Pipe Friction Lab Report
Mohammed Atheeq Nasir H00164902
Course: Mechanical Eng. Science 6 (B58EF) Lecturer: Dr. Mehdi Nazarinia
Summary/ Abstract:
We investigated the effect of pipe friction on head loss in different types of flow. To achieve this objective, we used a hydraulic bench with a hydraulic motor, test-pipe with a constant diameter and a head tank with stilling material inside it. It reflected that beyond a certain flow velocity, the type of flow changed from laminar to turbulent. There was found to be a linear relationship between Reynolds Number and Fanning friction factor.
Introduction:
Pressure drop or head loss in pipes is due to eddy currents caused by friction
between the pipe’s inner surface, as a result of its roughness, and the fluid it
contains. The frictional force acts tangential to the motion of the fluid and
results in a decrease in the overall energy of the fluid in motion. The study of
the frictional force between a moving fluid and the walls of a pipe and the
energy loss associated with it has numerous engineering applications in industry
The results of this experiment could be used in the oil pipe system design and
pump design industries where knowledge of different magnitudes of pressure
drop for different types of fluid flow is imperative to their work. In pipe system
design, the pressure drop between two locations determines the minimum
acceptable cross-sectional area of the pipeline given the flow rate requirements
for a desired output in a system.
Engineers in the oil pipe system design industry also use their knowledge of
pressure drops in piping networks to produce the most economical balance
between installation costs of the piping system and operational costs of the
pumps system.
In oil pump design, the knowledge of pressure drop is crucial to determining the
size of the pumps. After engineering calculations to find out the type of oil flow
using the dimensionless Reynolds Number, the pressure drop or head loss
between two points is determined. This value of pressure drop is then accounted
for by the pumps as the amount of power loss due to frictional losses in the pipe
is the power required to be added to the system by the booster pumps. These
booster pumps will be placed at points in the pipe system where maximum
pressure drops occur.
This pipe friction experiment aims to investigate the magnitude of pressure drop
for a broad range of flow rates that represent laminar, transitional and fully
turbulent types of flow and to calculate an estimate for the critical Reynold’s
number where the flow changes from laminar to turbulent in nature.
Theory:
The type of fluid flow in a system is found by calculation of the dimensionless Reynolds Number (ratio between inertial forces and viscous forces):
R eD=ρVDμ
The critical or transitional value of R eD , where the fluid changes from laminar to
turbulent in nature, is considered to be around 2000. Generally, there are three types of fluid flow in pipes:
Laminar flow
Transient or transitional Flow
Turbulent
Laminar flow occurs mainly in pipes with small-cross-sectional area, at low fluid flow velocities or with fluids of relatively high density. It is the flow in which viscous forces dominate inertial forces. Laminar flow is a smooth steady flow of a fluid where its particles move in layers that do not mix and are parallel to the wall. Shear stress depends solely on viscosity and is independent of density. Occurs below Re=2000
Turbulent flow occurs generally at high flow rates, in pipes with larger cross-sectional areas or with fluids of relatively low density. It is the flow in which inertial forces dominate viscous forces. Eddies and wakes mean the layers of particles are now mixed and the flow’s behavior is unpredictable. Shear stress for turbulent flow is directly related to the fluid’s density. Occurs above Re= 2000
Transient flow occurs when turbulent and laminar flows occur simultaneously with
turbulence in the middle of the flow and laminar flow at the sides. This occurs around Re= 2000.
The energy loss due to friction between the pipe’s inner surface and the fluid it contains can be derived from the Bernoulli’s Equation which describes the different forms of energy involved in the fluid:
L ¿
(
p1 γ + V12 2 g+Z1)
=(
p2 γ + V22 2 g+Z2)
+h¿ Where: p = Static Pressure in N/m2 γ = ρg = Specific weight of the fluid in N/m3
V = Average Velocity of the fluid in the pipe in m/s
Z = Elevation in pipe in m
hL = Energy loss per unit weight of fluid in Nm
g = Acceleration due to gravity in m/s2
The value of ΔZ (Z2 – Z1), the length of the tube, is 510mm which will be a
constant throughout the experiment. The change in fluid velocity is negligible, therefore, V2-V1= 0. Factoring these conditions into the Bernoulli’s Equation and rearranging to make hL the subject of the
formula will give us an expression to calculate the total head loss:
hL=p1
γ − p2
γ −∆ Z
In turbulent flow, the surface roughness of the pipe has a significant effect on the head loss but in turbulent flow, the surface roughness of the pipe has negligible effect on the head loss.
