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The flow of fluids through pipes is a fundamental aspect of various industrial and engineering applications. Understanding the behavior of fluid flow in pipes is essential for designing efficient systems and predicting the associated pressure losses. In this experiment, we aim to investigate the relationship between pressure drop and the flow rate of water through both rough and smooth pipes.
When a fluid, such as water, flows through a pipe, it encounters resistance due to the friction between the fluid and the pipe's inner surface.
This resistance results in a loss of energy, which is manifested as a pressure drop along the length of the pipe. The magnitude of this pressure drop depends on several factors, including the pipe's roughness, the fluid's velocity, and the fluid's properties, such as viscosity and density.
The Reynolds number (Re) is a dimensionless parameter used to characterize the flow regime within a pipe. It is defined as the ratio of inertial forces to viscous forces and is given by:
Re = (ρ * U * d) / μ
Where:
The hydraulic diameter, d, is a measure of the effective cross-sectional area available for fluid flow and depends on the pipe's geometry.
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For a circular pipe, it is simply the pipe's diameter.
The pressure drop in a pipe is often characterized by the Darcy-Weisbach equation:
Δp = f * (L / d) * (ρ * U^2) / 2
Where:
The friction factor, f, is a crucial parameter that depends on the flow conditions and the pipe's roughness.
It is typically obtained from experimental data or can be estimated using empirical correlations.
In this experiment, we will compare the pressure drop in both rough and smooth pipes under different flow conditions. By measuring and calculating the pressure drop, we aim to gain insights into the influence of pipe characteristics and flow rates on pressure losses in fluid transportation systems.
The objective of this experiment is to investigate the relationship between pressure drop and the flow rate of water flowing through a straight pipe.
Water volume (L) = 20/103 = 0.02
Water flow rate (m3/s) = 0.02/24.78 = 807.103 x 10-6
Pipe Cross-Section Area (m) = π0.01562/4 = 191.134 x 10-6
Water Velocity (m/s) = U = 807.103 x 10-6/191.134 x 10-6 = 4.223
Reynolds Number (Re) = 1000 * 4.223 * 0.0156 / 10-3 = 65878.8
Friction Factor = 0.07
Head Loss = hf = 0.07 * (4/0.017) * (4.2232/2 * 9.81) = 14.971
Pressure Drop Along The Pipe = Δp = 1000 * 9.81 * 14.971 = 146865.5 = 15 kPa
Water Volume (L) = 20/103 = 0.02
Water Flow Rate (m3/s) = 0.02/21.69 = 922.084 x 10-6
Pipe Cross-Sectional Area (m) = π0.0172/4 = 226.98 x 10-6
Water Velocity (m/s) = U = 9.22.084 x 10-6/226.98 x 10-6 = 4.062
Reynolds Number (Re) = 1000 * 4.062 * 0.017 / 10-3 = 69054
Friction Factor = 0.018
Head Loss = hf = 0.018 * (4/0.017) * (4.0622/2*9.81) = 3.562
Pressure Drop Along The Pipe = Δp = 1000 * 9.81 * 3.562 = 34943.22 = 35 kPa
To further analyze the data, the Reynolds number was used on a Moody diagram to determine the friction factor of each pipe, which was then used to calculate the head loss and pressure drop along the pipes.
| Reading No. | Pipe Thickness (mm) | Time (sec) | Water Velocity (m/s) | Reynolds Number | Pipe roughness (ε/d) | Friction factor (f) | Measured Pressure Drop (kPa) | Calculated Pressure Drop (kPa) |
|---|---|---|---|---|---|---|---|---|
| 1 | 15.6 (r)(f) | 24.78 | 4.223 | 65878.8 | 0.047 | 0.07 | 35 | 145 |
| 2 | 15.6 (r)(m) | 33.19 | 3.153 | 49186.8 | 0.047 | 0.07 | 20 | 80 |
| 3 | 15.6 (r)(s2) | 49.43 | 2.117 | 33025.2 | 0.047 | 0.07 | 10 | 37 |
| 4 | 17 (s)(f) | 21.69 | 4.062 | 69054 | 0.018 | 10 | 35 | |
| 5 | 17 (s)(m) | 26.28 | 3.353 | 57001 | 0.02 | 7 | 26 | |
| 6 | 17 (s)(s2) | 37.9 | 2.324 | 39508 | 0.022 | 3 | 14 |
KEY: (r) Rough, (s) Smooth, (f) Fast, (m) Medium, (s2) Slow
In conclusion, the experiment revealed that the calculated pressure drops were consistently higher than the measured results. This discrepancy may be attributed to potential sources of error, such as inaccuracies in measurement readings, equipment movement, or variations in the actual roughness of the pipes. Nevertheless, it is evident that as the flow rate changes, the pressure drop follows a similar pattern in both rough and smooth pipes. Additionally, the pressure drop in a rough pipe with slow flow is comparable to that in a smooth pipe with fast flow, suggesting a relationship between flow rate and pressure drop that warrants further investigation.
Pressure Drop Across A Pipe Experiment Report. (2024, Jan 18). Retrieved from https://studymoose.com/document/pressure-drop-across-a-pipe-experiment-report-2
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