POLYTECHNIC UNIVERSITY OF PUERTO RICO DEPARTMENT OF CHEMICAL ENGINEERING SAN JUAN, PUERTO RICO CHE 4111/14 FLUID FRICTION APPARATUS _____________________ MAYLA R. GONZÁLEZ RAMOS #53557 _____________________ ASHLYIE A. DÁVILA #51818 _____________________ MIGDELÍS HUERTAS #52336 i
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POLYTECHNIC UNIVERSITY OF PUERTO RICO
DEPARTMENT OF CHEMICAL ENGINEERING
SAN JUAN, PUERTO RICO
CHE 4111/14
FLUID FRICTION APPARATUS
_____________________ MAYLA R. GONZÁLEZ RAMOS #53557
_____________________ ASHLYIE A. DÁVILA #51818
_____________________ MIGDELÍS HUERTAS #52336
EXPERIMENT DATE: JANUARY 3, 2011
DUE DATE: FEBRUARY 17, 2011
PROF. ZULEICA LOZADA
i
Abstract
In the Fluid Friction Apparatus experiment we studied flow, flow measurement techniques and
losses in a wide variety of pipes and fittings. The experiment consisted in the following: the
relationship between the head loss due to fluid friction and velocity for flow of water through a
smooth bore pipe for both laminar and turbulent flow, the head loss associated with flow of
water through standard fittings used in plumbing installation, and the relationship between fluid
friction coefficient and Reynolds number for flow of water through a roughened pipe. For the
completion of this experiment a wide variety of equipment was used. Our general equipment
used was the hydraulic bench, which allows us to take a specific volume of the fluid. For the
first part of the experiment (part A) two runs were necessary were made for both laminar and
turbulent flow. The head loss was taken and the Reynold’s number was to be calculated to
determine the behavior of the flow. For laminar flow the Reynolds number for the necessary two
runs are: 725.25 and 365.46. The velocities were of 0.0433m/s and 0.0209m/s respectively. The
head loss was of 0.014 mH20 for the first laminar flow and 0.020 mH2O for the second. The
values for the Reynold’s number in turbulent flow are 29,714.0 and 41,055.0, with velocities of
1.7030 m/s and 2.3545 m/s respectively. The head losses for turbulent flow were the following:
0.242 mH20 and 0.394 mH20. After these calculations were made in the smooth tube, a graph of
heat loss versus velocity was plotted to see how the fluid acts in turbulent and laminar flow. For
the second part of the experiment the K values for various pipe fitting were calculated. The
fitting used were the ball valve, the globe valve, the 30º elbow and the 45º elbow. These k
values can be found in table 5 of the Appendix, in which all experimental data for analyzing the
head loss due to pipe fittings is tabulated. The last part of the experiment was conduction with
the same principle as the first part but for a roughened pipe. The Reynold’s number for the first
two runs are: 429.10 and 345.25. The velocities were of 0.0246 m/s, 0.0198 m/s respectively.
The head loss was of 0.027 mH20 for the first laminar flow and 0.025 mH2O for the second. The
values for the Reynold’s number in turbulent flow are: 25,439.0 and 25,949.0. The velocities
were of 1.4593 m/s and 1.4884 m/s. The head losses for turbulent flow were the 0.577mH20 and
0.502 mH20. A graph was made in which the friction factor was plotted versus the log of
Reynolds.
ii
INDEX
Abstract....................................................................................................................................................... ii
Taking a Set of Results.......................................................................................................................31
Results and Discussion...............................................................................................................................32
Experiment A: Fluid Friction in a Smooth Bore Pipe..............................................................................32
Experiment C: Head Loss Due to Pipe Fitting.........................................................................................34
Experiment D: Fluid Friction in a Roughened Pipe.................................................................................37
Figure 8 shows that, as the relative roughness becomes greater, the assumptions that went into
Equation (40) become better; f becomes a constant that is independent of diameter, velocity,
density, and fluid viscosity.
