a2 postlab
TRANSCRIPT
Problem A2
Mechanical Energy Losses
Due to Straight Pipes and Fittings in a Viscous Pipe Flow System
I. Abstract
Fluid flow in pipes has two primary flow patterns namely laminar and turbulent. Flow is
laminar when all of the fluid particles flow in parallel lines at even velocities. On the other
hand, turbulent flow is characterized by stochastic property changes or when the fluid
particles have a random motion interposed on an average flow in the general flow
direction. Fluid flow across a pipeline is caused by gravitational force or pressure drop. For a
horizontal pipe with constant-diameter, the pressure drop is the driving force for the fluid to
flow. Using the Overall Mechanical Energy Balance (OMEB) for this case, ΣF = -ΔP/ρ. Thus,
the pressure drop across a pipeline increases as the sum of the frictional forces increases.
Using actual data from the experiment, higher volumetric flow rate resulted in higher
pressure drop and mechanical energy losses. Using the same fluid flow system, straight
pipes and fittings have different mechanical energy losses and pressure drop values.
Theoretically and experimentally, the 90° elbow exhibited the smallest mechanical energy
loss, followed by the straight pipe and the tee, respectively.
II. Objectives
The main objectives of problem-A2 are concerned in the measurement of the energy
losses through the straight pipe and fittings in a pipe flow system and the determination of
the relation of energy losses to the volumetric flow rate in a pipe flow system from actual
data. Furthermore, the measurement of the experimental data for the performance of the
fluid flow system in the laboratory is related in comparison with the design calculations.
III. References
[1] Albright, Lyte, Albright’s Chemical Engineering Handbook, CRC Press, 2009.
[2] Perry, Robert and Green, D., Perry’s Chemical Engineer’s Handbook, 6th ed.,
McGraw-Hill, Inc., 1984.
[3] C. J. Geankoplis, Transport Processes and Unit Operations, 3rd edition, Prentice
Hall, Englewood Cliffs, NY: 1993.
IV. Equipment/Materials
Figure 1. Fluid Flow Apparatus
Figure 2. Drain Valve
Figure 3. Isolating Valves Figure 4. Feed Tank Figure 5. Rotameter
Figure 6. Entry Valve Figure 7. Switch Figure 8. Pump
Figure 11. Water Hoses
Figure 10. U-Tube Figure 12. Ruler Manometer Figure 9. Connection of U-Tube Manometer in the Pipe
Figure 13. Tee Fitting Figure 14. Elbow Fitting
V. Theory
The main principle regarding this problem relates with fluid flow in which is such a crucial
key to virtually every facet of the chemical processes and associated industries. The most
common application involves the transportation of fluids through piping systems containing
fittings, valves, etc., by means of a driving force such as that provided by a pump, static
elevation change, or some other source of pressure [1].
A fluid is a substance that undergoes continuous deformation and stress when force is
applied, unlike a solid, which would undergo only a finite deformation [2]. It is implied when
considering a fluid flowing from two different points; the flow is constricted and opposed by a
force equal to the force the fluid exerts on the walls. This opposing force can be viscous
resistance giving rise to frictional forces dissipating mechanical energy into heat and internal
energy. In effect the pressure across the points are varied that result to a pressure drop in
the system. The mechanical energy loss could be viscous dissipation, form drag, and
pressure drag. Viscous dissipation is a fictional force caused by shear and normal viscous
stresses while form drag is caused by shear stresses only. The last form of drag is due to
vertical pressure force.
The flow behavior of a fluid is determined by the fluid properties and how it responds to
the forces exerted on or within the fluid [1]. The flow pattern of fluid could either be laminar
or turbulent in reliance to the existing variables such as pipe diameter, fluid velocity, density
and viscosity. These variables are related to the Reynolds number which is the ratio of
inertial forces to viscous forces in the fluid [3]. In laminar flow, the fluid appears to slide one
another without the formation of eddies or vortices usually represented by a low velocity and
quantified by a Reynolds number below 2100. Turbulent flow, usually at higher velocities,
where eddies are formed giving the fluid a fluctuating nature and is quantified by a Reynolds
number over 4000.
