H08.docx

PRACTICUM REPORT OF MECHANICAL FLUID LAB

FLUID MECHANICS

BERNOULLI’S THEOREM

GROUP 21

Rivanto 1306437031

Danny Tirta Winata 1306437025

Rafitya Rahisa 1306437063

Zain Azzaino 1306437044

Fhassi Maulavi Anfiqi 1306437050

Day/Date : Friday, 3 October 2014Assistant : Approval : Grade :Signature :

LABORATORIUM HIDROLIKA HIDROLOGI DAN SUNGAIDEPARTEMEN TEKNIK SIPIL

FAKULTAS TEKNIKUNIVERSITAS INDONESIA

2014

Friction in Pipes

A. Objectivers1. Examining the change in pressure due to friction in the circular pipe with an average

flow rate

2. Indicate the presence of laminar flow and turbulent flow

B. Basic TheoryFlow pressure loss in the pipe caused by the force of the friction in the pipe. The

higher the flow rate, then greater the pressure loss. Fluid flow can be determine into

three types there are:

1. Laminar flow

Laminar flow is flow of the liquid that moves in layers, or lamina – lamina

with another layer which slide through smoothly. In laminar flow, viscosity

serves to reduce the tendency of the relative motion between the layers. So,

the laminar flow had fulfill the law of newton which is can be described as

τ=μ dudy (1)

2. Turbulent flow

Turbulent flow is a flow which the movement of the fluid particles is very

uncertain due to mixing and rotation of particles between the layers,

resulting in the exchange of momentum from one part of the fluid to another

fluid in large scale. In turbulent flow conditions, the turbulent that occurred

generate shear stress force the evenly distributed throughout the fluid that

resulting losses of flow.

3. Transitional flow

Transitional flow is a flow that is the transition between laminar to turbulent

flows.

Reynolds Number

Reynolds number is a dimensionless number that determined a flow into

laminar, transitional or turbulent. Reynolds number can be calculate using these

formula.

ℜ=VD . ρμ

(2)

Where,

V = the average speed of the fluid flow (m/s)

D = inner diameter of the pipe (m)

μ = dynamic viscosity of the fluid( kgm

. s)∨¿)

ρ = fluid density (kgm2 )

Judging from the flow velocity , Reynolds assumed or categorized laminar

flow when the flow has a number Re is less than 2300, for the transition flow is the Re

2300 and 4000 numbers are also commonly referred to as the critical Reynolds number,

whereas turbulent flow Re number has more than 4000.

Coefficient of friction

The coefficient of friction is influenced by the speed because the velocity

distribution in laminar flow and turbulent flow is different, then the friction coefficient

different for each type of flow. Pressure loss in the pipe flow arises due to friction in the

pipe. The higher the flow rate, the greater the pressure loss. Loss of energy (h f ) is equal

to the pressure loss (h2 - h1), because the velocity is constant along the pipe.

According to Poiseuille for the laminar flow:

h f=32. v .V . L

G. D2

Where,

h f=h2−h1

ρ = fluid density (kgm2 )

V = kinematic viscosity

v = average flow velocity

L = pipe length

D = Diameter of pipe

g = earth gravitation

Darcy and Weisback gives the relationship between pressure loss and velocity

turbulent flow as follows:

h f=f . L . v2

2. g . Df =friction factor

Which if Poiseuille dan Darcy-Weisback formula is merge then :

32. v . v . LG. D2 = f .L . v2

2. g . D

f =16. vD .v

=16ℜ →(ℜ=D . v

v )C. Apparatus

a. Hydraulic table

b. Stopwatch

c. Measuring Glass

d. Friction in pipe instruments

e. Hand pump

D. Procedurea. Water Manometer Procedure

1. Practitioner turning on the pump and opening the flow regulator valve on the

end of the pipe on the hydraulics table, let the water flow until all the air out.

2. Practitioner closing the valve and watching both of the water manometer gauge

until it gained in a balanced state.