Experiment A: Fluid Friction in a Smooth Bore Pipe
Graphs of h vs. u and log h vs. log u show the zones were the flow is laminar, turbulent, or in the
transition phase.
Figure 9: Graph of h plotted against u showing flow behavior in a smooth bore pipe.
20
Figure 10 Graph of log h vs. log u showing flow behavior in a smooth bore pipe.
Experiment C: Head Loss Due to Pipe Fitting
To calculate the head loss due to pipe fittings Bernoulli’s Equation must be applied:
Equation 45
The following assumptions were taken under consideration:
The flow is stationary
The velocity remains constant (v2=v1)
There is no work done on the system or the surroundings (W=0)
The change in height is negligible, h2=h1, (z was changed for h)
Subjected to these assumptions, Bernoulli’s Equation is reduced to:
Equation 46
Equation 47
21
As the fluid passes a fitting or accessory the friction can be put in the form of Equation 48.
Equation 48
Substituting Equation 45 in Equation 35 leads to:
Equation 49
Substituting P=ρgh in Equation 46 and rewriting it leads to:
Equation 50
A flow control valve is a pipe fitting which has an adjustable 'K' factor. The minimum value of
'K' and the relationship between stem movement and 'K' factor are important in selecting a valve
for an application. The 'K' values for various types of fittings are presented in Table 2 along with
their equivalent lengths.
Table 2: Equivalent lengths and K values for various kinds of fittings
Type of fitting Equivalent length, L/D, dimensionless
Constant, K, dimensionless
Globe valve, wide open 350 6.3
Angle valve, wide open 170 3.0
Gate valve, wide open 7 0.13
Check valve, swing type 110 2.0
90º standard elbow 32 0.74
45º standard elbow 15 0.3
90º long-radius elbow 20 0.46
Standard tee, flow-through run 20 0.4
Standard tee, flow-through branch 60 1.3
Coupling 2 0.04
22
Union 2 0.04
Head loss in a pipe fitting is proportional to the velocity head of the fluid flowing through the
fitting, setting h1 = 0 as reference rewriting eq. 47 leads to:
Equation 51
Where: K = fitting factor, v = mean velocity of water through the pipe (m/s), and g = 9.81
(acceleration due to gravity, m/s2).
Figure 11: Pipe fitting (45° elbow) to be used in experiment.
Experiment D: Fluid Friction in a Roughened Pipe
In a rough surface, like the one shown in Figure.13, turbulent flow is present, so turbulent flow
equations describe the movement inside a roughened pipe.
23
Figure 12: Fluid flow comparison through rough and smooth pipe
By empirical deduction it has been found that turbulent flow is proportional to the longitude and
the average velocity, and inversely proportional to the diameter of the pipe. Adding the friction
factor f , which is equal to half the proportionally constant in eq. 31 leads to:
Equation 52
Equation 53
Substituting P=ρgh in Equation 53 and rewriting leads to:
Equation 54
Where, ∆x= Length of pipe between tappings (m), D= internal diameter of the pipe (m), Vavg. =
mean velocity of water through the pipe (m/s), g = 9.81 (acceleration due to gravity, m/s2), f =
pipe friction coefficient (British), 4f = λ (American), and the roughness factor = k/ d where k is
the height of the sand grains.
24
25
Equipment
Description
All numerical reference relate to the ‘General Arrangement of Apparatus’. The test circuits are
mounted on a substantial laminate backboard, strengthened by a deep frame and carried on
tubular stands. There are six pipes arranged to provide facilities for testing the following:
Smooth bore pipes of various diameter (1), (2) and (4)
An artificially roughened pipe (3)
A 90 deg. bend (14)
A 90 deg. elbow (13)
A 45 deg. elbow (8)
A 45 deg. “Y” (9)
A 90 deg. “T” (15)
A sudden enlargement (6)
A sudden contraction (5)
A gate valve (10)
A globe valve (11)
A ball valve (7)
An in-line strainer (12)
A Venturi made of clear acrylic (17)
An orifice meter made of clear acrylic (18)
A pipe section made of clear acrylic with a Pitot static tube (16)
Short samples of each size test pipe (19) are provided loose so that the students can measure the
exact diameter and determine the nature of the internal finish. The ratio of the diameter of the
pipe to the distance of the pressure tappings from the ends of each pipe has been selected to
minimize end and entry effects. A system of isolating valves (V4) is provided whereby the pipe
to be tested can be selected without disconnecting or draining the system. The arrangement
allows tests to be conducted on parallel pipe configurations.
