1-Reynold s Experiment

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1 Lect.No.8 2 nd 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 19 th 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 ;

2 Lect.No.8 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 2 of 21 Fig.(1) : Experiments shows the flow state as demonstrated by Reynolds Observations (dye) Reynolds Number, R e Flow Classification <2000 Laminar Flow Transitional

3 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 3 of 21 Transitional/ Turbulent > 4000 Turbulent

4 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 4 of 21 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

5 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 5 of 21 The total friction head loss (h L ), can be calculated using Darcy Equation by well estimating of friction factor, f ; where :- Also the friction head loss (h L ), can be calculated by using Hazen William Equation, where ;

6 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 6 of 21

7 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 7 of 21

8 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 8 of 21 3-Head Loss versus Discharge

9 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 9 of 21 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

10 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 10 of 21 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 (δ v > e) (0.071e δ v e) (δ v < 0.071e) Turbulent (Smooth): Prandtle.. 1 f = 2 log ( R f 2.51 ) for R > 4000 Blasisus.. f = R 0.25 for 3000 < R < Turbulent ( Transitional) : Colebrook.. 1 f = -2 log [ e D R f ] Turbulent ( Wholly Rough ): Von- Karamen 1 f = 2 log ( 3.7 e D )

11 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 11 of 21 5-Minor Losses in Pipe Losses caused by fittings, bends, valves, enlargement, contraction. Losses are proportional to velocity of flow, geometry of device, where; h L = K (V 2 /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 :-

12 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 12 of 21 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

13 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 13 of 21 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. h L = K (V 1 2 /2g) K can be determined from Fig.(4), Below ; Fig.(4): Loss Factor for Gradual Enlargement

14 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 14 of 21 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. h L = 1.0 (V 1 2 /2g) where K=1 for this case of exit.

15 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 15 of 21 Sudden Contraction : Decrease in pipe diameter ; Loss is given by :- h L = K (V 2 2 /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.

16 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 16 of 21 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.

17 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 17 of 21 h L = K (V 2 2 /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

18 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 18 of 21 Entrance Losses :

19 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 19 of 21 Resistance Coefficient for Valves and Fittings : The minor losses resulting when using any fittings (such as valve, elbow, bend, etc. ) can be computed by :- h L = 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), f T = friction factor. The equivalent ratio (Le/D) for various valves/fittings, and f T 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 f T, for the zone of complete turbulence.

20 2 nd Semester Flow Dynamics in Closed Conduit (Pipe Flow) 20 of 21

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

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