3. Practitioner opening the valve on the flow hydraulics table.

4. Practitioner opening the valve on the pipe end slowly.

5. Practitioner noting the height difference in the water manometer.

6. Practitioner measuring the flow rate by using a measuring cup and a stopwatch.

7. Practitioner redoing step 4 to 7 for a range of different pressures until there are

7 variations.

b. Mercury Manometer procedure

1. Practitioner closing both of the valve, then removing the pipe connect to the

water manometer and connecting the pipe to the mercury manometer.

2. Practitioner turning on the pump and opening the flow regulator valve on the

end of the pipe on the hydraulics table, let the water flow until all the air out.

3. Practitioner closing the valve and watching both of the mercury manometer

gauge until it gained in a balanced state.

4. Practitioner opening the valve on the flow hydraulics table.

5. Practitioner opening the valve on the pipe end slowly.

6. Practitioner noting the height difference in the mercury manometer.

7. Practitioner measuring the flow rate by using a measuring cup and a stopwatch.

8. Practitioner redoing to step 5 to 8 for a range of different pressures until there

are 7 variations.

E. Data ProcessingL = 0.5 m T = 30° C

Pipe diameter = 3 x10−3 m g = 9,8 m /s2

v=0,802 ×10−6 Pipe diameter = 3 x10−3 m

Data Collection

Water (mm) Mercury (mm) Volume (ml) Time (s)h1 h2 h1 h2 Water mercury water mercury

204 230 258 280 24 32 14.87 2096188 240 248 290 48 49 15.2 3.08176 250 238 300 57 64 14.97 3.22163 260 228 310 69 74 15.2 3.1150 270 218 320 74 75 14.88 3138 280 208 330 76 90 14.9 2.88127 290 198 340 80 99 14.85 3.25

hf ≈|h1−h2|→hf waterhf ≈|h1−h2|×13,6 → hf mercur y

Q=volumeair (ml)/1000000

t→ Water Discharg e

f =2D . g .h f

L .V 2

ℜ=D .Vv

→ ReynoldsValue

Water Data Processing Results

h1 h2 hf Q A V f Re

0.20 0.23 0.03 1.61399E-060.00000706

50.228448

4 0.05 854.55

0.19 0.24 0.05 3.15789E-060.00000706

50.446977

3 0.03 1671.98

0.18 0.25 0.07 3.80762E-060.00000706

50.538940

6 0.03 2015.99

0.16 0.26 0.10 4.53947E-060.00000706

50.642529

9 0.03 2403.48

0.15 0.27 0.12 4.97312E-060.00000706

50.703909

2 0.03 2633.08

0.14 0.28 0.14 5.10067E-060.00000706

50.721963

4 0.03 2700.61

0.13 0.29 0.16 5.38721E-060.00000706

50.762520

2 0.03 2852.32Average 0.10 4.08285E-06

0.000007065

0.5778984 0.03 2161.71

Mercury Data Processing Result

h1 h2 hf Q A V f Re

0.258 0.280 0.299 1.52672E-080.00000706

5 0.0021617058.1754

3 8.08

0.248 0.290 0.571 1.59091E-050.00000706

52.251817

5 0.01241 8423.26

0.238 0.300 0.843 1.98758E-050.00000706

52.813273

4 0.01174 10523.47

0.228 0.310 1.115 2.3871E-050.00000706

5 3.378764 0.01076 12638.77

0.218 0.320 1.387 0.0000250.00000706

53.538570

4 0.01220 13236.55

0.208 0.330 1.659 0.000031250.00000706

5 4.423213 0.00934 16545.68

0.198 0.340 1.931 3.04615E-050.00000706

5 4.311612 0.01144 16128.22

Average 1.12 2.09118E-050.00000706

52.959915

91008.3204

8 11072.00

Linear regression relation between log hf and log V2, where X is log V2 and Y is loghf

