1-Reynold’s Experimentuotechnology.edu.iq/dep-building/LECTURE/dams and water/first_class... · 1-Reynold’s Experiment In 1883, Osborne Reynolds demonstrated that there are two

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Lect.No.8 Asst.Prof.Dr. Jaafar S. Maatooq

2nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 1 of 21

The flow in closed conduit ( flow in pipe ) is differ from this occur in open channel where the flow in pipe is at a pressure ( does not have a free surface ) .

The flow in pipe can be demonstrated such as :-

- Laminar flow , - Transitional flow , - Turbulent flow .

To distinction between the above features , the well known “ Reynold, s Number” can be used , according to experiments that given by “ Osborn Reynold in 19th century “ .

1-Reynold’s Experiment

In 1883, Osborne Reynolds demonstrated that there are two distinctly different types of flow by injecting a very thin stream of colored fluid having the same density of water into a large transparent tube through which water is flowing. And from the feature of streaming this dye fluid , Reynold give a number can be considered as a boundary between flow faces , this number is a function of , flow velocity , fluid density , pipe diameter , and fluid viscosity , where ;

R= f (V , ρ , υ (or μ ) , D ) …………………….. (1)

and then , R= VDρ/μ or R = VD/υ ;

R= Reynolds No.,

μ = dynamic viscosity ,

υ = kinematic viscosity .

See Figure(1) , below for Reynold”s experiments ;




Fig.(1) : Experiments shows the flow state as demonstrated by Reynolds

Observations (dye) Reynolds Number, Re

Flow Classification

<2000 Laminar Flow

2000 - 4000 Transitional




Transitional/ Turbulent

> 4000 Turbulent




2-Viscous (Real) Flow in Conduits ,Head Loss in Pipes from Friction ( Major Losses)

The head loss between two points in a circular pipe carrying a fluid under pressure can be found by ; hf= ΔP

γ

Where: ∆p = p1 − p2 , and can be measured by using piezometer tubes.

The velocity of the flow can be found by using a Pitot tube. The reading of the Pitot tube is the total head = pressure head + velocity head




The total “ friction head loss “ (hL) , can be calculated using “ Darcy Equation” by well estimating of “ friction factor , f “ ; where :-

Also the “ friction head loss“ (hL) , can be calculated by using Hazen William Equation , where ;










3-Head Loss versus Discharge




The friction factor of “Darcy Equation” can be estimated , using “ Moody Diagram”

as shown in Fig.(2) , below ;

Fig.(2): Friction Factor estimation as presented by Moody




4-Method to Determine Darcy-Weisbach friction factor ( f )

PIPE FLOWS

Laminar (R < 2,000) Turbulent (R > 4,000)

f = 64/R Smooth Transitional Wholly Rough (δv > e) (0.071e ≤ δv ≤ e) (δv < 0.071e)

Turbulent (Smooth):

Prandtle ……….. 1√f

= 2 log ( R√f2.51

) for R > 4000

Blasisus ……….. f = 0.316R0.25 for 3000 < R < 100000

Turbulent ( Transitional) :

Colebrook …….. 1√f

= -2 log [ eD

3.7 + 2.51

R√f ]

Turbulent ( Wholly Rough ):

Von- Karamen … 1√√√√f

= 2 log ( 3.7eD

)




5-Minor Losses in Pipe

Losses caused by fittings, bends, valves, enlargement , contraction .

Losses are proportional to – velocity of flow, geometry of device , where; hL= K (V2/2g)

The value of K is typically provided for various devices , where , K is a loss factor - has no units (dimensionless) .

The following variation in design and installation devices in pipe systems which cause “ minor losses “ :-




• Sudden enlargement :

Energy lost is because of turbulence. Amount of turbulence depends on the differences in pipe diameters . The values of K have been experimentally determined and provided in Fig.(3) , below .

Fig.(3): Loss Factor for Sudden Enlargement




• Gradual Enlargement : If the enlargement is gradual , the energy losses are less. The loss again depends on the ratio of the pipe diameters and the angle of enlargement.

hL= K (V1

2/2g)

K can be determined from Fig.(4) , Below ;

Fig.(4): Loss Factor for Gradual Enlargement




Notes ; • If angle increases (in pipe enlargement) – minor losses increase • If angle decreases – minor losses decrease, but you also need a longer pipe to make the transition – that means more FRICTION losses - therefore there is a tradeoff and minimum loss including minor and friction losses occur for angle of 7 degrees . • Exit Loss :

• Case of where pipe enters a tank – a very large enlargement , • The tank water is assumed to be stationery, that is, the velocity is zero. • Therefore all kinetic energy in pipe is dissipated .

hL= 1.0 (V1

2/2g) where K=1 for this case of exit .




• Sudden Contraction :

Decrease in pipe diameter ;

Loss is given by :-

hL= K (V22/2g)

Note that the loss is related to the velocity in the second (smaller) pipe . The loss is associated with the contraction of flow and turbulence at the change of diameter and vena contracta ,which is formed at the beginning of the smaller diameter . See fig.(10.8) , below .

The section at which the flow is the narrowest is called Vena Contracta , at vena contracta, the velocity is maximum . K can be computed based on diameter ratio and velocity of flow using Fig.(5) below. Note that the energy losses for sudden contraction are less than those for sudden enlargement .




Fig.(5): Loss Factor for Sudden Contraction • Gradual Contraction:

Again a gradual contraction will lower the energy loss (as opposed to sudden contraction). θ is called the cone angle.




hL= K (V22/2g)

K is given by Fig.(6) , below , Note that K values increase for very small angles (less than 15 degrees) .

Fig.(6): Loss Factor for Gradual Contraction




• Entrance Losses :




• Resistance Coefficient for Valves and Fittings :

The minor losses resulting when using any fittings (such as valve , elbow , bend , etc. ) can be computed by :-

hL= K (V 2/2g)

Where “ K “ is computed by using a so called “ Equivalent Length “ as :- K= Le

D f T

Le = equivalent length (length of pipe with same resistance as the fitting/valve) , fT = friction factor . The equivalent ratio (Le/D) for various valves/fittings , and “fT” for new steel pipe can be computed using Tables below ;

For OLD pipes however, fT cannot be computed by this table. You have to use the procedure we used for Moody’s diagram :-

• Get “ε” for the pipe type from Table(3.8) ,

• Determine “D/ ε” for the pipe ,

• Then use the Moody diagram to determine the value of “fT” , for the zone of complete turbulence .







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1-Reynold’s Experimentuotechnology.edu.iq/dep-building/LECTURE/dams and water/first_class... · 1-Reynold’s Experiment In 1883, Osborne Reynolds demonstrated that there are two