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

Friction flow in tube Chapter 9.

Laminar and turbulent flow Laminar flow Turbulent flow

Laminar and turbulent flow

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

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

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

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

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

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.

Nikuradse-diagram

Moody-diagram

Roughness of different materials k [mm] Riveted iron pipe 0.9 -9.0 Concrete 0.3 - 3.0 wood channel 0.18 - 0.9 Cast-iron 0.26-0.6 Zincked iron 0.1-0.15 Asphalted cast-iron Iron, (little rusted) 0.1-0.3 Iron 0.02-0.046 Drawn iron 0.0015-0.03 Glass smooth

Moody-diagram Haaland-formula

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".

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.

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

Material k [mm] Riveted iron pipe 0.9 -9.0 Concrete 0.3 - 3.0 wood channel 0.18 - 0.9 Cast-iron 0.26-0.6 Zincked iron 0.1-0.15 Asphalted cast-iron Iron, (little rusted) 0.1-0.3 Iron 0.02-0.046 Drawn iron 0.0015-0.03 Glass smooth

0,028 1250

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.

Dr. Szlivka: Fluid Mechanics 9. We don’t know the Re number, the velocity is unknown. So we assume beginning l0=0,02 - 0.03. In this case l0=0,02. 1250 Dr. Szlivka: Fluid Mechanics 9.

Make a formula from Darcy’s formula.

0,026 4,073*104

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

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:

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 .

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:

0,026 1068

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:

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%!

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.

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.

Fitting pressure losses

Valves Straight valve valve latch Butterfly valve One way valve

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

Elbows loss coefficience, and equivalent pipe length

Air filter pressure loss

Air heater pressure loss