Water Manometer Table Mercury Manometer Table

log V2 log Hf log V2 log hf

-1.28242 -1.58502665-

5.330707-

0.5240384

-0.69943 -1.283996660.705066

4-

0.2432118

-0.53692 -1.130768280.898423

9-

0.0740694

-0.38421 -1.013228271.057515

70.0473527

6

-0.30497 -0.920818751.097655

70.1421390

8

-0.28297 -0.847711661.291475

70.2198987

4

-0.2355 -0.78781241.269279

30.2858272

5

Water Manometer Table

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

-1.8-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0

f(x) = 0.741398606654533 x − 0.686657355993088R² = 0.955912896945201

log and log V2 ℎ𝑓Series2Linear (Series2)

Axis Title

Axis

Title

Mercury Manometer Table

-6 -5 -4 -3 -2 -1 0 1 2

-0.6-0.5-0.4-0.3-0.2-0.1

00.10.20.30.4

f(x) = 0.0974608877533021 x − 0.0346374735490893R² = 0.683834479505604

log and log V2 ℎ𝑓Series2Linear (Series2)

log V2

log 𝒉𝒇

Linear regression relation between log f (friction factor) and log Re, where log Re is X-axis and log f is Y-axis


log f log Re log Re log f-

1.2605789392.93173499

3 0.90759342 3.848692449

-1.542543696 3.22323237

3.925480084 -1.906254269

-1.551826131

3.304487776

4.022158823 -1.930469347

-1.586991012

3.380840223

4.101704746 -1.968139031

-1.573828071

3.420463509

4.121774729 -1.913492678

-1.522718044

3.431462044

4.218684742 -2.029553045

-1.510291203

3.455198254

4.207586554 -1.941428155

Water Manometer Graph

2.9 3 3.1 3.2 3.3 3.4 3.5

-1.8-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0

f(x) = − 0.517202786690946 x + 0.203304657618953R² = 0.725119177070956

Log f VS Log Re

Series2Linear (Series2)

Log Re

Log

f

Mercury Manometer Graph

0.5 1 1.5 2 2.5 3 3.5 4 4.5

-3-2-1012345

f(x) = − 1.80507822449339 x + 5.45683507567597R² = 0.994637626516196

Log f VS Log Re


Log Re

Log

f

Reynolds number and value of VC:

ywater= ymercury

−0 ,5172 x+0 ,2033=−1, 8051 x+5.4568

1 .2879 x=5.2535

x= 5.25351.2879

=4

ℜ=104

ℜ=0,003. V c

0,802 x10−6

104=0,003 .V c

0,802 x 10−6

V c=2,67 ms

Linear regression relation between log V and log ℎ𝑓 , where log V is X-axis and log ℎ𝑓 is Y-axis


log V log hf log V log hf-0.641211893 -1.585026652 -2.665353466 -0.524038411-0.349714517 -1.283996656 0.352533197 -0.243211801

-0.268459111 -1.13076828 0.449211936 -0.074069402-0.192106663 -1.013228266 0.52875786 0.047352761-0.152483378 -0.920818754 0.548827842 0.14213908-0.141484842 -0.847711656 0.645737855 0.219898739-0.117748633 -0.787812396 0.634639667 0.285827253

