Question: = H7.2 A viscous fluid with constant p and flows upwards through a vertical circular pipe with radius, R. The gravity vector, -gk, acts

= H7.2 A viscous fluid with constant p and flows upwards through

= H7.2 A viscous fluid with constant p and flows upwards through a vertical circular pipe with radius, R. The gravity vector, -gk, acts downward in the vertical direction. The flow is steady, incompressible, fully developed, axisymmetric, laminar, and there is no swirl. Assume both an applied constant pressure gradient, dp/dz, and gravity influence the flow. a. Determine the velocity distribution using continuity and Navier-Stokes equations (begin with equations (6.33), (6.128)). b. Derive expressions for the wall shear stress and volume flow rate. c. Sketch the velocity and shear stress radial profiles.

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