Question A2 a) Consider a steady, laminar flow through a straight horizontal tube having the x² constant elliptical cross section given by the equation DEN5242 (May 2019) QA2 continued 92x42 62 1 The streamlines are all straight and parallel. Investigate the possibility of using an equation for the z component of velocity of the form W = A(1.0-- exact solution to this problem (A is a constant). b as an

Elements Of Electromagnetics
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Question A2
a) Consider a steady, laminar flow through a straight horizontal tube having the
constant elliptical cross section given by the equation
2
DEN5242 (May 2019)
QA2 continued
The streamlines are all straight and parallel. Investigate the possibility of using an
equation for the z component of velocity of the form W = A(1.0--
exact solution to this problem (A is a constant).
expressed by: V₂ = V₂0 In
v.
X.
be
Incompressible
Fluid (.p)
a²
b) Consider two long concentric pipes with an incompressible fluid flow between them
(Figure QA2). The outer pipe moves axially with a constant velocity Vz0;
Solid Cylinder
at Rest
1- By using appropriate assumptions simplify the incompressible Navier-Stokes
Equations (i.e. conservation of mass and conservation of momentum) for this
particular problem. All the assumptions and the simplified equations should be
written;
Hollow Cylinder
1
2- Show that if aP / az=0 the velocity distribution between the two pipes can be
r
2017/12/1²/²
In
Figure QA2
2
as an
V/₂0
3- If μ=1.84×105 Ns/m², p= 1000 kg/m³, ½ = 15 mm, 1₂ = 5 mm and V₂0 = 20 m/s,
calculate the wall shear stress acting on the surfaces of the cylinders.
Transcribed Image Text:Question A2 a) Consider a steady, laminar flow through a straight horizontal tube having the constant elliptical cross section given by the equation 2 DEN5242 (May 2019) QA2 continued The streamlines are all straight and parallel. Investigate the possibility of using an equation for the z component of velocity of the form W = A(1.0-- exact solution to this problem (A is a constant). expressed by: V₂ = V₂0 In v. X. be Incompressible Fluid (.p) a² b) Consider two long concentric pipes with an incompressible fluid flow between them (Figure QA2). The outer pipe moves axially with a constant velocity Vz0; Solid Cylinder at Rest 1- By using appropriate assumptions simplify the incompressible Navier-Stokes Equations (i.e. conservation of mass and conservation of momentum) for this particular problem. All the assumptions and the simplified equations should be written; Hollow Cylinder 1 2- Show that if aP / az=0 the velocity distribution between the two pipes can be r 2017/12/1²/² In Figure QA2 2 as an V/₂0 3- If μ=1.84×105 Ns/m², p= 1000 kg/m³, ½ = 15 mm, 1₂ = 5 mm and V₂0 = 20 m/s, calculate the wall shear stress acting on the surfaces of the cylinders.
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