The flow behavior of fluids is governed by the basic laws for conservation of mass,
energy, and momentum coupled with appropriate expressions for the irreversible rate
processes (e.g., friction loss) as a function of fluid properties, flow conditions, geometry, etc
[1]. The working equation for this problem is the overall mechanical-energy balance, which
is a useful type of energy balance for flowing fluids and is a modification of the total energy
balance to deal with mechanical energy. A balance equation for the sum of kinetic and
potential energy may be obtained from the momentum balance by forming the scalar
product with the velocity vector [2]. This is represented by the equation,
where the ∑F is a term accounting for the dissipation of mechanical energy into thermal
energy by viscous forces. A fluid flowing under constant diameter with no elevation, the
kinetic and potential energy will be zero, respectively. Moreover, with no shaft work in the
system further simplifies the equation, the pressure drop being equal to the negative of the
sum of frictional forces multiplied with the density of the fluid. In the computation of the
frictional force, another term arises which is the friction factor represented by f to be the
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fanning friction factor. For smooth pipe, the friction factor is a function only of the Reynolds
number. In rough pipe, the relative roughness also affects the friction factor [2]. In a laminar
flow, the shear stress is not a function of density which reflects the cancelation of the density
term in the computation for pressure drop. Thus for turbulent flow, the pressure drop is a
function of the average velocity of the fluid, pipe length, measure of roughness of the pipe,
viscosity and density of the fluid.
VI. Operating Conditions and Procedure
For the Start-up Procedure:
1. The drain valve of the unit was closed first before running the apparatus. 2. The feed tank was filled by water until it is about ¾ full. 3. All of the isolating valves were opened for the water to flow in the pipes. 4. The entry valve located above the pump was opened 1/3 its fully open position. 5. The pump was switch on and the degree of opening of the entry valve was slowly
increased. The degree of opening was maintained for 15 minutes for the bubbles to disappear and attain the steady state flow. For the Experimental Procedure:
1. The designated horizontal run for the experiment was located keeping it closed while the other isolating valves were closed.
2. The entry valve of the designated degree of opening was opened in order to achieve the desired flow rate using the rotameter. The system was run for 5 minutes until it is in its steady state flow.
3. Using the U-Tube manometer, the steady state static pressure was measured. Pressures were recorded and 3 trials were taken.
4. Ten flow rates were set each with different manometer readings using a ruler. 5. Shifting from one horizontal run to another, the isolating valve of the desired horizontal
run was opened first before closing the isolating valve that was previously used. Shutting Down Procedure:
1. All the isolating valves of all horizontal runs were opened and the flow rate was reduced through reducing the degree of opening of the entry valve.
2. The switch of the pump was turned off and the drain valve was opened for the water to be drained in the unit.
VII. Data and Results
Straight Pipe
Trial 1