26
An all GRP floor standing service module incorporates a sump tank (23) and a volumetric flow
measuring tank (22). Rapid and accurate flow measurement is thus possible over the full
working range of the apparatus. The level rise in the measuring tank is determined by an
independent sight gauge (25). A small polypropylene measuring cylinder of 250ml capacity (28)
is supplied for measuring the flow rate under laminar conditions (very low flows).
Ported manometer connection valves (V7) ensure rapid bleeding of all interconnecting pipe
work.
The equipment includes a submersible, motor-driven water pump (24) and the necessary
interconnecting pipe work to make the rig fully self-contained. A push button starter (26) is
fitted, the starter incorporating overload and no-volt protection. An RCCB (ELCB) is also
incorporated.
Each pressure tapping is fitted with a quick connection facility. Probe attachments with an
adequate quantity of translucent polythene tubing are provided, so that any pair of pressure
tapping can be rapidly connected to one of the two manometers supplied. These are a mercury
manometer (20) and a pressurized water manometer (21).
NOTE: To connect a test probe to a pressure point, simply push the tip of the test probe
into the pressure point until it latches. To disconnect a test probe from a pressure
point, pressure point, press the metal clip of the side of the pressure point to
release the test probe. Both test probe and pressure point will seal to prevent loss
of water.
F1-10 Hydraulics Bench:
The F1-10 Hydraulics Bench, shown in Figure (8) allows us to measure flow by timed volume
collection. It also provides the necessary facilities to support a comprehensive range of
hydraulic models each of which is designed to demonstrate a particular aspect of hydraulic
theory.
Stopwatch:
A stopwatch allows students to determine the rate of a flow of water.
27
Schematic representation of the system:
Figure 13: Schematic diagram of The Friction Apparatus
Index sheet for C6 arrangement drawing
V1 SUMP TANK DRAIN VALVE
V2 INLET FLOW CONTROL VALVE
V3 AIR BLEED VALVE
V4 INSOLATING VALVES
V5 OUTLET FLOW CONTROL VALVE (FINE)
V6 OUTLET FLOW CONTROL VALVE (COARSE)
V7 MANOMETER VALVES
1 6mm SMOOTH BORE TEST PIPE
2 10mm SMOOTH BORE TEST PIPE
3 ARTIFICIALLY ROUGHENED TEST PIPE
28
4 17.5mm SMOOTH BORE TEST PIPE
5 SUDDEN CONTRACTION
6 SUDDEN ENLARGEMENT
7 BALL VALVE
8 45 deg. ELBOW
9 45 deg. “Y” JUNCTION
10 GATE VALVE
11 GLOBE VALVE
12 IN-LINE STRAINER
13 90 deg. ELBOW
14 90 deg. BEND
15 90 deg. “T” JUNCTION
16 PITOT STATIC TUBE
17 VENTURI METER
18 ORIFICE METER
19 TEST PIPE SAMPLE
20 1m MERCURY MANOMETER
21 1m PRESSURISED WATER MANOMETER
22 VOLUMETRIC MEASURING TANK
23 SUMP TANK
24 SERVICE PUMP
29
25 SIGHT TUBE
26 PUMP START/STOP
27 SIGHT GAUGE SECURING SCREWS
28 MEASURING CYLINDER (Loose)
29 DUMP VALVE
30
Procedure:
Operational Procedures
Flow rates through the apparatus may be adjusted by operation of outlet floe control
valve (V6).