Through experimental observations, Darcy and Weisbach developed an expression to calculate the energy loss in both laminar and turbulent flow:
Rearranging the expression allows us to calculate the friction factor, f , which relates the head loss to the fluid’s flow velocity:
f = hL
4 LV
2
2 Dg
f = Frictional Factor , Dimensionless
L = Length of test pipe in m V = Velocity of the fluid in m/s
D = Diameter of pipe in m
g = acceleration due to gravity in m/s2
The friction factor can then be compared to the Moody
Diagram using the values of surface roughness and
Reynold’s Number to reflect how close the experimental
value was to the theoretical value of friction factor. The
Moody Diagram is a graph that reflects the relationship
between surface roughness, Friction factor and
Reynold’s Number.
1)Stopwatch- To
measure time
taken for water
to be
2)Measuring
Beaker- To
measure
volume of
water
collected
3) Hydraulic Bench:
A vertical piping
system with 3
valves in the rear
to switch
between
different types of
flow. A hydraulic
motor pumps
water up the
pipe and into the
head tank with
the stilling
matter for
laminar flow. The
motor is
connected
directly to the
test pipe by
adjusting the
valves to obtain
a higher flow
rate. (Turbulent
flow)
Procedure:
V
1, V
2, V
3,V
4 Laminar Flow:To obtain a laminar flow for the test, adjust the 3 valves at the back of the bench. Engage Valve V1 and close valve V2 to allow the water to flow to the reservoir.
Set the over flow tube at the required water level in the head tank. Open valve V3 to allow the fluid to flow through the stilling material and into the test pipe.
Control the volumetric flow rate using valve V4. Start the stopwatch when the valve V4 is opened.
Close V4 and stop the timer simultaneously.
Record readings on the mercury manometer, reflecting pressure loss in the test pipe between the 2 test points, and the water level reading on the measuring water.
Repeat 4,5 and 6 for other rates of flow. Turbulent Flow:
Disengage valves V2 and V3 and open valve v2 to allow water to flow directly from the hydraulic bench into the test pipe to obtain a higher rate of water flow.
Repeat 4,5 and 6 for a range of flow rates.
Results and Discussion:
h1 (cm .Hg) h2 (cm. Hg) Δh (cm. H20 ) Head Loss (m) Volum e (m3) Time(s ) Flow Rate (m3/s ) Velocit y (m/s) Reynold s Number Fanning friction (Experimen tal) Fanning Friction (Moody diagram ) 22 22.5 0.5 0.505 0.0001 14.2 7.042 25E-06 0.9962 76 2598.98 1 0.01467987 0.015 23 21.4 1.6 0.494 0.0001 13.3 7.518 8E-06 1.0636 93 2774.85 2 0.0125975 0.013 21 23.5 2.5 0.485 0.0001 10.5 9.496 68E-06 1.3435 06 3504.79 8 0.007752694 0.0076 24 20.5 3.5 0.475 0.0001 8.75 1.142 86E-05 1.6168 13 4217.77 4 0.005242807 0.0049 23.7 20.9 2.8 0.482 0.0001 9.56 1.046 03E-05 1.4798 24 3860.41 1 0.006350632 0.0064 3.4 3.45 3.5 3.55 3.6 3.65 -2.5 -2 -1.5 -1 -0.5 0
Laminar Flow
log(Re) log(f) h1 (cm.H g) h2 (cm.H g) Δh (cm.H2 0) Hea d Los s (m) Volume (m3)Time(s) Flow Rate (m3/s) Velocity (m/s) Reynol ds Numbe r Fanning friction (Experimen tal) Fanning Friction (Moody diagram) 5.5 0.45 5 0.000 1 9.8 7 1.013 E-05 1.4333 45 3739.161 623 0.006389 985 0.006 2 3.572774
4.5 0.46 5 0.000 1 9.6 6 1.035 E-05 1.4645 05 3820.447 746 0.006255 49 0.006 2 3.582114 -2.20374 7.5 0.43 5 0.000 1 7.0 3 1.422 E-05 2.0123 92 5249.719 093 0.003099 232 0.003 1 3.720136 -2.50875 8.4 0.42 6 0.000 1 6.5 3 1.531 E-05 2.1664 81 5651.688 396 0.002618 726 0.003 3.752178 -2.58191 9.7 0.41 3 0.000 1 5.7 5 1.739 E-05 2.4603 68 6418.352 213 0.001968 52 0.002 5 3.807424 -2.70586
Turbulent Flow Results:
3.55 3.6 3.65 3.7 3.75 3.8 3.85 -3 -2.5 -2 -1.5 -1 -0.5 0
Turbulent Flow
log (Re) log (f)It is clearly reflected in both the graphs that the relationship between the Fanning’s friction factor and the Reynolds Number, thus, the flow rate, is linear. For each test, the friction factor calculated from the experimental results was fairly close to the theoretical value taken from the Moody Diagram within an acceptable margin of error which will be reflected in the calculations portion below.