Q (gal/hr) Δh (cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.3 0.46 0.37 456.28 370.87 18.72
360 0.4 0.63 0.50 627.50 494.50 21.20
420 0.5 0.82 0.62 822.28 618.12 24.83
480 0.7 1.04 0.87 1039.93 865.37 16.79
540 0.9 1.28 1.11 1279.92 1112.61 13.07
600 1.0 1.54 1.24 1541.77 1236.24 19.82
660 1.2 1.83 1.49 1825.09 1483.49 18.72
720 1.4 2.13 1.73 2129.53 1730.73 18.73
780 1.6 2.46 1.98 2454.78 1977.98 19.42
840 1.8 2.81 2.23 2800.56 2225.23 20.54
Trial 2
Q (gal/hr) Δh
(cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.4 0.46 0.50 494.50 456.28 8.38
360 0.5 0.63 0.62 618.12 627.50 1.50
420 0.6 0.82 0.74 741.74 822.28 9.79
480 0.7 1.04 0.87 865.37 1039.93 16.79
540 0.9 1.28 1.11 1112.61 1279.92 13.07
600 1.1 1.54 1.36 1359.86 1541.77 11.80
660 1.2 1.83 1.49 1483.49 1825.09 18.72
720 1.5 2.13 1.86 1854.36 2129.53 12.92
780 1.7 2.46 2.11 2101.60 2454.78 14.39
840 1.9 2.81 2.35 2348.85 2800.56 16.13
Trial 3
Q (gal/hr) Δh
(cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.5 0.46 0.62 456.28 618.12 35.47
360 0.5 0.63 0.62 627.50 618.12 1.50
420 0.7 0.82 0.87 822.28 865.37 5.24
480 0.9 1.04 1.11 1039.93 1112.61 6.99
540 1 1.28 1.24 1279.92 1236.24 3.41
600 1.1 1.54 1.36 1541.77 1359.86 11.80
660 1.3 1.83 1.61 1825.09 1607.11 11.94
720 1.5 2.13 1.86 2129.53 1854.36 12.92
780 1.7 2.46 2.11 2454.78 2101.60 14.39
840 1.9 2.81 2.35 2800.56 2348.85 16.13
90° Elbow
Trial 1
Q (gal/hr) Δh (cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.2 0.32 0.25 319.40 247.25 22.59
340 0.3 0.40 0.37 397.44 370.87 6.69
380 0.4 0.48 0.50 482.89 494.50 2.40
420 0.5 0.58 0.62 575.59 618.12 7.39
460 0.7 0.68 0.87 675.41 865.37 28.12
500 0.8 0.78 0.99 782.23 988.99 26.43
540 0.8 0.90 0.99 895.94 988.99 10.39
580 0.9 1.02 1.11 1016.46 1112.61 9.46
620 1.0 1.15 1.24 1143.69 1236.24 8.09
660 1.1 1.28 1.36 1277.56 1359.86 6.44
700 1.2 1.42 1.49 1418.01 1483.49 4.62
Trial 2
Q (gal/hr) Δh
(cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.2 0.32 0.25 319.40 247.25 22.59
340 0.3 0.40 0.37 397.44 370.87 6.69
380 0.4 0.48 0.50 482.89 494.50 2.40
420 0.5 0.58 0.62 575.59 618.12 7.39
460 0.6 0.68 0.74 675.41 741.74 9.82
500 0.8 0.78 0.99 782.23 988.99 26.43
540 0.9 0.90 1.11 895.94 1112.61 24.18
580 1 1.02 1.24 1016.46 1236.24 21.62
620 1.0 1.15 1.24 1143.69 1236.24 8.09
660 1.1 1.28 1.36 1277.56 1359.86 6.44
700 1.3 1.42 1.61 1418.01 1607.11 13.34
Trial 3
Q (gal/hr) Δh
(cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa) ΣF % error
300 0.3 0.32 0.37 319.40 370.87 16.12
340 0.3 0.40 0.37 397.44 370.87 6.69
380 0.5 0.48 0.62 482.89 618.12 28.00
420 0.6 0.58 0.74 575.59 741.74 28.87
460 0.7 0.68 0.87 675.41 865.37 28.12
500 0.8 0.78 0.99 782.23 988.99 26.43
540 0.9 0.90 1.11 895.94 1112.61 24.18
580 0.9 1.02 1.11 1016.46 1112.61 9.46
620 1.1 1.15 1.36 1143.69 1359.86 18.90
660 1.2 1.28 1.49 1277.56 1483.49 16.12
700 1.2 1.42 1.49 1418.01 1483.49 4.62
Tee
Trial 1
Q (gal/hr) Δh (cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.6 0.69 0.74 741.74 684.42 8.38
340 0.8 0.85 0.99 988.99 851.66 16.12
380 1 1.04 1.24 1236.24 1034.77 19.47
420 1.2 1.24 1.49 1483.49 1233.41 20.27
460 1.5 1.45 1.86 1854.36 1447.31 28.12
500 1.7 1.68 2.11 2101.60 1676.20 25.38
540 1.9 1.92 2.35 2348.85 1919.88 22.34
580 2.1 2.18 2.60 2596.10 2178.12 19.19
620 2.5 2.46 3.10 3090.59 2450.77 26.11
660 2.7 2.74 3.34 3337.84 2737.64 21.92
700 3.1 3.04 3.84 3832.34 3038.59 26.12
Trial 2
Q (gal/hr) Δh
(cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.4 0.69 0.50 684.42 494.50 27.75