Simultaneous operation of inlet flow control valve (V2) will permit adjustment of the
static pressure in the apparatus together with the flow rate.
Fine outlet control valve (V5) will permit accurate control at very low flow rates.
Suitable selection and operation of these control valves will enable tests to be performed
at different, independent combinations of flow rate and system static pressure.
Measurement of Flow Rates using the Volumetric Tank
The service module incorporates a molded volumetric measuring tank (22) which is
stepped to accommodate low or high flow rates.
A stilling baffle is incorporated to reduce turbulence.
A remote sight gauge (25), consisting of a sight tube and scale, is connected to a tapping
in the base of the tank and gives an instantaneous indication of water level.
The scale is divided into two zones corresponding to the volume above and below the
step in the tank.
A dump valve in the base of the volumetric tank is operated by a remote actuator (29).
In operation, the volumetric tank is emptied by lifting the dump valve, allowing the
entrained water to return to the stump (23).
When test conditions have stabilized, the dump valve is lowered, entraining the water in
the tank.
Timings are taken as the water level rises in the tank.
Low flow rates are monitored on the lower portion of the scale corresponding to the small
volume beneath the step.
Larger flow rates are monitored on the upper scale corresponding to the main tank.
Before operation, the position of the scale relative to the tank should be adjusted as
described in the commissioning section.
31
When extremely small volumetric flow rates are to be measured, the measuring cylinder
(28) should be used rather than the volumetric tank.
When using the measuring cylinder, diversion of the flow to and from the cylinder should
be synchronized as closely as possible with the starting and stopping of a watch.
Do not attempt to use a definite time or a definite volume.
Operation of the Self-Bleeding manometers
Both pressurized water manometer installed on the apparatus are fitted with quick
connection test probes and self-bleeding pipe work.
Each pressure point on the apparatus is fitted with a self-sealing connection.
To connect a test probe to a pressure point, simply push the tip of the test probe into the
pressures point until it latches.
To disconnect a test probe from a pressure point, press the metal clip of the side of the
pressure point to release the test probe.
Both test probe and pressure point will seal to prevent loss of water.
Each test probe is connected to the limb of a manometer via a vented ball valve which is
situated over the volumetric tank.
In operation, the connecting valves are set to the 90o position and the test probes screwed
onto the required test points.
Pressure in the test pipe, drives fluid along the flexible connecting pipe pushing air
bubbles to the valve where the mixture of air and water is ejected into the volumetric tank
via the vent in the body.
In this condition the valve connection to the manometer remains sealed keeping the
manometer fully primed.
When all air bubbles have been expelled at the vent, the valve is turned through 90o to the
live position connecting the test point directly to the manometer.
Prior to removal of the test probe, the valve is returned to the 90o position to prevent loss
of water from the manometer.
Using this procedure, the manometers once primed will remain free from air bubbles
ensuring accuracy in readings.
The pressurized water manometer incorporates a Schrader valve which is connected to
the top manifold.
32
This permits the levels in the limbs to be adjusted for measurement of small differential
pressures at various static pressures.
Then hand supplied will be required to effect reduction of levels at high static pressures.
Alternatively a foot pump (not supplied) may be used.
Experiment A: Fluid Friction in a Smooth Bore Pipe
Equipment Set-Up
Refer to the diagram “General Arrangement of Apparatus”.
Valve Settings
Close V1, 10, V4 in test pipe 3
Open V2
Open V 4 in test pipe 1, V 4 in test pipe 2 or 7 in test pipe 4 as required.
Open A and B or C and D after connecting probes to tappings.
Taking a Set of Results
Prime the pipe network with water.
Open and close the appropriate valves to obtain flow of water through the required test
pipe.
Measure flow rates using the volumetric tank in conjunction with flow control valve V6.
For small flow rates use the measuring cylinder in conjunction with flow control valve
V5 (V6 closed).
Measure head loss between tappings using the Hg manometer or pressurized water
manometer as appropriate.
Obtain readings on test pipe 4.
