Calculation of the Flow Rate in a Pipeline
CHEG 1810 Fall 2017
Submission due: December 11, 2017
Office Hours: Tue and Wed 10:00 AM – 11:00 AM
Statement:
Figure 1 shows a pipeline (smooth) that delivers water in turbulent flow at a constant
temperature (T) from point 1 where the pressure is p1 = 150 psig and the elevation is
z1=0 ft to point 2 where the pressure is atmospheric and the elevation is z2 = 300 ft. The
effective length of the pipeline is L and its diameter is D.
Figure 1. Water Flow in a Pipeline
Questions:
Part 1.
1. Calculate the flow rate q (in gal/min) for the pipeline with various diameters (D) and
length (L) for water at 60 ℉ using the following equations (1-6)
Table 1
L (ft) D = 4 in D = 5 in D = 6 in D = 8 in
800
1000
2000
4000
8000
10000
20000
Equations (1-6):
(1) The density (𝜌) of the water can be calculated from the following Eq.1:
𝜌 = 62.122 + 0.0122 * T – 1.54 x 10-4 * T2 + 2.65 x 10-7 * T3 – 2.24 x 10-10 * T4
where T is in ℉, and 𝜌 is in lbm/ft3
2
(2) The viscosity (𝜇) of the water can be calculated from the following Eq. 2:
𝑙𝑛𝜇 = −11.0318 +
1057.51
𝑇 + 214.624
where T is in ℉, and 𝜇 is in lbm/ft.s
(3) The flow velocity (𝜐) can be calculated from the following Eq. 3:
−6
7 𝜐7 + 𝑔 ∗ Δ𝑧 + <=∗ Δ>
? + 2 @A∗B∗CD
E = 0
where 𝜐 is the flow velocity in ft/s,
g is the acceleration of gravity given by g=32.174 ft/s2,
Δ 𝑧 = z2 –z1 is the difference in elevation (ft),
gc is a conversion factor (in English units gc = 32.174 ft.lbm/lbf.s2),
Δ P= P2 – P1 is the difference in pressure lbm/ft2,
fF is the Fanning friction factor,
L is the length of the pipe (ft),
D is the inside diameter of the pipe (ft).
Note: Pay attention to all units. Also, convert the pressure unit from psig to lbf/ft2
(4) The Reynold’s number (Re) can be calculated from the following Eq. 4:
𝑅𝑒 = 𝜐 ∗ 𝜌 ∗ 𝐷/𝜇
where 𝜐 is the flow velocity in ft/s, 𝜌 is the density of the water in lbm/ft3, D is the inside
diameter of the pipe in feet, and 𝜇 is the viscosity of water in lbm/ft.s
(5) The Fanning friction factor (fF) can be calculated from the following Eq. 5:
𝑓K =
0.316
𝑅𝑒6/L
(6) The flow rate (𝑞) can be calculated by multiplying the flow velocity by the cross
section of the pipe (Eq.6).
𝑞 = 𝜐 ∗ 𝜋 ∗ ED
L *7.481*60
where 𝜐 is the flow velocity in ft/s, and D is the inside dimeter of the pipe in feet.
3
2. Calculate the flow rate (q) under other temperature (40 ℉ and 100 ℉) when the
diameter D= 6 in and length L= 1000 ft
Temperature (℉) 40 60 100
q (gal/min)
3. Prepare plots of flow rate (q) versus D and L.
4. Add Trendline, display Equation, and R-squared value on those plots.
5. Discuss effects of diameter, length, and temperature on the flow rate, and draw your
conclusions.
Part 2. Use VBA to calculate the Reynold’s number of the given flow (The diameter
D= 6 in, length L= 1000 ft, and Temperature T=100 ℉)
1. Record a VBA macro that will calculate the Reynold’s number using the key stroke
Control+R. Copy and paste the macro cod in your excel spreadsheet.
2. Create a custom VBA function named as ReynoldNum performing the abovementioned
calculation. Copy and paste the program code of this function into the
spreadsheet.
3. Create a VBA form named as Reynold’s Number Calculator that will allow you to
input those parameters (velocity, density, pipeline diameter, and viscosity) and
output the Reynold’s number. You need to use the refEdit input variants. Copy
and paste the command button cod in the spreadsheet.
4. Test each of your macro, function, and form to calculate the Reynold’s number of
the given flow.