3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear stress in the fluid at the wall of the pipe (Just use symbols). (c) If the given profile persists a distance L along the pipe, what is the force on the wall due to the moving water and what is its direction? (Hint: The force on the wall is equal in magnitude but in the opposite direction of that in the fluid.)

Question
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is
parabolic:
u(0) -4J
Figure 2
where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the
radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic
velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use
symbols). (b) Develop an equation for shear stress in the fluid at the wall of the pipe (Just use
symbols). (c) If the given profile persists a distance L along the pipe, what is the force on the wall
due to the moving water and what is its direction? (Hint: The force on the wall is equal in
magnitude but in the opposite direction of that in the fluid.)

Image Transcription

3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear stress in the fluid at the wall of the pipe (Just use symbols). (c) If the given profile persists a distance L along the pipe, what is the force on the wall due to the moving water and what is its direction? (Hint: The force on the wall is equal in magnitude but in the opposite direction of that in the fluid.)

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