Lecture 3 - Fundamentals of internal flows (KARIMI)

Question 1

What is internal flow convection?

Answer 1

Convective heat transfer from fluid flow inside a conduit

Question 2

What happens with velocity boundary layer at the beginning of the pipe/channel?

Answer 2

Boundary layer forms. The flow is divided into two distinctive regions: velocity boundary layer containing strong viscous effects and effectively inviscid core.

Question 3

What happens to the BL during the entrance region?

Answer 3

The boundary layer grows and the inviscid core shrinks. The velocity profile is constantly changing.

Question 4

Can you draw the diagram of velocity gradients and BL for internal flows?

Answer 4

YES OR NO

Question 5

What happens in the fully developed region?

Answer 5

The BL fills the total volume of the pipe. The velocity profile remains unchanged.

Question 6

What is HYDRONAMICALLY FULLY DEVELOPED FLOW?

Answer 6

u is not a function of x and the velocity only varies transversely.

Question 7

For what value of Re_D is the pipe flow laminar and what is another name for this value?

Answer 7

Critical Reynolds Number, Re_D </= 2300

Question 8

What value is flow fully turbulent?

Answer 8

Re_D > 10000

Question 9

What does the length of the entrance region depend on?

Answer 9

The state of the flow (laminar or turbulent and Re)

Question 10

Expression for laminar flow relating pipe distance to Re?

Answer 10

x_fd,h/D = 0.05 Re_D, where x_fd,h is the minimum length of the pipe downstream of that the flow is hydrodynamically fully developed (or length of the entrance region).

Question 11

Range of distance/diameter for turbulent flows?

Answer 11

10</= 60

Question 12

Can you derive the expression for Um?

Answer 12

Yes or no.
M dot = rho.u_m.Ac
M dot = integral (overAc) of rho.u(r,x).dAc
Equate for u_m to get an expression relating u_m, r and u(r,x)

Question 13

Why is nu = 0?

Answer 13

du/dx + dv(nu)/dy = 0 for conservation of mass. Flow is fully developed so du,dx, dv,dy=0. From continuity: dv/dy=0 and therefore v=0. This makes sense because if the velocity in the y direction wasn’t zero, fluid would be flowing through the pipe wall. In the fully developed region, velocity field has only one axial component which remains unchanged along the pipe.

Question 14

Expressions for Um and U(r)/Um?

Answer 14

Um = m dot / rho.Ac = -(R^(2)/8mu)(dP/dx)
U(r)/Um=2[1-(r/R)^2]
where U(r) = 1/4mu(dP/dx)(r^2-R^2)

Question 15

Expression for shear stress in relation to Um?

Answer 15

tau = 8.mu.Um/D

Question 16

A new expression for skin friction coefficient also known as fanning friction coefficient?

Answer 16

Cf = 2tau/rho.Um^2 = 16/Re_D

Question 17

Why is pressure drop in pipe flow a very important engineering issue?

Answer 17

Increases the pumping power, signifies the required energy and cost of the process.

Question 18

How do we evaluate this pressure drop effect (laminar)?

Answer 18

Friction factor is used:

f = -(dP/dx).D/rho.(Um^2/2)

Question 19

Fanning friction coefficient in relation to friction factor?

Answer 19

Cf=f/4

Question 20

Show that for fully developed laminar flow f=64/Re_D

Answer 20

Cf=f/4 =16/Re_D => f= 4Cf = 4*16/Re_D = 64/Re_D

Question 21

How are results of pressure drop effect in turbulent flow shown?

Answer 21

Much more complicated so empirical results are frequently used (MOODY DIAGRAM)

Question 22

In practise, what is pressure drop dominated by?

Answer 22

Re and surface roughness of the pipe.

Question 23

Can you draw the diagram for thermal gradient and BL in internal flow?

Answer 23

YES OR NO

Question 24

When does a thermal boundary layer develop?

Answer 24

When the pipe surface temp is different to that of the fluid.

Question 25

In what way is the thermal boundary layer similar to velocity boundary layer?

Answer 25

Grows and eventually meet (at the thermally fully developed region). The temp field varies across the pipe cross section.

Question 26

What does the shape of the temp profile in the fully developed region depend upon?

Answer 26

The relative temp of the duct and the fluid.

Question 27

Expression for laminar flow relating pipe distance (wrt time) to Re?

Answer 27

x_fd,h/D = 0.05 Re_D.Pr

Question 28

Expression for rate of internal energy transported?

Answer 28

E dot = integral (over Ac) rho.c_v.T.dAc

Question 29

If the mean temp is defined such that E dot = m dot.c_v.Tm then what is Tm?

Answer 29

Tm = (2/Umr_o^2) . integral between 0 and r_o u.Tr.dr

Question 30

If the surface temp of the pipe is Ts then what is the local heat flux?

Answer 30

q”=h(Ts - Tm) (q”=q/A)