Consider a Poiseuille flow of a fluid with density 1000 kg/m and viscosity 0.001 kg/(m sec)...

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Consider a Poiseuille flow of a fluid with density 1000 kg/m³ and viscosity 0.001 kg/(m sec) through a pipe with inner radius 0.05 m and a pressure gradient of 10 N/m³. After some distance L from the pipe inlet, the flow will reach a laminar fully-developed steady flow. Obtain the resulting volume flow rate Q, and the approximate distance L for the entrance region. (8 points) Consider a Poiseuille flow of a fluid with density 1000 kg/m³ and viscosity 0.001 kg/(m sec) through a pipe with inner radius 0.05 m and a pressure gradient of 10 N/m³. After some distance L from the pipe inlet, the flow will reach a laminar fully-developed steady flow. Obtain the resulting volume flow rate Q, and the approximate distance L for the entrance region. (8 points)