1) Executive Summary: 2

2) Introduction: 2

3) Theory: 3

a. Equations 3

b. Calculating Theoretical Pressure Drop 3

i. Assumptions 3 ii. Derivation of Darcy Weisbach Equation 4

4) Method: 5

a. Apparatus and Setup 5

b. Method 5

5) Results: 7

a. Pipe 1 (7mm Diameter) 7

b. Pipe 2 (7mm Diameter) 8

c. Pipe 3 (4mm Diameter) 9

6) Analysis of Results 11

7) Conclusion 11

8) References 11

9) Appendices 11

Executive Summary:

Introduction:

The aim of the experiment was to calculate the pressure drop in three different pipes of different geometries, and then compare this experimental value of pressure drop to its theoretical value with the use of the Darcy-Weisbach equation (The Engineering ToolBox, 2017). The pressure drop in a pipe

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D/4 = τ(dL)

dP = 4τ/D(dL)

∆P = ∫▒〖4τ/D(dL)〗 = 4τL/D

(τ = ∅ ρu^2)

∆P = (4∅ρLu^2 )/D

To use this version of the Darcy Weisbach equation, a friction coefficient (∅) needs to be calculated. In laminar flow, the friction coefficient is calculated using equation [3] above, and for turbulent flows, a moody chart provided on the laboratory worksheet (see appendices) was used to calculate the friction coefficient (as the pipes were assumed to be smooth, friction coefficient values were calculated from the bottom line on the graph). Method: Apparatus and Setup

For this experiment, the pressure drop was recorded across the three pipe geometries outlined below: Nominal 10 mm external, nominal 7 mm internal diameter pipe, 1 m long (p_(1,) p_2) Nominal 10 mm external, nominal 7 mm internal diameter pipe, 1 m long (p_(6,) p_7) Nominal 6 mm external, 4 mm internal diameter pipe, 1 m long 〖(p〗_(9,) p_10).

Figure 2: Setup and apparatus used in the experiment.

Experimental

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Pipe 2 (7mm Diameter)

Internal Diameter of Pipe (cm) Volumetric Flowrate, Q (L/min) Reynolds Number, Re Friction Factor, ∅ Experimental Pressure Drop, ∆P (Pa) Theoretical Pressure Drop, ∆P (Pa) Percentage Error (%)

7.0 2.0 404 0.0200 16.5 10.2 38.2

7.0 4.0 808 0.0099 41.6 20.5 50.7

7.0 6.0 1213 0.0066 72.1 30.7 57.4

7.0 8.0 1617 0.0050 111.0 41.0 63.1

7.0 10.0 2021 0.0058 136.2 75.0 44.9

7.0 20.0 4042 0.0048 449.5 248 44.8

7.0 30.0 6063 0.0044 937.5 512 45.4

7.0 40.0 8084 0.0040 1777.5 828 53.4

Table 2: Experimental data for pipe