Lab manuals CHEE 314 2022_updated1

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McGill University *

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314

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Mechanical Engineering

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Apr 3, 2024

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CHEE 314: Fluid Mechanics Lab Manual Page 1 of 5 Lab Reports and Expectations: You will work in groups of 4 students per group , and sign-up sheets have been posted on myCourses – you may work with whoever you choose. For this year, students will do two labs simultaneously, drag flow (Experiment 1: terminal velocity of spheres) and tank drainage (Experiment 3). The remaining lab for fluid flow (Experiment 2) will be done separately. Each report should be original work of ALL the group members. There should be no copying (in whole or in part) from another source, without explicitly citing the reference. One report per group (with every group member clearly identified) is to be submitted as a single PDF file. The deadline for the lab reports is the last day of classes: December 5 by 11:59 PM . You may submit your reports at earlier dates (I strongly suggest you do not wait until the last minute). The penalty for submitting reports late is 40%, with an additional 20% for every 48 hours the report is overdue. Electronic files of reports are to be submitted as a single PDF on the myCourses Assignments folder. These reports are NOT formal lab reports , and you should ONLY answer the questions provided in the ‘Report’ section of each lab procedure. No cover pages are needed. Experiment 1. Terminal velocities of spheres Devices used : 1. Different sized spheres, 2. Column filled with glycerine 3. Stopwatch Objectives 1. Familiarize yourselves with drag force and terminal velocity 2. The effect of different parameters on the terminal velocity of an object Theory The frictional force exerted on a solid body by fluid flow is termed drag. The magnitude of the drag force depends on the geometry of the solid, the fluid properties and the flow conditions. As a particle falls freely in a liquid medium, its velocity increases to the terminal velocity. The terminal velocity, u t is reached when the forces acting on the particle are balanced (i.e. steady flow). The force balance from the free-body diagram can be written as follows: ! ࠵? ⃗ ! = ࠵?࠵? ⃗ = 0 ࠵? = ࠵? − ࠵? " F B = buoyancy force D = drag force W = force due to gravity

CHEE 314: Fluid Mechanics Lab Manual Page 2 of 5 For a sphere, the frictional drag is: ࠵? = # $ ࠵?࠵? $ ࠵?࠵? % where U = velocity of the moving object, A = cross-sectional area of the sphere, and C D is the drag coefficient, which is dependent on the Reynolds number. ࠵? % = 24 ࠵?࠵? (࠵?࠵? < 0.4) ࠵? % = 10 √࠵?࠵? (0.4 < ࠵?࠵? < 500) ࠵? % = 0.44 (500 < ࠵?࠵? < 200 000) Re is defined as: ࠵?࠵? = &’% ( with r = density, μ = viscosity, U = velocity and D = hydraulic diameter (in this case, the diameter of the sphere). Protocol: For balls of each diameter, record the time taken for the ball to fall in the glycerin column. Repeat this measurement 3 times for each ball. Convert this data to obtain an experimental terminal velocity and then compare this to the theoretical terminal velocity from the force balance. Report 1. Take the data in raw form and then please form a table with the calculated values for the terminal velocity. (1 point) 2. In the form of an appropriate graph: What was the terminal velocity of each ball? (1 point) What was the average terminal velocity for similar balls? (1 point) Comment on the spread in the data (1 point) (Hint: look up “box-and-whisker plots”). 3. Calculate and report the drag coefficient (C D ) for each ball. Calculate appropriate averages and standard deviations (3 points for drag coefficient of each ball size). Does this value depend on ball size and mass? (1 point) 4. Suppose we have two spheres of the same size. One is plastic and the other is steel. Which one will have a higher terminal velocity in the glycerine column? (1 point) Why? (1 point)

