Fluid Mechanic Lab Report

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Fluid Mechanics

Laboratory 2
Report

Robby Joseph
14103508

1.0 Introduction
This experiment was undertaken for the study of flow in pipes and the factors that affect it in both laminar and turbulent regimes. The transitional regime between laminar and turbulent flow will also be studied. The experiment was done using a pipe with a known diameter, and water was pumped in from a tank. Throughout the process, measurements of the quantity of water and time were taken as well as the hydraulic gradient. With these different parameters, the flow rate, Reynolds number and friction factor were able to be calculated for each test for water and mercury. The main purpose of the process was to analyse and identify the regions of laminar flow, and turbulent flow, as well as the transitional region in between. These values enable the calculation of the friction factor of the pipes for specific flow rates. 2.0 Background

The viscosity (µ) in the pipe flow of a fluid produces friction (shear stress) between lumps of fluid as they pass each other. This causes the fluid to cling to the boundary in the flow field. Reynolds number (Re) is the ratio of fluid momentum to viscous forces. Re=ρVDμ

This ratio allows the flow of a fluid to be distinguished; this flow can either be laminar, turbulent or transitional. Laminar flow only occurs when the flow of a fluid is smooth and steady; a small Reynolds number defines a flow as laminar (less than 2300). Turbulent flow is the opposite of laminar flow; here the flow is unsteady and has random fluctuations. A large Reynolds number defines a flow as turbulent (greater than 4000). For turbulent flow the viscous affects are negligible and turbulent flow is therefore known as inviscid. Transitional flow is a mixture of the two flows, as it is neither completely steady nor unsteady, and sits in between the change from laminar to transitional with a Reynolds number in between (greater than 2300 but less than 4000) Figure 1 As shown in the above figure Laminar flow is smooth and steady through the pipe whereas the turbulent flow is messy and unsteady through the pipe. Transitional flow will show a mix of both these arrows through the pipe showing the steadiness and unsteadiness mix in the flow. The friction factor of flow through a pipe is defined as the ratio between wall shear stress and the inertial force of the flow as it interacts with the boundary or pipe walls through friction, this friction affects the flow of the fluid. The greater the Reynolds number, hence the faster the fluid is flowing the less friction there is between the fluid and the pipe walls. The friction factor is proportional to 1/Re for laminar flow.

For Laminar Flow, f= 64Re
For turbulent flow the friction factor is defined different to laminar flow, it is still a function of Reynolds number.
For TurbulentFlow, f=0.316Re1/4
The Moody Chart (Figure 2) is also used to calculate the friction factor of a flow with a known Reynolds number and pipe roughness as turbulent flow is a function of the pipes roughness as well.

3.0 Apparatus

Figure 2

The apparatus used in this lab for the measurement of friction loss is a small horizontal pipe of nominal diameter 3 mm. Figure 1 shows the arrangement in which water from a supply tank is led through a flexible hose to the bell-mouthed entrance to a straight pipe, along which the frictional loss will be measured. Piezometer tappings exist at an upstream section which lies approximately 45 pipe diameters away from the pipe entrance, and at a downstream section which lies approximately 40 pipe diameters away from the pipe exit. These clear lengths upstream and downstream of the test section are required to prevent the results from being affected by disturbances near the entrance and exit of...
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