1. Heat and Flow Technology I.
ÓBUDA UNIVERSITY
Heat and Flow Technology I.
Use only inside
Dr. Ferenc Szlivka
Professor
Dr. Szlivka: Heat and Flow Technology I_9

2. Friction flow in tube Chapter 9.

3. Laminar and turbulent flow
Laminar flow
Turbulent flow

4. Laminar and turbulent flow

5. Laminar and turbulent flow
a./ Laminar flow
b./ Turbulent flow

6. Turbulent flow
Smog flow
Flow around a cylinder (Kármán vortex street)

7. Pressure loss in a straight pipe
There is a friction loss
Darcy-formula

8. Solution of Navier-Stokes equation in tube
„l" is the length , with Dp’the pressure loss

9. Solution of Navier-Stokes equation in tube for laminar flow
Darcy-formula
where Re is the Reynolds’ number

10. Straight pipe pressure loss in turbulent flow
Reynolds’ number
"v" is the average velocity,
"d" is the pipe diameter
"r" density of fluid
"m" dynamic viscosity.
The pipe wall is not smooth because of the producing process or the corrosion. The average roughness is k and the relative roughness k/d, or the reciprocal of it is d/k.

11. Nikuradse-diagram

12. Moody-diagram

13. Roughness of different materials
k [mm]
Riveted iron pipe
Concrete
wood channel
Cast-iron
Zincked iron
Asphalted cast-iron
Iron, (little rusted)
Iron
Drawn iron
Glass
smooth

14. Moody-diagram
Haaland-formula

15. Three different pipe problems
Given the diameter of the pipe "d", the length of pipe „l", the average diameter "v" , or the volume flow rate „ qv ", and the data of fluid: density "r" and viscosity "m", The question is the pressure loss "Dp".
II. Given the diameter of the pipe "d", the length of pipe „ l ", and the pressure loss Dp', and the data of fluid: density "r" and viscosity "m",
The question is the volume flow rate " qv ".
III. Given the length of pipe „ l ", the pressure loss Dp', the volume flow rate „qv", and the data of fluid: density "r" and viscosity "m„.
The question is the diameter of the pipe "d".

16. I. pipe problem
Calculate the pressure loss in an asphalted cast-iron pipe. Water is flowing in it
data:
Solution:
From the 8.1 table look out the dynamic viscosity.

17. 10 1
10-1
10-2
1,3*10-3
10-3
10-4
10-5

18. Material
k [mm]
Riveted iron pipe
Concrete
wood channel
Cast-iron
Zincked iron
Asphalted cast-iron
Iron, (little rusted)
Iron
Drawn iron
Glass
smooth

19. 0,028
1250

20. II. pipe problem
Calculate the average velocity in an asphalted cast-iron pipe!
data:
Solution:
We don’t know the average velocity (or the volume flow rate) so we can’t calculate the "l"-and the Re number. So we should make an iteration process. Fortunately the process is fast.
Look out the roughness and the.

21. Dr. Szlivka: Fluid Mechanics 9.
We don’t know the Re number, the velocity is unknown. So we assume beginning l0=0, In this case l0=0,02.
1250
Dr. Szlivka: Fluid Mechanics 9.

22. Make a formula from Darcy’s formula.

23. 0,026
4,073*104

24. Check the relative error between two steps
If the difference is biger than 10% , we calculate once more!

25. A new l from the Moody diagram.
Check the relative error.
The difference is smaller than 10%, so it is the final result.
The average velocity is:

26. III. pipe problem (design problem)
data:
Solution:
The question is the diameter „d”.
"l", and the Re-number, are depending on the velocity (which is unknown) we should make an iteration process.
To solve the problem we choose a standard pipe diameter, which can be bought.
The usual average velocity is 1-2 m/s .

27. The diameter was choosen 5 in d=128,2 mm.
Nominal diameter
[in]
Effective diameter
[mm] 2
52.5
2 1/2
62.7 3
77.9
3 1/2
90.1 4
102.3 5
128.2 6
154.1 8
202.7 10
254.5
The diameter was choosen 5 in d=128,2 mm.
The solution after is the I. problem. In these case:

28. 0,026
1068

29. Put the volume flow rate into the Darcy’s formula:
The calculated pressure loss is bigger than the given pressure loss. So we should choose a bigger diameter but only with one step bigger diameter ! (Unless the pipe is to expensive.)
The calculated pressure loss is smaller than the given one. With a trothling we it can be made the difference.
Nominal diameter
[in]
Effective diameter
[mm]] 2
52.5
2 1/2
62.7 3
77.9
3 1/2
90.1 4
102.3 5
128.2 6
154.1 8
202.7 10
254.5
Comment:
Put the volume flow rate into the Darcy’s formula:

30. Comment:
Puting the volume flow rate into the Darcy’s formula:
The formula shows: If the diameter is 10% smaller the pressure loss rises approximately 50%!

31. Noncircular duct loss coefficience
where "K" is the circumference connected with the fluid , (example : Open channel ),
"A" is the cross section area filled with fluid.

32. Noncircular duct loss coefficience
Let us see a circle pipe, which has the the same pressure loss than in a noncircular duct on the same length and the same shear stress on the wall. Find the diameter of this circular pipe, This diameter is called equivalent diameter.

33. Fitting pressure losses

34. Valves
Straight valve
valve
latch
Butterfly valve
One way valve

35. Valves, taps, pressure loss coefficience, and equivalent pipe length
Valves, taps, etc. pressure loss coefficience, and equivalent pipe length
Type
Loss coefficience z
Streight valve fully open
6.8
340
Corner valve fully open
2.9
145
Tolózár teljesen nyitva
0.26 13
1/4 open 18
900
1/2 open
3.2
160
3/4 open
0.7 35
One way valve
2.7
135
Ball way valve 3
150
Butterfly valve fully open
0.3 15
Valves, taps, pressure loss coefficience, and equivalent pipe length

36. Elbows loss coefficience, and equivalent pipe length

37. Air filter pressure loss

38. Air heater pressure loss