CHEE 314: Fluid Mechanics Lab Manual Page 3 of 5 Experiment 2a. Flow rate measurement Devices used : 1. Linear meter (Rotameter) 2. Restriction meter (Orifice meter) 3. Manometer Objectives 1. Familiarize yourselves with different types of flow meters 2. Apply the orifice meter equation to determine the flow rate 3. Verify the accuracy of the meters by comparing the flow rates measured by two devices Theory A differential static pressure measurement can be used to estimate the flow rate given known obstruction geometry. An orifice meter is the simplest form of an obstruction meter, which consists of an accurately machined plate mounted between two flanges with an orifice (opening) concentric with the pipe in which it is mounted (Figure 1). The reduction in cross-sectional area increases the velocity head and reduces the pressure between the two walls mounted pressure taps. The equation for an ideal orifice meter is derived in the course textbook. The derivation is initially for frictionless flow and is later corrected to account for the real losses that occur when flow passes through an orifice meter. It can be shown that for the orifice meter shown in Figure 1: Equation 1. Orifice meter flowrate equation, where C 0 is the dimensionless discharge coefficient (Figure 2) and β=d/D. Figure 1. Orifice meter Q = C 0 Q ideal = C 0 A 0 2( P 1 - P 2 ) r (1 - b 4 )

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CHEE 314: Fluid Mechanics Lab Manual Page 4 of 5 Figure 2. Orifice meter discharge coefficient for various values of b Connected to the experimental apparatus is a rotameter. A rotameter uses the drag created by fluid flow past a float to measure the flow rate. Once calibrated, the position of the float can be used to determine the flow rate. The rotameter on this experiment has been calibrated and the calibration curve will be presented to you in the following form. ࠵? = ࠵? + ࠵?࠵? Equation 2. Flowrate equation from the calibrated rotameter used in this experiment. Q has units of mL/s and Z is the position of the float on the rotameter. Protocol Measure 4 different flow rates with the rotameter and determine the pressure differential between two sides of the orifice meter for each flow rate. Report 1. Present your raw recorded data and any calculated values in table form. (1 point) 2. Is there any variation between the flow rates measured by the two devices? If yes, why? (2 points) 3. We use the Orifice equation to calculate the flow rate. However, to find the discharge coefficient, you need to use the Reynolds number that involves the flow rate itself. How did you find the Reynolds number? (Hint: do not use the rotameter measurements) (2 points)

CHEE 314: Fluid Mechanics Lab Manual Page 5 of 5 Experiment 2b. Frictional head losses in pipes Devices used: 1. Different pipes 2. Rotameter 3. Manometer Objective To demonstrate frictional losses caused by pipe material and geometry. Theory For pressure-driven flow in a horizontal pipe, pipe material and geometry may contribute to frictional effects that reduce flow rates. Viscous losses should always be considered when pumping fluid, as the head loss created by friction alone can be significant. Energy is lost as a result of the presence of pipe components (i.e., bends, elbows and valves), and in a straight pipe due to friction with the walls. But how big is this effect? Protocol For each type of pipe, measure 4 different flow rates with the rotameter and determine the pressure drop (P 1 -P 2 ) for each flow rate. Report 1. Present your raw recorded data and any calculations in table form. (1 point) 2. Should the flow rate be directly or inversely proportional to pressure drop? (1 point) 3. Is the relationship between pressure drop and flow rate consistent between each of the pipes? (1 point) Do changes depend on pipe diameter, or on material properties? (1 point) Why might this be? (1 point for explanation)

CHEE 314: Fluid Mechanics Lab Manual Page 6 of 5 Experiment 3. Tank drainage rate Devices used: 1. Tank filled with water and 2. Stopwatch Objective: Apply Bernoulli’s equation in real fluid flow situation Theory: Along a streamline, Bernoulli’s equation for idealized flow dictates that: ࠵? # $ 2࠵? + ࠵? # ࠵?࠵? + ࠵? # = ࠵? $ $ 2࠵? + ࠵? $ ࠵?࠵? + ࠵? $ where the subscripts 1 and 2 denote different locations along the streamline, P i = Pressure; V i = velocity and z i = height. Where fluid is exposed to atmosphere, the pressure P = P atm . Bernoulli’s equation can be used to analyze drainage in a tank along the following streamline: Protocol: Measure the time the water takes to drain and drop the water level at each 5 cm. Repeat this measurement 3 times. Calculate the velocity of fluid at the exit, and at the tank surface at various heights in the tank. Report 1. Present your raw recorded data and any calculated values in table form. (1 point) 2. Plot drainage rate versus water height. (1 point for plot) Is there any variation between the drainage rates at different water levels? (0.5 points). If yes, explain the reasoning behind this behavior. (0.5 points for explanation) 3. Are the theoretical drainage rates comparable with the experimental one? (1 point) Why or why not? (1 point)

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