Experiment C: Head Loss Due to Pipe Fittings
Equipment Set-Up
Refer to the diagram “General Arrangement of Apparatus”.
33
Taking a Set of Results
Prime the network with water.
Open and close the appropriate valves to obtain flow of water through the ball valve.
Measure flow rates using the volumetric tank in conjunction with flow control valve V6.
Measure differential head between tappings on each fitting using the pressurized water
manometer.
Measure differential head between tappings on test valves using the pressurized water
manometer and mercury manometer as appropriate for different valve settings (open to
dosed).
Repeat this procedure for the following fittings: the ball valve, the globe valve, the 30º
elbow and the 45º elbow.
Experiment D: Fluid Friction in a Roughened Pipe
Equipment Set Up
Refer to the diagram "General Arrangement of Apparatus".
Valve Settings
Close V1, 10
Close V4 in test pipe 1, V 4 in test pipe 2 and 7 in test pipe 4.
Open V2
Open V 4 in test pipe 3 (roughened)
Open A and B or C and D after connecting probes to tappings.
Taking a Set of Results
Prime the pipe network with water.
Open and close the appropriate valves to obtain flow of water through the roughened
pipe.
34
Measure flow rates using the volumetric tank in conjunction with flow control valve V6.
For small flow rates use the measuring cylinder in conjunction with flow control valve
V5 (V6 dosed).
Measure head loss between the tappings using the pressurized water manometer as
appropriate.
Estimate the roughness factor k/ d.
Obtain readings on test pipe 3
35
Results and Discussion
Experiment A: Fluid Friction in a Smooth Bore Pipe
Part A of the experiment consisted in determining the relationship of the head loss due to friction
in both, laminar (Re<2000) and turbulent (Re>4000) flow. Two runs were necessary for each
type of flow, for which the head loss was taken and the Reynold’s number was to be calculated
to determine the type behavior, laminar or turbulent. Using the fluid friction apparatus it’s easier
to apply a relatively large velocity and to measure a large flow rate, therefore the turbulent flow
was easier to achieve than the laminar flow. To achieve an acceptable laminar flow the flow
rate, Q, had to be greatly reduced.
At the beginning, the first values of the Reynold’s number calculated, for each different type of
flow rate (Q), were all over 4000 (Re>4000) meaning that the flow remained turbulent. To
achieve the laminar flow, the flow rate, Q, was successfully reduced and was measured using a
test tube. The Reynolds numbers for the two runs in laminar flow are: 725.25 and 365.46. The
velocities were of 0.0433m/s and 0.0209m/s respectively. The head loss was of 0.014 mH20 for
the first laminar flow and 0.020 mH2O for the second. The values for the Reynold’s number in
turbulent flow are 29,714.0 and 41,055.0, with velocities of 1.7030 m/s and 2.3545 m/s
respectively. The head losses for turbulent flow were the following: 0.242 mH20 and 0.394
mH20. From these results we can see that the head loss for turbulent flow is bigger than that of a
laminar flow in a smooth pipe.
The linear regression of a h vs. u graph is plotted in Figure 14, where h is the head loss and u is
the velocity. In this graph we can see that the laminar flow for the 0.0175m smooth bore pipe is
a straight line but when the flow is turbulent the is a slight curvature. Also the lineal regression
of a log h vs. log u graph is plotted, where h is the head loss and u is the velocity (see Figure 15).
The behavior in Figure 15 does not compare to its theoretical graph presented in the theory. This
36
difference is because of experimental errors during the procedure and handling of the equipment.
One of the possibilities is that there was air in the pipes we didn’t notice. The water manometer
lacks accuracy and the water inside it wasn’t clean, there were several noticeable particles.
Water was also coming out of the threads, which can also cause experimental errors. Personal
errors are another source due to poor handling of the equipment or wrong calculations.
Figure 14: Graph showing h(m) vs u(m/s) behavior for a smooth bore pipe.
Figure 15: Graph showing log h vs log u behavior for a smooth bore pipe.
