Friction Factor Due to Length of Pipe
Ryan Baker
10/29/2013
Abstract: Tests were conducted on copper pipe with diameters of 1/2in and 3/8in at lengths of
2ft and 5ft. The data showed the head loss across these pipes to be in correlation with pipe size,
length and flow rate. The 3/8in 5ft section of copper displayed the largest head loss with a 3.5psi
drop at 200GPH, whereas the 1/2in 2ft section displayed the least drop in pressure with only
1.6psi drop at 300GPH.
Introduction: Head loss due to friction between a fluid and a conduit is a common problem
facing all industries. Understanding the causes of the friction can play a vital role in limiting
these adverse effects. Friction in pipe can be contributed to a number of factors from the
roughness of the interior of the pipe to the design of the fittings within the piping system. It is
important to be able to calculate the pressure drop of a system such as to know how much power
a pump needs to overcome the friction loss or what will a pressure be at an exit of a system.
Objectives: The purpose of this experiment is to show the correlation of head loss, due to
friction, within the inside diameter and length of a pipe section.
Materials and Methods: All testing was performed using the Technovate fluid circuit
system equipped with attached manometers. The system has been tested and calibrated from a
previous experiment by comparing flow rates across the Venturi and orifice meters with
volumetric discharge. However, the flow rate across the orifice meter was only used in this
procedure. Two separate sections of the Technovates copper pipe were tested for head loss along
its length. The 1/2 in. diameter section was first tested allowing a volumetric flow rate of
100,200,300,400 and 500GPH along a 2 foot then 5 foot length respectively. A 3/8 in. diameter
section would be tested the same. However, the manometer could not read at all of these
pressures so alternate volumetric flow rates of 50,100,150,200 and 250GPH were used. The
volumetric flow rate was estimated as an average 2 in. pressure drop across the orifice meter for
every 100GPH. The exact volumetric flow rate was then calculated using equation 1 below:
𝑄̇ = 97.689(∆𝑃)0.486
Equation 1
Results and Discussion: As seen in figure 1, pipe length and diameter as well as flow rate,
are all in direct correlation with increasing head loss. The 5ft section of 3/8in copper displayed
the highest amount of head loss, reaching a maximum above 3.5 psi head loss at around
200GPH. In contrast, the 1/2in 2ft section peaked right above 1.5 psi head loss at a flow rate of
300GPH.
4
Pressure Loss (psi)
3.5
1/2" 2'
3
1/2" 5'
2.5
3/8" 2'
2
3/8" 5'
1.5
Poly. (1/2" 2')
1
Poly. (1/2" 5')
0.5
Poly. (3/8" 2')
0
Poly. (3/8" 5')
0
100
200
300
400
Volumetric Flow (GPH)
Figure 1: Comparison of volumetric flow rate to pressure loss along the 2ft and 5ft sections of
1/2in. and 3/8in copper pipe.
Figure 2 shows the comparison of the pressure loss versus the square of the flow velocity. Here
as in figure 1, the longer the section of pipe and the smaller the diameter, the more friction
occurs. These results can supported by equation 2, the theoretical head loss
equation.(Cengel,2010,pp. 345)
ℎ𝑓 = 𝑓
𝐿 𝑣2
𝐷 2𝑔
Equation 2
The equation shows any increase in length (L) or flow rate (v²) will result in an increase in head
loss (ℎ𝑓 ). Also, a decrease in diameter will contribute to an increase in pressure reduction. The
friction factor (𝑓) can be found by taking the slope of the individual line when the x-y intercept
is set to zero. The 1/2in 5ft section has the highest friction factor of 0.0385 followed by the 3/8in
5ft section with 0.034 then the 1/2in 2ft section with 0.0248 and lastly the 3/8in 2ft section with
0.0218.
4
y = 0.034x
Pressure Loss (psi)
3.5
1/2" 2'
3
1/2" 5'
y = 0.0385x
2.5
y = 0.0218x
2
3/8" 2'
3/8" 5'
y = 0.0248x
1.5
Linear (1/2" 2')
1
Linear (1/2" 5')
0.5
Linear (3/8" 2')
0
Linear (3/8" 5')
0
50
100
150
Square of Flow Rate (V²/s²)
Figure 2: Plot of the square of the flow rate against the pressure drop along the 2ft and 5ft sections
of 1/2in and 3/8in copper pipe.
Inserting the friction factor values given in figure 2 into equation 2, a theoretical head loss value
can be determined, shown in table 1.
Table 1: Head Loss calculated using theoretical head loss equation
Theoretical Head Loss (ft)
1/2"
Flow Rate
2'
(v²/s²)
13.88319 0.021403
27.23268 0.041982
40.38788 0.062263
53.41847 0.082351
66.35719 0.102297
3/8"
Flow Rate (v²/s²)
5'
0.047034
0.09226
0.136827
0.180973
0.224807
22.36881
43.87773
65.0736
86.06871
106.9158
2'
5'
0.040417
0.07928
0.117578
0.155513
0.19318
0.157589
0.30912
0.458445
0.606356
0.753224
Another comparison that can be made with the friction factors found in figure 2 is that of the
Colebrook equation, equation 3.(Cengel,2010, pp.357)
1
√𝑓
= −2.0log⁡(
𝜀
𝐷
3.7
+
2.51
𝑅𝑒√𝑓
)
Equation 3
The Colebrook equation can be solved implicitly for the force factor (𝑓). The relative roughness
𝜀
(𝐷) is the relationship of the pipe roughness (𝜀) to diameter (D). The pipe roughness for copper is
taken as (0.000005ft). The Reynolds Number (Re) can be calculated as shown in equation
4.(Cengel,2010, pp.340)
𝑅𝑒 =
𝜌𝑉𝐷
Equation 4
𝜇
Where density (𝜌) of water is taken as (62.30lbm/ft³) and viscosity of water (𝜇) is taken as (6.733
x 10^-4 lbm/ft s). Inserting the values for the found Reynolds numbers and the relative
roughness, the friction factor can be found through iterations. Microsoft Excel was used in this
example. Arbitrary values were set for the “f” value and then the “What-if” analysis was run to
set a goal of finding the f value that satisfies the equation. The results are shown in table 2. All
Reynolds numbers were over 4000 indicating the flow through the pipes was turbulent. The f
values decreases slightly as the flow velocity increases. Theoretically this decrease will have
little impact on the head loss because of the squaring of the velocity. The friction values found in
figure 2 are very similar to the calculated values using the Colebrook equation.
Table 2: Friction factors (f) calculated using Colebrook Equation
1/2”
V(ft/s)
3.726015
5.218494
6.355146
7.308794
8.145993
Re
14371.64
20128.29
24512.48
28190.81
31419.97
f(ft)
0.028329
0.026104
0.024926
0.024141
0.023559
3/8”
V(ft/s)
4.729568
6.624026
8.066821
9.277322
10.34001
Re
13681.84
19162.19
23335.95
26837.72
29911.89
f(ft)
0.02875
0.026496
0.025305
0.024513
0.023926
Conclusion: This experiment proved that any increase in pipe length, pipe diameter or flow
rate will increase the head loss produced in a system. A small long pipe will present more
problems with friction than that of one the same length with a larger diameter.
References:
Cengel, Y.A. and J.M. Cimbala 2010. Fluid Mechanics: Fundamentals and Applications. 2nd ed,
New York, NY: McGraw-Hill