ° m'/s and the following varying radii along its length, %3D %3D х, ст 4 6 7 10 T, mm 1.35 1.34 1.6 1.58 1.42 (b) Compare your result with the pressure drop that would have occurred if the tube had a constant radius equal to the average radius. (c) Determine the average Reynolds number for the tube to verify that flow is truly laminar (Re = pvD/p < 2100 where v = velocity). %3D

24.54 The pressure gradient for laminar flow through a constant radius tube is given by dp dx 8µ Q where p = pressure (N/m), x = distance along the tube's centerline (m), u = dynamic viscosity (N s/m²), Q = flow (m³/s), and r = radius (m). (a) Determine the pressure drop for a 10-cm length tube for a vis- cous liquid (u = 0.005 N s/m, density = p = 1 x 10 kg/m³) with a flow of 10 × 10 ° m'/s and the following varying radii along its length, %3D %3D х, ст 4 6 7 10 T, mm 1.35 1.34 1.6 1.58 1.42 (b) Compare your result with the pressure drop that would have occurred if the tube had a constant radius equal to the average radius. (c) Determine the average Reynolds number for the tube to verify that flow is truly laminar (Re = pvD/p < 2100 where v = velocity). %3D

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24.54 The pressure gradient for laminar flow through a constant radius tube is given by dp 8µ Q dx where p = pressure (N/m), x= distance along the tube's centerline (m), u = dynamic viscosity (N s/m²), Q = flow (m/s), and r = radius (m). %3D (a) Determine the pressure drop for a 10-cm length tube for a vis- cous liquid (u = 0.005 N s/m², density =p = 1 x 10° kg/m') with a flow of 10 × 10-6 m/s and the following varying radii along its length, %3D х, ст 4 5 6 10 r, mm 1.35 1.34 1.6 1.58 1.42 (b) Compare your result with the pressure drop that would have occurred if the tube had a constant radius equal to the average radius. (c) Determine the average Reynolds number for the tube to verify that flow is truly laminar (Re pvD/p < 2100 where v = velocity).
Transcribed Image Text:24.54 The pressure gradient for laminar flow through a constant radius tube is given by dp 8µ Q dx where p = pressure (N/m), x= distance along the tube's centerline (m), u = dynamic viscosity (N s/m²), Q = flow (m/s), and r = radius (m). %3D (a) Determine the pressure drop for a 10-cm length tube for a vis- cous liquid (u = 0.005 N s/m², density =p = 1 x 10° kg/m') with a flow of 10 × 10-6 m/s and the following varying radii along its length, %3D х, ст 4 5 6 10 r, mm 1.35 1.34 1.6 1.58 1.42 (b) Compare your result with the pressure drop that would have occurred if the tube had a constant radius equal to the average radius. (c) Determine the average Reynolds number for the tube to verify that flow is truly laminar (Re pvD/p < 2100 where v = velocity).
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