Objectives 1. To refine the Bernoulli’s equation by introducing the frictional head
loss, hf . 2. To investi investigat gate e the pressur pressure e loss loss due to frictio friction n in straig straight ht pipes. pipes. (D1=10mm, D2=7mm) 3. To compar compare e the calcul calculate ated d fricti friction on factor factor to the estima estimated ted fricti friction on factor from the Moody diagram.
Introduction Fluid flow can be either laminar or turbulent or transitional. The factor that determines which type of flow is present is the ratio of inertia forces to viscous forces within the fluid, expressed by the nondimensional Reynolds Number, Reynolds number : Re= ρVD μ
where V and D are a fluid characteristic velocity and distance. For example, for fluid flowing in a pipe, V could be the average fluid velocity, and D would be the pipe diameter. Typically, viscous stresses within a fluid tend to stabilize and organize the flow, whereas excessive fluid inertia tends to disrupt organized flow leading to chaotic turbulent behaviour. Fluid flows are laminar for Reynolds Numbers up to 2000. Beyond a Reynolds Number of 4000, the flow is completely turbulent. Between 2000 and 4000, the flow is in transition between laminar and turbulent, and it is possible to find subregions of both flow types within a given flow field.
Procedures 1. the pum pump p is start started ed and and water water will will start start to flow flow 2. the swivel swivel tube is is raise raise so that it it close close to the the vertical. vertical. 3. the benchbench-reg regula ulatin ting g valve valve is adjust adjusted ed so that there there is small small overflow overflow from the inlet inlet tank and overflow tank. 4. series series of of flow cond conditi ition on with with outlet outlet head head is set. set. 5. at each conditio condition n , the flow flow rate is measure measure using using volumet volumetric ric tank and and a stopwatch stopwatch 6. steps steps 1-5 1-5 is is repea repeated ted for for 10 10 mm mm pipe pipe 7. graph graph of log log (hf/L (hf/L)) vs log log (V) is is plotte plotted. d. 8. the fricti friction on factor factor is estim estimated ated from from Moody Moody Diag Diagram ram..
Results
Pipe, D = 7mm #
Outlet head (cm)
Inlet head, h1
Inlet head, h 2
Time, t
(cm)
(cm)
(second)
1
35
400
285
78
2
30
380
255
67
3
25
299
185
59
4
20
268
131
53
5
15
234
75
47
Inlet head, h1
Inlet head, h 2
Time, t
(cm)
(cm)
(second)
Pipe, D = 7mm #
Outlet head (cm)
1
35
367
285
78
2
30
333
255
67
3
25
299
185
59
4
20
268
131
53
5
15
234
75
47
Calculated data Pipe, D = 7mm #
Volumetric flow rate Q (m3/s)
Average velocity V (m/s)
Re # (dimensionless)
Fraction head loss hf (m)
Friction factor, f (dimensionless)
Log of Frictional head loss per unit length, log (hf / L)
Log of average velocity Log (V)
1
3.85x10-5
1.00
7832.77
0.82
0.31
0.36
0.00
2
4.48x10-5
1.16
9086.02
0.78
0.22
0.34
0.06
3
5.09x10-5
1.32
10339.26
1.14
0.25
0.50
0.12
4
5.66x10-5
1.47
11514.18
1.37
0.24
0.58
0.17
5
6.38x10-5
1.66
13002.40
1.59
0.22
0.65
0.22
Pipe, D = 10mm #
Volumetric flow rate Q (m 3/s)
Average velocity V (m/s)
Re # (dimensionless)
Fraction head loss hf (m)
Friction factor, f (dimensionless)
Log of Frictional head loss per unit length, log (hf / L)
Log of average velocity Log (V)
1
6.00x10-5
0.76
8504.15
0.60
0.56
0.22
-0.12
2
3.53x10-5
0.45
5035.35
0.79
2.21
0.34
-0.35
3
4.11x10-5
0.52
5818.63
1.00
2.02
0.44
-0.28
4
9.38x10-5
1.19
13315.71
1.17
0.45
0.51
0.08
5
4.48x10-5
0.57
6378.11
1.32
2.16
0.56
-0.24
Friction factor, f D = 7mm
D = 10mm
#
Calculated
Moody diagram
Calculated
1
0.31
0.22
2
0.22
0.34
3
0.25
0.44
4
0.24
0.51
5
0.22
0.56
Moody diagram
CALCULATION:
1. Volu Volume metr tric ic flow flow 3 3L=0.003 m Q (m3/s) = Volume (m 3) / Time= (0.003m3) /78= 3.846 x 10 -5m3/s
2. Avera Average ge veloci velocity ty Area of pipe= π (D²/4) = π (0.007²/4) =3.8485x10 -5 m2 V (m/s) = Q/A= (3.846 x 10 -5m3/s)/ (3.8485x10-5 m2) = 1.00 m/s
3. Reyn Reynol olds ds # _ Reynolds # = ρ (kg/m3) x V (m/s) x d (m) µ (Ns/m2)
= (997.0x1.00x0.007)/ (0.891x10 -³) = 7832.77
