Project: Calculation of the Flow Rate in a Pipeline

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 (p2 = 0) and the elevation is z₂ = 300 ft. The effective length of the pipeline is L and its diameter is D.

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^oF using the following equations (1-6)

Table 1

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 ^oF, and ρ is in lb_m/ft³

(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 ^oF, and μ is in lb_m/ft.s

(3) The flow velocity (v) can be calculated from the following Eq. 3:

-½v² + g * Δz + (g_c*ΔP/ρ) + 2(f_F*L*v²/D) = 0

where v is the flow velocity in ft/s,

g is the acceleration of gravity given by g = 32.174 ft/s²,

Δz = z₂ - z₁ is the difference in elevation (ft),

g_c is a conversion factor (in English units g_c = 32.174 ft.lb_m/lb_f.S²),

?P = (p₂ - p₁)*144 is the difference in pressure lb_f/ft²,

f_F 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.

(4) The Reynold's number (Re) can be calculated from the following Eq. 4:

Re = v * ρ * D/μ

where v is the flow velocity in ft/s, ρ is the density of the water in lb_m/ft³, D is the inside diameter of the pipe in feet, and μ is the viscosity of water in lb_m/ft.s

(5) The Fanning friction factor (f_F) can be calculated from the following Eq. 5:

f_F = 0.316/Re^¼  

(6) The flow rate (q) can be calculated by multiplying the flow velocity by the cross section of the pipe (Eq.6).

q = v * π * D²/4 * 7.481*60

where v is the flow velocity in ft/s, and D is the inside diameter of the pipe in feet.

2. Calculate the flow rate (q) under other temperature (40 ^oF and 100 ^oF) when the diameter D= 6 ft and length L= 1000 ft

3. Prepare plots of flow rate (q) versus D and L.

4. Add Trend line, 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 ft, length L= 1000 ft, and Temperature T = 100 ^oF)

1. Record a VBA macro that will calculate the Reynold's number using the key stroke Control+R. Copy and paste the macro code 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 code in the spreadsheet.

4. Test each of your macro, function, and form to calculate the Reynold's number of the given flow.