代写ENGR30002、Java/Python编程代做

日期：2024-08-22 09:59

ENGR30002 Fluid Mechanics

Practical 1: Fluid Flow in a Smooth Pipe

Aims

1. To investigate the variation in pressure drop with the volumetric flow rate of water in a circular

pipe

2. To construct a plot of friction factor versus Reynolds number

3. To observe the transition from laminar flow to turbulent flow by injecting a dye into water flowing

in a pipe

4. To observe various types of pressure gauges in operation

Scenario

You have started working as a graduate engineer in a company which manufactures pipelines. The first

task given to you by your boss is to study the correlation between the Fanning friction factor and the

Reynolds number of water flowing in a pipe and therefore, construct a Moody diagram. To complete

this task, you have been given access to the company’s laboratory, where you will conduct scientific

experiments to achieve your goal. In particular, you will have access to pressure gauges, flow meters,

and a straight glass pipe. A description of the apparatus is provided below:

Pressure Gauges

A pressure gauge is used to measure pressure by analysing the force applied by a fluid on a surface.

Various types of pressure gauges are used to measure different pressure ranges. In the laboratory, you

will have access to a inverted water-air manometer (inclinable; measures up to 5 kPa), and a wet-wet

digital pressure gauge (measures up to 100 kPa). You will need to choose the appropriate pressure

gauge to ensure accuracy. To measure the pressure, simply read off the pressure reading when using the

wet-wet digital pressure gauge. For the inverted inclinable water-air manometer, you will need to use

hydrostatic pressure concepts to calculate the pressure difference. The resolution of the wet-wet digital

pressure gauge is 0.1 kPa, while the manometer scale has 1 mm demarcations and is inclinable in 15

degree increments from vertical to horizontal.

Flow Meters

A flow meter is used to control the flow rate of a fluid. You will have access to three rotameters which

can control water flow rates up to 70, 250, and 1600 L/h respectively. A rotameter is an example of a

variable area flow meter, where a weighted float rises in a tapered tube as the flow rate increases. The

floatstopsrisingwhentheareabetweenthefloatandthetubeislargeenoughfortheweightofthefloat

to be balanced by the drag of fluid flow. Rotameters are available for a wide range of liquids but are

most commonly used with water or air. They can reliably measure flow down to 1% accuracy.

Pipe

In the laboratory, you will also have access to a glass pipe which is 12.6 mm in diameter and 1.5 m in

length.

1

Figure 1: The two types of pressure gauges in the laboratory. (a) inverted water-air manometer and (b)

wet-wet digital pressure gauge.

Figure 2: (a) A rotameter to be used in the experiment. (b) A schematic diagram of a rotameter. The

flow of liquid creates an upward force opposing the weight of the float, creating an equilibrium

situation such that the float will remain stationary to indicate the flow rate.

Task

You will conduct experiments to measure pressure drop values that correspond to various volumetric

flow rates between 0 to 1600 L/h for the flow of water in a straight glass pipe. You should consider the

following when writing up your experimental protocol and constructing your schematic diagram:

? Are there any safety checks or calibrations required before switching on the pressure gauges and

flow meters?

? What are the parameters to be measured in this experiment?

? What calculations are required to obtain the Fanning friction factor and Reynolds number?

2

? How many flow rates should you run for each of the three flow meters?

? Should you start the pipe flow at a high or low flow rate? Why?

? How do you decide the type of pressure gauge to use in order to maintain accuracy? Why is the

inclinable feature of the inverted water-air manometer useful and when/how should this be used

to maintain accuracy?

? Show all pipelines and how the experimental apparatus are connected in the schematic diagram

? Think about how the different pressure gauges should be connected to the pipe

? Again, think about how the flow meters should be connected to the pipe. Should they be put

towards the start or the end of the pipe? Why?

Theory

For fluid to flow in a pipe, a driving force in the form of a pressure drop (?P) is required. The pressure

drop required depends on the average velocity (V), fluid density (ρ), fluid viscosity (μ), pipe diameter

(D), and pipe length (L). The pressure change in a fluid under steady-state flow conditions is described

by the mechanical energy balance:

P 1 P 1

1 + V2+z = 2 + V2+z +h

ρg 2g 1 1 ρg 2g 2 2 L

In the equation above:

? P: pressure in the fluid

? ρ: density of the fluid

? g: acceleration due to gravity

? V: velocity of the fluid

? z: elevation of the fluid

? h : head loss due to friction

L

For flow in a horizontal pipe at a constant velocity, z =z and V =V . Therefore, it follows that:

1 2 1 2

P ?P

h = 1 2

L ρg

Thatis,thedropinpressureisduetofluidfrictionaloneandisnotduetochangesinkineticorpotential

energy.

