5. Water (density is 1000 kg m?³, viscosity is 1 x 10?³ Pa s) is pumped upwards from a lower to a higher reservoir through a 500 meter long, 1 meter diameter smooth pipe at a flow rate of 785 kg s?¹. The height difference between the reservoir surfaces is 10 m. (a) Calculate the Reynolds number for the pipe flow (b) Sketch the pipe flows' cross-sectional velocity profile, and label the distance of the boundary of each flow regime from the pipe wall as a multiple of Re_y. (c) Calculate i) the viscous sub-layer thickness ii) the flow velocity 0.1 m from the pipe wall. (d) Calculate the power input to the pump, clearly listing any assumptions you make in your calculation.
Added by John F.
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The Reynolds number (Re) is given by the formula: Re = (ρVD) / μ where ρ is the density of the fluid (1000 kg/m³), V is the flow velocity, D is the pipe diameter (1 m), and μ is the dynamic viscosity of the fluid (1 x 10⁻³ Pa s). To find the flow velocity (V), Show more…
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