A Newtonian fluid is flowing in an infinitely long round pipe of diameter M or radius N = M/2 and inclined at angle α with the horizontal line. Consider the flow is steady (dρ/dt=0), in-compressible, and laminar. There is no applied pressure gradient (dP/dz= 0) applied along the pipe length (z-direction). The fluid flows down the pipe due to gravity alone (gravity acts vertically downward). Adopt the coordinate system with z axis along the centre line of the pipe along the pipe length.Derive an expression for the z-component of velocity u as a function of radius N and the other parameters of the problem. The density and viscosity of the fluid are ρ and u, respectively.
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A Newtonian fluid is flowing in an infinitely long round pipe of diameter M or radius N = M/2 and inclined at angle α with the horizontal line. Consider the flow is steady (dρ/dt=0), in-compressible, and laminar. There is no applied pressure gradient (dP/dz= 0) applied along the pipe length (z-direction). The fluid flows down the pipe due to gravity alone (gravity acts vertically downward). Adopt the coordinate system with z axis along the centre line of the pipe along the pipe length.Derive an expression for the z-component of velocity u as a function of radius N and the other parameters of the problem. The density and viscosity of the fluid are ρ and u, respectively.
Please list all necessary assumptions.
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