Pressure Drop Across A Pipe Experiment Report

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Introduction

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.

Background

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.

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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:

Re is the Reynolds number
ρ is the fluid density
U is the fluid velocity
d is the hydraulic diameter of the pipe
μ is the dynamic viscosity of the fluid

The hydraulic diameter, d, is a measure of the effective cross-sectional area available for fluid flow and depends on the pipe's geometry.

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:

Δp is the pressure drop
f is the friction factor
L is the length of the pipe
d is the hydraulic diameter
ρ is the fluid density
U is the fluid velocity

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.

Objective

The objective of this experiment is to investigate the relationship between pressure drop and the flow rate of water flowing through a straight pipe.

Calculations

Rough Pipe, Fast Flow

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

Smooth Pipe, Fast Flow

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.

Measurements and Results Table

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

Conclusion

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.