37
Experiment C: Head Loss Due to Pipe Fitting
The fitting factor (K) was calculated as the slope from the lineal regression of a ∆h vs. v2/2g
graph, where ∆h is the head loss, v is the velocity and g is the acceleration due to gravity. The
fittings used were the following: ball valve, 30º elbow, 45º elbow, and globe valve. The
theoretical value was calculated with the following equation:
The values calculated for the k values of the various pipe fittings in laminar flow are the
following:
Table 3: Values of the fitting factor, k, for various pipe fittings in both laminar and turbulent flow.
Fitting factor k theoretical
Fitting factor k experimental
Difference %
Globe valve 0.6004 0.5625 6.51
Ball valve (open) 0.7621 0.493 42.88
Ball valve
(semi open)
0.9006 0.6457 32.96
30°elbow 0.6090 0.599 1.65
45°elbow 0.4754 0.550 14.55
For a globe valve got a fitting factor (K) of 0.5625, a difference of 6.51%. In this way, one can
notice a good approximation to the theoretical value (0.6004). In an open ball valve fitting
yielded a factor (k) of 0.4930 and a difference value of 42.88% while in a semi-open ball valve
was obtained an experimental value of 0.6457 for a 32.96% difference. This compared with a
theoretical value of 0.7621 and 0.9006, demonstrating a difference much larger than the globe
valve.
In a 30-degree elbow fitting yielded a factor of 0599 and compared with theoretical value of
38
0.6090, remained a difference of 1.65%. While for an elbow of 45 degrees was fitting factor of
0.550 and the difference was 14.55%, which compared with its theoretical value of 0.4754.
Demonstrating a lower value approximation to 30-degree elbow.
Figure 16: Graph showing h (mH2O) plotted versus u2/2g behavior for a globe valve in laminar and turbulent flow.
Figure 17: Graph showing h (mH2O) plotted versus u2/2g behavior for a 30º elbow in laminar and turbulent flow.
39
Figure 18: Graph showing h (mH2O) plotted versus u2/2g behavior for a 45º elbow in laminar and turbulent flow
Figure 19: Graph showing h (mH2O) plotted versus u2/2g behavior for a ball valve wide open in laminar and turbulent flow
40
Figure 20: Graph showing h (mH2O) plotted versus u2/2g behavior for a semi open ball valve in laminar and turbulent flow
Experiment D: Fluid Friction in a Roughened Pipe
Part D of the experiment consisted in determining the relationship of the head loss due to friction
in both, laminar (Re<2000) and turbulent (Re>4000) flow for a roughened pipe. Two runs were
necessary for each type of flow, for which the Reynold’s number was to be calculated to
determine the type behavior, laminar or turbulent. Using the friction apparatus it’s easier to
apply a relatively large velocity and to measure a large flow rate, therefore the turbulent flow
was easier to achieve than the laminar flow. To achieve an acceptable laminar flow the flow
rate, Q, had to be greatly reduced. The Reynold’s number for the first two runs are: 429.10 and
345.25. Given that the Reynold’s numbers are smaller than 2000 (Re<2000) the flow is laminar.
This laminar flow was achieved reducing the flow rate, Q, which was measured using a test tube.
The velocities were of 0.0246 m/s, 0.0198 m/s respectively. The head loss was of 0.027 mH 20
for the first laminar flow and 0.025 mH2O for the second. The values for the Reynold’s number
in turbulent flow are: 25,439.0 and 25,949.0. The velocities were of 1.4593 m/s and 1.4884 m/s.
The head losses for turbulent flow were the 0.577mH20 and 0.502 mH20. From these results we
can see that the head loss for turbulent flow is bigger than that of a laminar flow in a roughened
pipe. In Figure 21 the relation between the Reynold’s number and the friction coefficient for a
roughened pipe.
41
Figure 21: Experimental data of λ=4f plotted against Re in logarithm scale graphic showing the relation between the pipe friction factor and Reynolds’s Number of roughened pipe
Figure 21 does not compare to the graph stipulated by the theory for this part of the experiment.
