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This report discusses the experiment conducted using a pipe friction apparatus and a hydraulic bench.

The objectives of this experiment are twofold. First, to investigate the laws governing friction losses in pipe flows by measuring the friction factor as a function of the Reynolds number, considering both laminar and turbulent flows. Second, to experimentally determine the major losses due to friction in a fully developed pipe flow.

The following relations were utilized in the calculations of these experiments:

1. Reynolds Number:

The Reynolds number (Re) is calculated using the formula:

Re = ^{ρuD}/_{μ} = ^{uL}/_{ν}

Where,

- Re = Reynolds Number
- ρ = Density (ρ = 1000 kg/m³)
- u = Velocity
- D = Diameter of Pipe (m)
- μ = Dynamic Viscosity of the Fluid
- ν = Kinematic Viscosity of the Fluid
- L = Characteristic Linear Dimension

2. Friction Factor (f):

The friction factor is determined from the following equation:

f = ^{4L}/_{ρVD²g}

Where,

- f = Friction Factor (f)
- L = Length between two pressure tapping (L = 0.94 m)
- ρ = Density (ρ = 1000 kg/m³)
- V = Velocity
- D = Diameter of Pipe (m)
- g = Acceleration Due to Gravity (g = 9.
81 m/s²)

The experiment was conducted in two parts. In the first part, data such as pipe diameter, velocity, and area were collected to calculate the friction factor and Reynolds number, allowing us to investigate friction losses in pipes for both laminar and turbulent flow. In the second part, a fully developed flow was established in the pipe, and the major losses due to friction were determined.

The apparatus used for this experiment included a Pipe Friction Apparatus, two manometers, and a hydraulic bench.

The Reynolds number is a dimensionless quantity that characterizes the nature of fluid flow within a pipe. It is the ratio of inertial forces to viscous forces and predicts the flow regime of the fluid. A high Reynolds number indicates turbulent flow, while a low Reynolds number indicates laminar flow. Reynolds numbers falling between these extremes suggest transient flow.

For laminar flow, Re < 4000.

Where:

- ρ is the density of the fluid
- u is the flow speed
- L is a characteristic linear dimension
- μ is the dynamic viscosity of the fluid
- ν is the kinematic viscosity of the fluid

When Osborne Reynolds plotted the results of his investigation of energy head loss versus flow velocity, he identified two distinct regions separated by a transition zone. In the laminar region, the hydraulic gradient is directly proportional to the mean velocity, while in the turbulent flow region, the hydraulic gradient is proportional to the mean velocity raised to a power influenced by the roughness of the pipe wall. Smooth pipes, very rough pipes, and the transition region each have specific characteristics in terms of flow behavior.

The friction factor is a measure of the resistance to fluid flow and is influenced by the irregularities in the pipe's internal surface. Higher irregularities or roughness lead to greater friction. The Moody chart represents the friction factor as a function of the relative roughness (e/D) of the pipe against the Reynolds number. The chart distinguishes between flow in the wholly turbulent and laminar regions.

Roughness is a measure of irregularities along the boundary of the pipe's internal surface. It significantly affects the flow of the fluid passing through the pipe. Smooth-walled pipes promote smooth, laminar flow at low Reynolds numbers, while rough-walled pipes result in non-smooth, turbulent flow.

- Place the hydraulic bench on a smooth, level surface.
- Drain the water from the tank by opening the drain valve and then closing it.
- Partially open the bypass valve, which is used to vary the flow rate, and fully open the inlet and outlet valves.
- Connect one end of the pipe to the outlet of the pump and the other end to the test section.
- Use an additional flexible pipe to connect the outlet of the test section, with the other end placed in the tray of the hydraulic bench.
- Turn on the pump of the hydraulic bench and record the time it takes for the volume to reach 3 liters using the flow meter.
- Record the volume of water from the sensor on the outlet pipe and then reset the sensor.
- Record the values of h1 and h2 on the manometer.
- Repeat the above steps, varying the flow rates.
- Repeat the entire procedure for other pipes.

Volume (L) | Time (s) | Volumetric Flow Rate (L/s) | Volumetric Flow Rate (m³/s) | Density (kg/m³) | Area (m²) | Dynamic Viscosity (kg/m·s) | Velocity (m/s) |
---|---|---|---|---|---|---|---|

5 | 23.1 | 0.052756529 | 5.27565E-05 | 1000 | 9.25E-05 | 8.00E-04 | 1.581686037 |

5 | 24.2 | 0.097895252 | 9.78953E-05 | 1000 | 9.25E-05 | 8.00E-04 | 1.509791217 |

5 | 25.0 | 0.141043724 | 0.000141044 | 1000 | 9.25E-05 | 8.00E-04 | 1.461477898 |

5 | 25.1 | 0.169491525 | 0.000169492 | 1000 | 9.25E-05 | 8.00E-04 | 1.455655277 |

5 | 25.8 | 0.191204589 | 0.000191205 | 1000 | 9.25E-05 | 8.00E-04 | 1.416160754 |

Diameter (mm) | Kinematic Viscosity (m²/s) | h1 (m) | h2 (m) | hf (m) | Gravity (m/s²) | Length (m) | Reynolds Number | Friction Factor |
---|---|---|---|---|---|---|---|---|

10.86 | 8.00E-07 | 0.344 | 0.33 | 0.014 | 9.81 | 1 | 26097.8196 | 0.0346908 |

10.86 | 8.00E-07 | 0.36 | 0.3 | 0.06 | 9.81 | 1 | 24911.5551 | 0.0350517 |

10.86 | 8.00E-07 | 0.37 | 0.27 | 0.1 | 9.81 | 1 | 24114.3853 | 0.02063861 |

10.86 | 8.00E-07 | 0.386 | 0.22 | 0.166 | 9.81 | 1 | 24018.3121 | 0.01170228 |

10.86 | 8.00E-07 | 0.392 | 0.202 | 0.19 | 9.81 | 1 | 23366.6524 | 0.00412136 |

Friction factor = 0.315 * (2 * (9.81 / 1.581686037^2)) * (0.01086 / 1) = 0.0346908

Reynolds Number = (1.581686037 * 0.01086) / (8 * 10^(-7)) = 26097.8196

The purpose of this experiment is to calculate the Reynolds number and friction factor. To achieve this, various data points were collected, including:

- Volume and time measurements
- Density of water (ρ)
- Area of the pipe (A)
- Velocity of the fluid
- Diameter of the pipe (D)
- Three different values of head (h1, h2, hf)
- Gravitational acceleration (g)
- Length of the pipe (L)

All of these parameters were used in the calculations for both the Reynolds number and friction factor, making them essential experimental data.

A pipe with a diameter of 10.86 mm was used in the experiment. For this pipe, the Reynolds number ranged from 2.6E+4 to 2.3E+4, while the friction factor ranged from 3.48E-2 to 0.41E-2. A consistent trend is observed in both cases. As the Reynolds number decreases, the friction factor also decreases, indicating that laminar flow corresponds to lower Reynolds number values, resulting in lower friction factors. Conversely, as the Reynolds number increases, the friction factor also increases, indicating turbulent flow.

The transitional phase between laminar and turbulent flow is characterized by Reynolds numbers falling in this range, suggesting a transitional flow regime.

Several sources of error may have influenced the experimental results:

- Human error: This is a major source of error as all readings depend on the handling of equipment and the performance of procedures by the operator.
- Systematic error: Incorrect connections of apparatus components could introduce systematic errors.
- Measurement error: Values that are measured inaccurately or gauges that are not properly calibrated may contribute to measurement errors.

To minimize errors and improve the reliability of the results, the following suggestions can be considered:

- Reduce apparatus error by thoroughly checking all connections and avoiding any unnecessary contact with the apparatus during operation.
- Minimize measurement error by ensuring that all gauges are properly calibrated to provide accurate readings.
- Human error can be minimized by employing skilled operators who are trained in handling the equipment and conducting procedures accurately.
- Control the fluid velocity according to the specific requirements of the experiment. Lower fluid velocities can be used to observe the effects of laminar flow on the friction factor, while higher velocities can be used to study turbulent flow effects.

For future experiments in this area, the following recommendations can be explored:

- Investigate conditions that could make the observed trends more regular, such as varying velocity and pipe bore size.
- Explore the effects of laminar and turbulent flow on the friction factor separately to gain deeper insights into each regime.
- Alter the values of head to observe their impact on both the Reynolds number and friction factor.

Reynolds Number | Friction Factor |
---|---|

26097.819607092897 | 3.4690860543329857E-2 |

24911.555079497768 | 3.5051716415518692E-2 |

24114.385316953845 | 2.063861547020689E-2 |

24018.312068679119 | 1.1702280719146535E-2 |

23366.652438908754 | 4.1213664004765508E-3 |

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