The critical Reynolds Number where the type of flow changes from laminar to turbulent was estimated to be 2680 from the table of results above. This estimation was calculated from the tests
immediately before the significant rise in Reynolds Number which was the indicating factor that the type of flow had changed from laminar to turbulent. This number falls within the acceptable critical Reynolds Number range of 2000 to 4000.
According to the Darcy and Weisbach expression to calculate friction factor, the Fanning friction factor is inversely proportional to the square of the flow velocity. This relationship is reflected in the table of results
as a small increase the flow velocity leads to a significant fall in the friction factor.
The fluid, water, was assumed to be an ideal fluid in the calculations which is not the case in reality and this contributed to an error in the calculation for the experimental friction factor.
It was observed that the friction factor for laminar flows was
significantly lower than the friction factor for turbulent flows. As the head loss is directly related to the friction factor, it is observed that the head loss in laminar flow is much higher than the head loss in
turbulent flow.
Calculations:
The sample calculations to calculate the Fanning friction factor and Reynold’s number from the results of each test are as follows:
∆ h=h2−h1 = 25 – 29.5 = 5.5cm (Hg) ∆ hwater=5.5 cm
hL=∆ h−∆ Z →∨¿ 0.055 – 0.510| = 0.455m
Flow rate Q=Volume Time → 0.0001 9.87 =1.013 m3 sec=1.013 ×10 −5m s −6 π × 2.25× 10¿ ¿ Velocity v=Q÷(π r2)=(1.013 ×10−5 )/¿ Frictional Factor f = hL 4 L D V2 2 g = 0.455 4 × 0.51 0.003× 1.4332 2× 9.81 =0.00639 R eD=ρVD μ = VD ν = 1.43335 ×3 ×10−3 1.15 ×10−6 =¿ 3739.161623 Percentage error:
f (experimental)−f (Moody Diagram)
f (Moody Diagram) ×100 =
0.005243−0.0049
0.0049 ×100 = 7%
Largest percentage error in friction factor (turbulent flow):
f (experimental)−f (Moody Diagram)
f (Moody Diagram) ×100 =
0.001969−0.0025
0.0025 ×100 = 21.3 %
The percentage error for turbulent flow was much larger than that of laminar flow as the much higher velocities needed highly accurate
mechanism for time measurement, which meant that, human error had a much greater impact on the calculation of the friction factor.
Possible Sources of Error:
1) Human Error: Parallax error while reading the levels of manometric fluid in the manometer and the volume of water in the measuring beaker. Delay in recording the time taken for a volume of water to be collected.
2) Diameter of test pipe: The diameter of the test pipe might vary slightly through its length which would greatly affect the accuracy of the
readings as the readings are very susceptible to changes in pipe
diameter. This is because the diameter affects the flow rate calculation and in turn, the calculation for the friction factor which is directly related to the square of the flow velocity.
3) Fluctuations in Manometer: Air bubbles coul have been formed during the calibration of the manometer which would lead to an error in the readings for pressure difference.
Precautions:
1) Ensure test-pipe is properly fit into the head tank.
2) Check if the heights of manometric fluid in the columns are the same. 3) Ensure pipe doesn’t touch the water in the measuring beaker.
4) Practice caution while handling the flexible tube delivering water into the measuring beaker in order to avoid causing back pressure.
Improvements:
1) Place measuring beaker at an appropriate height to avoid parallax error rather than a relatively low height in the sink.
2) Use a stand to hold the delivery tube in order to avoid causing unwanted fluctuations in pressure difference due to varying elevation.
The head loss in the test-pipe was found to be proportional to the flow velocity of the fluid. The findings of the experiment have shown that the head loss due to friction in laminar flow is much larger than in turbulent flow. It reflected that beyond a certain flow velocity, the type of flow changed from laminar to turbulent. This laboratory experiment proved that the Fanning friction factor was directly related to the Reynold’s Number for both laminar flow and turbulent flow which was expressed in the log graphs plotted from the results. It also showed that the friction factor for laminar flow was significantly larger than for turbulent flow. References: