Fluid Mechanics Lab Report

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Curtin University *

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12925

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Mechanical Engineering

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Oct 30, 2023

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docx

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1. Introduction The following laboratory looks to develop one’s understanding with the study of flow in pipes by applying the Fluid Mechanics principles and theories learnt from the unit ENGR2000. Flow in pipes can vary from laminar, transitional and turbulent. This experiment looks to examine the differences between three flow regimes, and in order to do so, differentiate the variations between these types of flows. As well as this, the following experiment will look at the Hydraulic Gradient in the pipe. From this, the results will be used to evaluate Reynolds Number ( R e ¿ and the relative roughness of the pipe wall ( ϵ / D ¿ . This in order to determine the different flow conditions using a Moody Chart by looking at the pipe’s Friction Factor ( f ¿ . 2. Background Reynolds Number ( R e ) is a dimensionless number which is used to indicate the state of a fluid flow as it passes a body. By examining this number, a fluid can be determined to be either laminar, transitional or turbulent. R e = ρ ∗ U m ∗ L μ R e = Reynolds Number ( non- dimensional ) ρ = Density of fluid ( kg / m 3 ) U m = Average velocity of flow ( m / s ) L = Length scale of flow perpendicular to surface ( m ) μ = Viscosity of fluid ( N s / m 2 ) From the following equation, we can see Reynolds Number ( R e ) is the ratio of inertial forces to viscous forces. The distinctive flow regimes in a pipe can be seen in Figure 1, and are as follows: Figure 1: Flow Differences Between Laminar, Transitional and Turbulent. 1 Laminar: R e < 2100 Transitional: 2100 ¿ R e < 4000 Turbulent: R e > 4000

The relative roughness of the pipe wall is its roughness ( ϵ ¿ divided by the inner diameter ( D ). This can then be used on a Moody Chart, to find the corresponding predicted values of Friction Factor ( f ¿ . The Moody chart relates Reynolds Number, relative roughness and the Darcy-Weisbach equation all collectively. The Darcy-Weisbach equation is as follows: h L = f ∗ L ∗ V 2 2 ∗ g ∗ D h L = ¿ Friction head loss ( m ¿ f = ¿ Darcy resistance factor ( non- dimensional ) L = Length of the pipe ( m ) D = Pipe Diameter ( m ) V = Mean velocity ( m / s ) g = Acceleration due to gravity ( m / s 2 ¿ Hydraulic Gradient due to friction ( i ) is the ratio of head loss to the length. The equation is as follows: i = h L L Darcy’s Friction Factor ( f ¿ is used to calculate the friction factors for the flow regimes. It is dependent on Reynolds Number R ¿ ¿ ¿ ) and to the relative roughness ( ϵ / D ) . Whereby: Laminar Flow: f = 64 R e Turbulent Flow: f = 0.316 R e 1 4 As mentioned, these formulae are all related to the Moody Chart, which is a graph in a non- dimensional form. It is conventionally used to find the estimated friction factor for the flow regimes. There are several factors that can affect the fluid flow in a pipe, and these needed to be taken into consideration whilst the experiment was conducted. They are as follows:  The viscosity, velocity and density of the fluid  The inner diameter and length on a pipe  The temperature of the fluid 2

 The inner roughness of the pipe  Entrance and the exit conditions of the pipe (Lekner 2007) 3. Objective The main objectives of the laboratory are to identify the specific values of Reynolds Number ( R e ), in relation to the laminar, transition and turbulent regimes of flow in a pipe with a circular cross-section, to understand the concept of friction factor whilst it is applied in pipe flow, and to understand the principle of the Darcy-Weisbach equation. By the end of the experiment, one should sufficiently understand the theory relative to flow through pipes. 4. Apparatus I. Small horizontal pipe with a nominal diameter 3 mm II. Water tank III. Flexible hose IV. Bell-mouthed entrance leading to a straight pipe V. Piezometer tapping’s, upstream approximately 45 pipe diameters away from pipe exit VI. Piezometer tapping’s connected to an inverted U-tube manometer VII. Water Manometer VIII. Mercury Manometer IX. Stop watch X. Water XI. Plunger 3

Figure 2: Mercury Manometer Figure 3: Water Manometer 5. Experimental Procedure I. The experimental procedure was read to understand the objectives of the laboratory. II. Discussion between group members so everyone understood the experiment. III. Apparatus level was checked. This is so the manometers stood vertically. IV. Visual inspection to see the connection of the manometer to the pipe being tested. V. Pressure lowered to zero to eliminate the air bubbles in the water. VI. Reads were taken in two sets, one using a water manometer and other using mercury manometer. VII. Water manometer (readings 1-12): The bench supply valve was opened, until a steady flow is obtained at the supple tank overflow pipe. VIII. From this, the isolation tap is turned to read the values on the water manometer. This was done by looking at the needle valve. IX. Readings of the water manometer were noted ( h 1 and h 2 ) as well as time ( s ). X. After this, the flow’s rates were regulated quarterly through the pipe for the 12 readings. XI. All results were noted XII. Mercury manometer (readings 13-30): higher flow rate needed, so the supply pipe is from the bench supply, not the elevated tank. 4

XIII. Water manometer was isolated to read the mercury manometer. This was done by the isolating tap. XIV. Needle value was turned off the stop the flow, and to check that the mercury levels in the two sections of the manometer were level. XV. The needle value was used to regulate the flow rate in the pipe, similar to the water manometer readings. Turned quarterly. XVI. Small differences in the flow were observed and noted as this corresponded to the transitional flow. XVII. Readings of the mercury manometer were noted ( h 1 and h 2 ) as well as time ( s ) XVIII. After all the values for readings (13-30) were obtained, flow rates were calculated. XIX. All results were summarised in the instruction sheet. 6. Results Diameter of Pipe D = 3 mm Length of Pipe between Piezometer Tapping’s L = 524 mm Roughness height of Pipe-Wall Material ϵ = 0.0015 mm Density of Water ρ H 2 O = 1,000 kg / m 3 Dynamic Viscosity of Water μ = 1.002 ∗ 10 − 3 N . s / m 2 Density of Mercury ρ Hg = ¿ 13,500 kg / m 3 Table 1: Properties of Pipe, Water and Mercury Test No. Water Quantity W (ml) Time Taken ∆t (s) Flow Rate Q ( m 3 /s) Manometer Reading h 1 (mm) Manometer Reading h 2 (mm) 1 20 11.37 1.75901 * 10 − 6 331 310 2 20 10.91 1.83318 * 10 − 6 344 292 3 20 6.53 3.06279 * 10 − 6 356 275 4 50 11.63 4.29923 * 10 − 6 368 261 5 50 10.18 4.91159 * 10 − 6 380 243 6 50 8.56 5.84112 * 10 − 6 395 224 7 50 7.66 6.52742 * 406 209 5

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