Water Manometer Graph

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

-1.8-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0

f(x) = 1.48279721330906 x − 0.686657355993089R² = 0.955912896945201

Log v VS log hf


Log hf

Log

V

log hf =a+b . logV

log hf =−0,6867+1,4828 log(0,53¿)¿

hf =10a .V b=k .V b hf water=10−0,6867 . (0,53¿¿1,4828)=0.08 ¿

Mercury Manometer Graph

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1

-0.6-0.5-0.4-0.3-0.2-0.1

0

0.10.20.30.4

f(x) = 0.194921775506604 x − 0.0346374735490893R² = 0.683834479505604

Log v VS Log hf


Log hf

Log

V

log hf =a+b . logV

log hf =−0 , 0346+0.1949 . log (2,67 ¿)¿

hf =10a .V b=k . V b hf water=10−0 , 30 46 .(2,67 ¿¿0.1949)=0,6¿

Error Calculation

Hf Relative Mistake=|hf rumus−hf rerata

hf rerata|×100 %

Error Calculation of hf water

hf water=¿ 0,07

hf average water=0,08

¿|0,07−0,080,08 |× 100 %=1 %

Error calculation of hf mercury

hf mercury=¿ 0,6

hf rerata=1,02

¿|0,6−1,021,02 |×100 %=41.17 %

F. Analysis

Procedure Analysis

This experiment aims to determine the change in pressure due to friction

in a circular pipe with an average flow velocity and to know what kind of stream

of water flowing in the pipe. In the lab will use two kinds of pressure gauge

manometer and the mercury manometer. In preparation, laboratory assistant

and the practitioner prepare equipment to be used by placing it on the table as

well as the end of the pipe hydraulics experimental apparatus connected with

the supply of the table hydraulics. Practitioner begins with an explanation by the

assistant to do the reading on the manometer. At first practitioner open flow

regulator valve and drain the water until all the air squeezed out until there are

no air bubbles in the pipeline. The entire air bubbles must be removed from the

tube in order to obtain accurate data by value, because air pressure can affect

the reading on the manometer.

Next the practitioner closes the flow, then set until the pressure in both

pipes are in a stable state. Furthermore measurement of the flow rate out of a

pipe test performed using a closed tube and stopwatch. When reading the water

from the manometer we used about 15 second for discharge measurement,

since the discharge flow is likely to be small. The measurement was performed at

different pressure by regulating the flow of water to the height h1 with 7

repetitions. Whenever repetition of the different pressure readings do not forget

to also measure the flow rate.

In subsequent readings, the reading of the mercury manometer, valve

closed again, and so release the hydraulics pipe enters the table and then

connect it to the tank. Make sure the water supply of the table hydraulics

connected to the tank, to start reading on a mercury manometer. Practitioner

perform the same procedure as in the water manometer readings, the first

pressure stabilized beforehand so that h1 and h2 indicate the same figure, the

following readings were taken at different pressures to see h2 are decreasing

according to 7 data variables. In contrast to the use of water manometer,

mercury manometer discharge measurement take only 3 second due to debit

that tend to be larger than the water manometer.

Graphs and Result Analysis

From the table it appears that the data on both the manometer, the

value of Re increases with increasing flow rate. The increasing value of Re can

also be seen in the higher flow rate.

There are at least four graphs of water and mercury manometer

consisting of a graph of the logarithm Reynolds number (Re log) and the

logarithm of the frequency of friction (log f) and velocity logarithmic relationship

graphs (log V) with a total head logarithmic (log hf). The graph is the result of the

use of the method of linear regression equation to the data obtained practicum.

2.9 3 3.1 3.2 3.3 3.4 3.5

-1.8

-1.4

-1

-0.6

-0.2

f(x) = − 0.517202786690946 x + 0.203304657618953R² = 0.725119177070956

Log f VS Log Re


Log Re

Log

f

0.5 1 1.5 2 2.5 3 3.5 4 4.5

-3-2-1012345

f(x) = − 1.80507822449339 x + 5.45683507567597R² = 0.994637626516196

Log f VS Log Re


Log Re

Log

f

The first two graphs shows the relationship between log Re (X) and log f

(Y) on a water manometer, where the regression equation is y = -0.5172x +

0.2033 and y = -1.8051x + 5.4568. This shows that the value of a growing log Re

will decrease the value of log f, which means there is a reverse ratio between the

values of Re and f.

Finding the critical velocity in this experiment, using linear regression

relationship between log v log hf. From the linear regression equation log f vs log

Re which has been obtained from the manometer (water and mercury), obtained

the value of x to find the critical Vc = yraksa yair using the equation, where the

next value of x that has been obtained is used to find the critical value of Re for

speed (Re for critical velocity = (Re) 10x). Kinematic viscosity of water at a

temperature of 30 ° C is equal to 0,802 ×10−6 m2 / s.

