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Later on in the course, you will learn how to use the Navier-Stokes equations to predict the flow behaviour of Newtonian fluids in various systems
Later on in the course, you will learn how to use the Navier-Stokes equations to predict the flow behaviour of Newtonian fluids in various systems with fairly simple geometries. Below is a schematic for the pressure-driven flow of a Newtonian fluid in the annular space between two concentric cylinders - the inner cylinder has radius Ri and the outer cylinder has radius Ro. Four of your colleagues attempted to solve the Navier-Stokes equations to determine an expression for Q, the volumetric flow rate of fluid, in terms of the following parameters: - the applied pressure (P) - the length of the annular space (L) - the viscosity of the fluid () Unfortunately they each came up with a different expression for Q : Q=8Ro2LP[1(RoRi)4ln(RiRo)[1(RoRi)2]2]Q=8Ro4LP1(RoRi)4ln(RiRo)[1(Ro2Ri)]2Q=8Ro2LP1(RoRi)4ln(RiRo)[1(Ro2Ri)]2Q=8Ro4LP1(RoRi)4ln(RiRo)2][1(RoRi)2]2] Using a dimensional analysis, determine which (if any) of the four might be the correct equation for
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