The sources of the experimental errors are the following: there might have been air in the pipes
we didn’t notice. The water manometer lacked accuracy and the water inside it wasn’t clean,
there were several noticeable particles. Water was also coming out of the threads, which can
also cause experimental errors. Personal errors are another source due to poor handling of the
equipment or wrong calculations.
42
Conclusion
Fluid Friction in a Smooth Bore Pipe
The Reynolds numbers for the two runs in laminar flow are: 725.25 and 365.46. The velocities
were of 0.0433m/s and 0.0209m/s respectively. The head loss was of 0.014 mH20 for the first
laminar flow and 0.020 mH2O for the second. The values for the Reynold’s number in turbulent
flow are 29,714.0 and 41,055.0, with velocities of 1.7030 m/s and 2.3545 m/s respectively. The
head losses for turbulent flow were the following: 0.242 mH20 and 0.394 mH20.
The linear regression of h vs. u graph is plotted in Figure 14, where h is the head loss and u is the
velocity. In this graph we can see that the laminar flow for the 0.0175m smooth bore pipe is a
straight line but when the flow is turbulent the is a slight curvature. From this graph we can
conclude that at small velocities the flow is laminar and at high velocities the flow is turbulent.
The previous statement validated the theory established for laminar and turbulent flow in a
smooth bore pipe. The linear regression of a log h vs. log u shown in Figure 15 does not
compare to its theoretical graph presented in the theory. This difference is because of
experimental errors during the procedure and handling of the equipment. One of the possibilities
is that there was air in the pipes we didn’t notice. The water manometer lacks accuracy and the
water inside it wasn’t clean, there were several noticeable particles. Water was also coming out
of the threads, which can also cause experimental errors. Personal errors are another source due
to poor handling of the equipment or wrong calculations.
Head Loss Due to Pipe Fitting
The fitting factor (K) in a globe valve was calculated as the slope from the lineal regression of a
∆h vs. v2/2g graph, as seen in the results calculated the value of fitting factor (K), is 0.5625 and a
percent (%) difference of 6.51%, which means the value calculated agree with the theoretical
value (0.6004). In an open ball valve there was a difference of 42.98% in its fall in fitting factor,
which makes seeing the change from laminar flow and turbulent flow much more precise in the
chart. While for the same semi open the valve fitting factor was a 32.96% difference and graphic
43
contrast decreases with the valve open. Demonstrating a higher pressure drop in the semi-open
ball valve. The 30 degree elbow fitting factor is a difference of 1.65% which clearly demonstrates the
transition period is increasing so it counts down to a turbulent flow. While for the 45-degree elbow
fitting factor (k) is 14.55% and has a very similar graph but with a fall in pressure much faster
shown in the chart. Some of the errors that can make the difference values are large, may arise
due to air in the sleeves, a visual readout of the pressure drop, some error when working on the
valve or system, accuracy by looking at the stopwatch , among other small errors that can arise
while and performed an experiment.
1. Fluid Friction in a Roughened PipeThe Reynold’s number for the first two runs are: 429.10 and 345.25. Given thess Reynold’s numbers are smaller than 2000 (Re<2000) the flow is laminar. The velocities were of 0.0246 m/s, 0.0198 m/s respectively. The head loss was of 0.027 mH20 for the first laminar flow and 0.025 mH2O for the second. The values for the Reynold’s number in turbulent flow are: 25,439.0 and 25,949.0. The velocities were of 1.4593 m/s and 1.4884 m/s. The head losses for turbulent flow were the 0.577mH20 and 0.502 mH20. The relation between the Reynold’s number and the friction coefficient for a roughened pipe was plotted in Figure 21, which does not compare to the graph stipulated by the theory for this part of the experiment. There were various sources for experimental errors which are explained in the results and discussion.
44
ReferencesDe Nevers, N. (2005), Fluid Mechanics for Chemical Engineers, 3rd
Edition, Mc Graw-Hill company, International Edition, USA, ISBN: 007-