(Solved by Humans)-(a) Using integral conservation of momentum i-Draw and label a

Question

(a) Using integral conservation of momentum?

1. i-Draw and label a control volume that can be used to relate the shear and normal stresses to the x-momentum change in the fluid.?
2. ii-Clearly show the forces/integral conservation of momentum relationship as applied to your CV.?
3. iii-Using the expression from (ii) show how the pressure gradient along the pipe (dp/dx) and wall ?shear stress (t) are related??

(b) Use the differential conservation of momentum (Navier-Stokes equation) to show the same relationship between pressure gradient (dp/dx) and wall shear stress (t) exists. (HINT: you may find ?Poiseille Flow analysis will help)

2. 20Pts: Consider the following circular cross section pipe:

Figure 1: The water pipe flow problem.
Answer the following questions:
(a) Using integral conservation of momentum
i. Draw and label a control volume that can be used to relate the shear and normal stresses to
the x-momentum change in the fluid.
ii. Clearly show the forces/integral conservation of momentum relationship as applied to your
CV.
@p
iii. Using the expression from (ii) show how the pressure gradient along the pipe ( @x
) and wall
shear stress (? ) are related?
(b) Use the di?erential conservation of momentum (Navier-Stokes equation) to show the same rela@p
tionship between pressure gradient ( @x
) and wall shear stress (? ) exists (hint: you may find a
Poiseille Flow analysis will help).

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