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A fluid of viscosity n flows steadily through a horizontal cylindrical pipe of radius R and length L, as shown in Fig. 16-41. (a) Consider an arbitrary cylinder of fluid of radius r. Show that the viscous force F due to the neighboring layer is F =η (2πrL)dv/dr. (b) Show that the force ‘F’=(πr 2 )∆p. (c) Use the equilibrium condition to obtain an expression for dv in terms of dr. Integrate the expression to obtain Eq. 16-18.

A fluid of viscosity n flows steadily through a horizontal cylindrical pipe of radius R and length L, as shown in Fig. 16-41. (a) Consider an arbitrary cylinder of fluid of radius r. Show that the viscous force F due to the neighboring layer is F =η (2πrL)dv/dr. (b) Show that the force ‘F’=(πr2)∆p. (c) Use the equilibrium condition to obtain an expression for dv in terms of dr. Integrate the expression to obtain Eq. 16-18.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
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