340 0.8 0.85 0.99 851.66 988.99 16.12
380 1 1.04 1.24 1034.77 1236.24 19.47
420 1.2 1.24 1.49 1233.41 1483.49 20.27
460 1.4 1.45 1.73 1447.31 1730.73 19.58
500 1.6 1.68 1.98 1676.20 1977.98 18.00
540 1.8 1.92 2.23 1919.88 2225.23 15.90
580 2.1 2.18 2.60 2178.12 2596.10 19.19
620 2.3 2.46 2.85 2450.77 2843.35 16.02
660 2.8 2.74 3.47 2737.64 3461.47 26.44
700 3.2 3.04 3.96 3038.59 3955.96 30.19
Trial 3
Q (gal/hr) Δh
(cm) ΣF theo (kJ/kg)
ΣF actual (kJ/kg)
ΔP theo (kPa)
ΔP actual (kPa)
ΣF % error
300 0.5 0.69 0.62 684.42 618.12 9.69
340 0.7 0.85 0.87 851.66 865.37 1.61
380 0.9 1.04 1.11 1034.77 1112.61 7.52
420 1.1 1.24 1.36 1233.41 1359.86 10.25
460 1.4 1.45 1.73 1447.31 1730.73 19.58
500 1.6 1.68 1.98 1676.20 1977.98 18.00
540 1.8 1.92 2.23 1919.88 2225.23 15.90
580 1.9 2.18 2.35 2178.12 2348.85 7.84
620 2.5 2.46 3.10 2450.77 3090.59 26.11
660 2.6 2.74 3.22 2737.64 3214.22 17.41
700 3.0 3.04 3.72 3038.59 3708.71 22.05
VIII. Treatment of Results
Figure 1. Volumetric Flow Rate vs. Measured Pressure Drop
Figure 2. Theoretical Total Mechanical Energy Losses vs. Volumetric Flow Rate for Straight
Pipe
200
300
400
500
600
700
800
900
0 500 1000 1500 2000 2500 3000 3500 4000
Vo
lum
etr
ic F
low
Rat
e (g
al/h
r)
Actual Pressure Drop (Pa)
Volumetric Flow Rate vs. Measured Pressure Drop
Trial 1-Straight PipeTrial 2-Straight PipeTrial 3-Straight PipeTrial 1-Elbow
Trial 2-Elbow
Trial 3-Elbow
0
0.5
1
1.5
2
2.5
3
0 200 400 600 800 1000
Vo
lum
etr
ic F
low
Rat
e (g
al/h
r)
ΣF (J/kg)
Theoretical and Actual Mechanical Energy Losses vs. Volumetric Flow Rate for Straight Pipe
Theoretical
Trial 1
Trial 2
Trial 3
Figure 3. Theoretical Total Mechanical Energy Losses vs. Volumetric Flow Rate for 90° Elbow
Figure 4. Theoretical Total Mechanical Energy Losses vs. Volumetric Flow Rate for Tee
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
200 300 400 500 600 700 800
Vo
lum
etr
ic F
low
Rat
e (g
al/h
r)
ΣF (J/kg)
Theoretical and Actual Mechanical Energy Losses vs. Volumetric Flow Rate for 90° Elbow
Theoretical
Trial 1
Trial 2
Trial 3
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
200 300 400 500 600 700 800
Vo
lum
etr
ic F
low
Rat
e (g
al/h
r)
ΣF (J/kg)
Theoretical and Actual Mechanical Energy Losses vs. Volumetric Flow Rate for Tee
Theoretical
Trial 1
Trial 2
Trial 3
Figure 5. Theoretical Pressure Drop vs. Volumetric Flow Rate
IX. Analysis/Interpretation of Results
Figure 1 shows the volumetric flow rate vs. actual pressure drop of the straight pipe, 90°
elbow and tee for the three trials. The graph shows that the pressure drop increases as the flow
rate increases. Comparing the three cases (straight pipe, 90° elbow and tee), it was observed
that the 90° elbow has the lowest pressure drop. Its pressure drop values are just close to the
straight pipe. The tee exhibited higher pressure drop values and was way larger than the other
two cases.
The actual pressure drop values were dependent on the U-tube manometer readings.
The 90° elbow showed the lowest change in height readings followed by the straight pipe and
the tee. Thus, higher the manometer readings translate to higher pressure drop.
Figure 2, 3 and 4 shows the theoretical and actual mechanical energy losses vs. the
volumetric flow rate of each case for the three trials. For the straight pipe, the actual values
were lower than that of the theoretical values. On the other hand, the actual values for the 90°
elbow and tee were lower than that of the theoretical values.