4. Frict Friction ional al head head loss loss hf (m) hf = h1(m) – h 2(m) = 0.285m – 0.367m = 0.82m
5. Friction Friction factor, factor, f (dimen (dimension sionless less)) ƒ=
2gDhf LV2
=
2(9. 2( 9.81 81 m2/s) (0.00 (0 .007m) 7m) (0.8 (0 .82m) 2m) 0.36m x (1.0m/s)
2
6. Log of frict frictiona ionall head loss loss per unit unit length, length, log( log( hf / L )
= 0.312 0.3 128 8
log(hf / L ) = log
0.82m
= 0.3575
0.36m
7. Log of of averag average e velocit velocity, y, log( log( V ) Log V = log (1.00 m/s) = 0
Discussion
From this experiment will obtain data that will tell us whether the water flow is turbul turbulent ent or lamina laminar. r. From From the results results we manage manage to get, get, we calcula calculated ted the Reynol Reynold’s d’s Number. All the Reynold’s Number that we calculated show values higher higher than 4000. This shows that the water flow is completely turbulent. We also manage to observe the head loss that that occu occurs rs in a pipe pipe.. This This is due due to frict frictio iona nall resi resist stan ance, ce, hydr hydrau auli licc grad gradie ient nt,, and and the the relationship between head loss and the Reynold’s number. We also manage to see that when the diameter is larger, the Reynold Number will be higher as well as the volume flow rate. This is due to the equation Reynolds # = ρ (kg/m3) x V (m/s) x d (m) µ (Ns/m2)
That shows diameter is increased, the viscousity will decrease and average velocity of water will increase. All these will lead to higher Reynld Number. There are several things we need to observe when doing the experiment. Since this experiment involving taking reading, our eyes level should be parallel to the reading to avoid parallax error. We also must take the reading immediately after the volumetric tank stop. Members in the group should cooperate well to have better result fom the experiment.
Conclusion We manage to finished our experiment succesfully without many problem. We also manage manage to unders understan tand d Reynol Reynold d Number Number clearly clearly.. We also also manage manage to use use Moody Moody Chart Chart correct correctly ly and manage manage to differ different entiate iate between between turbul turbulent ent and lamina laminarr flow. flow. Overal Overall, l, the experiment is a success.
References: 1.
Fluid Mechanics Laboratory Guidelines for Biotechnology Engineering Lab 1, 3 edition (Jan 2007), Syed Abu Bakar Al-Saggoff. Fluid Mechanics Fundamental and Applications, Yunus A. Cengel, John M. Cimbala rd
2.
QUESTIONS:
Part I:
1. Derive the the Bernoulli’s Bernoulli’s equation equation from from the First Law Law of Thermodynamics. During the derivation, state all assumption and consideration clearly. Pout /ρ + V2out/2 + gzout = Pin/ρ + V2in/2 + gzin
Assumptions:
Inviscid flow
Incompressible flow
Steady flow
2. What are the Hydraulic Grade Line and Energy Grade Line? How 2 lines are relates to each other? How the 2 lines relates with Bernoulli equation?
Hydraulic Grade Line Line is line that shows shows the sum sum of the static pressure and the elevation heads, P/ρg + z.
Energy Grade Line is line that shows the total head of the fluid, P/ρg + V2/2g + z
Thus, relationship between the lines is when the Energy Grade Line rise to a distance V2/2g above the Hydraulic Hydraulic Grade Line, Energy Grade Line = Hydraulic Grade Line + 2 V /2g.
Besides, both are part of the Bernoulli equation.
3. What is the the re restri strictio ction n of Bernou Bernoulli lli equation? equation?
Bernoulli’s equation is only applicable in certain conditions which are:
Steady flow Frictionless; along a streamline in the core region, not along a streamline close to the surface.
Not applicable in flow section involves pump, turbine or fan.
No temperature change.
4. By using using all answers answers for for the questio questions ns above, above, explain explain what you you should should do in the experiments in order to achieve the objectives.
We must define head loss in order to apply the frictional effect into Bernoulli equation. Thus, I should follow the restriction of Bernoulli equation in term of frictional effect.