Finding the critical velocity in this experiment, using linear regression

relationship between log v log hf. From the linear regression equation log f vs log

Re which has been obtained from the manometer (water and mercury), obtained

the value of x to find the critical Vc = yraksa yair using the equation, where the

next value of x that has been obtained is used to find the critical value of Re for

speed (Re for critical velocity = (Re) 10x). Kinematic viscosity of water at a

temperature of 30 ° C is equal to 0,802 ×10−6 m2 / s.

From the following equation obtained critical velocity of 2.67 m / s. When

a fluid flows through a circular pipe with a certain flow rate, fluid experience

friction due to the viscosity and leads to a change in pressure. When the fluid

moves through a pipe with constant diameter and with a low speed, the

movement of each particle along a line generally parallel to the pipe wall. When

the flow rate increases, the peak point reached when the particle motion

becoming more random and complex. Speed, about which this change occurs is

called the critical velocity (Vc), and flow at a higher velocity levels called

turbulent and at a pace lower level is called laminar. The critical speed can also

describe the Reynolds number at the transition state that determines the

boundary between laminar and turbulent flow patterns.

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1

-0.6-0.5-0.4-0.3-0.2-0.1

00.10.20.30.4

f(x) = 0.194921775506604 x − 0.0346374735490893R² = 0.683834479505604

Log v VS Log hf


Log hf

Log

V

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0

-1.8-1.6-1.4-1.2

-1-0.8-0.6-0.4-0.2

0

f(x) = 1.48279721330906 x − 0.686657355993089R² = 0.955912896945201

Log v VS log hf


Log hf

Log

V

The next 2 graphs also important because it has the relationship between

log V (X) and log hf (Y) where the water manometer regression equation is y =

0.1949x - 0.0346, while the mercury manometer is y = 1,4828x – 0.6867

This graph gives an overview of the results to changes in pressure,

determine the hf pressure difference at each flow rate. It appears that if the

average speed is less than the critical speed, the hf value found using the mean

velocity. Conversely, if the average speed is greater than the critical speed, the

value hf searched using the critical velocity.

Using the linear equations obtained by the graph, we use the following forula to find hf

log hf = a + b log V

hf = 10a . Vb

hf at Water Manometer = 0.08

hf at Mercury Manometer = 0.6

Then we determine the type of the flow using these standards

0<ℜ≤ 2000, Laminer

2000<ℜ≤ 4000, Transition

ℜ>4000, Turbulent

Water Mercury

ReFlow Type Re

Flow Type

854.5451102 laminer8.08338790

6 laminer

1671.984972 laminer8423.25762

5 turbulent

2015.987224 transition10523.4664

9 turbulent

2403.478398 transition12638.7681

2 turbulent2633.076692 transition 13236.5477 turbulent

2700.611074 transition16545.6846

2 turbulent

2852.320042 transition16128.2242

7 turbulent

c. Error Analysis

The value of relative error of hf which is obtained at water manometer is

1% and for mercury manometer is 41.17%.

The error might be caused by :

Error on inaccurate measurement of time possible suppression of

late stopwatch to measure the resulting differences in the flow

rate.

error reading the volume of water in a measuring cup

errors reading manometer scale due to fluctuation

G. Conclusion

The value of critical velocity is Vc = 2.67 m/s

More friction causes less pressure.

Laminar flow requires Re < 4000.

Transition Flow requires 2000 < Re <4000.

Turbulent flow requires Re > 4000.

H. Reference

Exoeriment Guidance Fluid Mechanics and Hydraulics. Laboratory Hydraulics,

Hidrology dan river Civil Engineering University of Indonesia. Depok. 2014.

Potter, Merle. C and Wiggert, David. C. Mechanics of Fluids. Prentice Hall

Englewood Cliffs : NJ 07632.

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