The theoretical mechanical energy losses were dependent on the length/equivalent
length, diameter and volumetric flow rate. For the three cases, the variable in the experiment
was the length/equivalent length. As the length/equivalent length increased, the mechanical
energy losses also increased. The 90° elbow had the lowest equivalent length, followed by the
straight pipe and the tee, respectively. Thus, the tee has the biggest contribution to the
mechanical energy losses. This explains why the 90° elbow has the lowest actual pressure drop
while the tee has the highest. Another factor that may have affected the pressure drop was the
0
500
1000
1500
2000
2500
3000
3500
200 400 600 800 1000
ΔP
(kP
a)
Volumetric Flow Rate (gal/hr)
Pressure Drop vs. Volumetric Flow Rate
Straight PipeElbow
pipe wall roughness. A smoother pipe has lower mechanical energy losses and lower pressure
drop. On the other hand, the actual mechanical energy losses were dependent on the U-tube
manometer readings.
Figure 5 shows the theoretical pressure drop vs. the volumetric flow rate of the three
cases for three trials. Similar to the actual pressure drop values, it was evident in the theoretical
values that the 90° elbow has the lowest pressure drop, followed by the straight pipe and the
elbow.
X. Answers to Questions
1. Based on the result of the experiment, which between form friction and skin friction contributes more to the total mechanical energy losses? Prove your answer by showing a comparative tabulation of pertinent data. Form friction is the friction in the pipe due to the obstructions present in the line of flow, it may be due to a bend or a control valve or anything which changes the course of motion of the flowing fluid while skin friction is due to the roughness in the inner part of the pipe where the fluid comes in the contact of the pipe material
Based on Figure 1, pressure drops in the straight pipe and elbow fitting were almost the same. However, a large effect was observed in the tee fitting. This shows that form friction contributes more to the total mechanical energy loss in the pipes than to skin friction.
2. In case where the changes in the potential energy and the kinetic energy are considerable, how would the total mechanical energy loses be affected? Prove your answer using the mathematical energy representations.
With potential and kinetic energy being considered in the system, these would add to the total mechanical energy loss in the system resulting to a large pressure drop that would occur in the unit.
3. In cases where there is desired flow rate, what design considerations must be specified in the pipe system if the mechanical energy losses were to be minimum? Discuss your answer briefly.
To minimize the mechanical energy loss in the pipe system, the design consideration would be putting a pump providing power to the fluid or by eliminating the potential energy by putting the pipe in a horizontal position.
SWPEKEPVF
XI. Findings, Conclusion and Recommendation
Two forms of friction in the pipe cause mechanical energy loss. When a fluid is flowing through a straight pipe, only skin friction exists. Whenever there are disturbances in fluid flow due to a change in the direction of flow or a change in the size of the pipe or due to the presence of fittings and valves in the flow system, form friction is also generated in addition to skin friction. From the data gathered in the experiment, form friction from the pipe contributes more to the mechanical energy losses. This results to a large pressure drop occurred in the experimental data with increase in volumetric flow rate which is very significant in the tee fitting. Fittings and valves disturb the normal flow line and cause friction that leads to greater frictional loss than in straight pipes. Fluids running with increase in volumetric flow rate cause viscous dissipation resulting mechanical energy loss from shear and normal viscous stresses in the pipe. Frictional energy loss can be overcome through the means of the pump providing power to the fluid and by making use of a horizontal pipe.
We therefore conclude that several factors affect the mechanical energy losses such as
the pipe roughness, pipe length, diameter and volumetric flow rate. Comparing a straight
pipe, 90° elbow and tee, it was observed that the 90° elbow had the lowest mechanical
energy losses while the tee had the largest. Varying the volumetric flow rates, it was
observed that increasing rates caused increase in energy losses and increase in pressure
drop.
Percentage errors reach up to 30% and this might be caused by the fluid flow instrument
as there were leaks in some valves and some dirt in the pipe might have affected its
roughness. Human error in measuring the change in height may also be a factor because
using the ruler as a measuring device was limited to one decimal place only.
Appendix
Calculation of mechanical and energy losses:
Q = 300 gal/hr = 0.000315 m3/s
D = 0.025 m
Where ε = 0.00152 mm
f = 0.006911
f = 0.006911, u = Q/A = 0.4135 m/s, L = 2 m, D = 0.025 m
Calculation of actual ΔP:
ρm = 13600 kg/m3, ρf = 998.1875 kg/m3, Rm = 1.6 cm
15654)00102495.0)(025.0(14.3
)1875.998)(00315.0(44Re
D
QN
29.0
Re
727.0log4
NDf
Dg
LfuFF
c
L
22
kgJF /6857.0
PVF
PF
cf
mm
f g
gR
P1
2/12.6181875.99881.911875.998
13600
100
5.0mNP