4. An incompressible fluid with viscosity u and density p was contained in pipe of length...
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4. An incompressible fluid with viscosity u and density p was contained in pipe of length L and radius R. Initially the fluid is in rest. At t = 0, a pressure difference of AP is applied across the pipe length which induces the fluid flow in axial direction (1₂) only varies with time (t) and pipe radius (r). There is no effect of gravity. To describe the fluid flow characteristics, after the pressure gradient is applied, answer the following questions: a) Use appropriate equation of continuity and Navier-stokes equations to generate the differential equations to describe the fluid flow by stating all the conditions. State the initial and boundary conditions to solve the equation. (no need to solve the differential equation). (4 points) PRY 07 an 26 b) Velocity profile two different fluids, fluid A and B examined under this condition was plotted in the following diagram, where dimensionless velocity (v₂ = is plotted against dimensionless radius (r =) at Vmax different dimensionless time (t =). Based on this profile compare the viscosity and density p of fluid A and B. Explain your answer. (4 points) as 03- 44 04 0.4 43 42 a 0₂ 44 DE dimiras ( di velocity ( 4:02 at D DA 43 dineless radin (2) 13 4. An incompressible fluid with viscosity u and density p was contained in pipe of length L and radius R. Initially the fluid is in rest. At t = 0, a pressure difference of AP is applied across the pipe length which induces the fluid flow in axial direction (1₂) only varies with time (t) and pipe radius (r). There is no effect of gravity. To describe the fluid flow characteristics, after the pressure gradient is applied, answer the following questions: a) Use appropriate equation of continuity and Navier-stokes equations to generate the differential equations to describe the fluid flow by stating all the conditions. State the initial and boundary conditions to solve the equation. (no need to solve the differential equation). (4 points) PRY 07 an 26 b) Velocity profile two different fluids, fluid A and B examined under this condition was plotted in the following diagram, where dimensionless velocity (v₂ = is plotted against dimensionless radius (r =) at Vmax different dimensionless time (t =). Based on this profile compare the viscosity and density p of fluid A and B. Explain your answer. (4 points) as 03- 44 04 0.4 43 42 a 0₂ 44 DE dimiras ( di velocity ( 4:02 at D DA 43 dineless radin (2) 13
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Incompressible NavierStokes equations convective form du uVuzVuVug t The HagenPoiseuille equation ca... View the full answer
Related Book For
Fundamentals of Thermal-Fluid Sciences
ISBN: 978-0078027680
5th edition
Authors: Yunus A. Cengel, Robert H. Turner, John M. Cimbala
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