The head loss (h ) may also be expressed in terms of a Fanning friction factor (f ):

L F

2f LV2

h = F

L Dg

Experimentation has shown the following to be true for fluid flow in a smooth horizontal pipe:

1. The head loss varies directly with the length of the pipe

2. The head loss varies almost directly with the square of the velocity

3. The head loss varies almost inversely with the diameter of the pipe

4. The head loss depends on the fluid’s properties (density and viscosity)

5. The head loss is independent of pressure

3

The Fanning friction factor (f ) is a function of fluid velocity (V), pipe diameter (D), fluid density (ρ),

F

and fluid viscosity (μ), and the only way to make it dimensionless is as follows:

(cid:16)ρVD(cid:17)

f =f

F μ

The group ρVD is known as the Reynolds number. Hence, the Fanning friction factor is a function of

μ

only the Reynolds number.

When the flow rate through the pipe is low, the flow pattern is smooth and steady. A dye solution

carefully injected into the pipe will trace out a straight line. This orderly flow is referred to as laminar

flow. As the flow rate increaseds the stream of dye loses its steadiness and begins to vacillate. This

vacillation increases as the velocity of the fluid increases. At sufficiently high velocity, the dye solution

no longer retains its identity and is dispersed across the pipe. It becomes completely mixed with the

surrounding liquid, and the flow pattern is no longer steady and smooth - it has become chaotic. The

flow is now said to be turbulent.

The transition from laminar to turbulent flow occurs at different velocities for different fluids and differ-

ent pipe sizes. However, when expressed in terms of Reynolds number, the transition occurs at a fairly

well-defined Reynolds number value. This is known as the critical Reynolds number for pipe flow. In

this experiment, the critical value may be determined by observing the gradual change to a disordered

state of a line of dye injected into the centre of a flowing water stream.

The flow patterns of laminar, transitional, and turbulent flow will be demonstrated by injecting a dye

into the water flow channel at various flow rates.

Safety & Student Dress Code

It is a University requirement that student dress code and behaviour in the laboratory conform to the

following safety standards:

1. Safetyglasses,long-sleeve,andlong-legclothingarecompulsory(otherwiselabcoatsmustbeworn)

2. Do not take your safety glasses off while in the lab

3. Footwear must completely cover feet

4. No smoking, drinking, or eating in the lab

5. No sitting on the table or on the floor

6. Let the demonstrator know if you need to leave the lab

7. Keep the table/work area tidy, and notes and other items away from chemicals

8. Handle chemicals and equipment with care

9. Follow the lab supervisor’s instructions in the event of an emergency evacuation

10. Ask questions if you are unsure of anything during the practical session

Thelaboratorydemonstratorwilldeterminewhetherornotstudentsmeettheserequirements. Students

not meeting these requirements will be asked to leave the laboratory and will receive zero for this part

of the subject assessment.

4

Submission Instructions

Please watch the accompanying lab video (available on the LMS) before you complete the lab report. It

provides important information on the experimental setup and gives you an idea of what to expect in

this practical.

Your lab report is due on 14/4 (Sunday) at 11.59pm. Upload your report via the LMS. Late

submissions will receive a 10% deduction for each day past the deadline.

Your lab report should be typed, not handwritten (handwritten calculations are accepted only in the

Appendix section). It should follow the format below:

Lab Report Format

1. Cover Page

? Student Name (official, not preferred)

? Student ID

2. Abstract

3. Aims/Methods

? Summarise the aims of this practical

? Draw a schematic diagram of the apparatus used in this experiment. Show and label all

components, material flow, and direction of flow

? Provide specific step-by-step procedures as dot points

4. Experimental Results

5. Questions/Discussion

(a) From the experimental results, construct a log-log plot of f versus Re, clearly showing the

F

three flow regimes. Draw a straight line of best fit through the data points in the laminar flow

region and determine the slope of this line.

(b) What is the theoretical relationship between f and Re in the laminar flow regime for pipe

F

flow? Statetheexpectedvalueoftheslopeofthelogf versuslogReplotinthisregime. Does

F

the plot you obtained in Part (a) agree with that reported in the literature? If not, explain

why this is so.

(c) For the data point corresponding to the maximum flow rate, present a sample calculation to

show how V, Re, f , and h are calculated. Show all steps, parameter values, units, and

F L

equations used. Do these values agree with theoretical values? By how much do they differ?

(d) A viscous liquid (ρ=1460 kg/m3, μ=5.2×10?1 Ns/m2) is to be pumped through a smooth

pipe 0.1 m in diameter at a rate of 5×10?2 m3/s. Use your friction factor versus Reynolds

number plot to estimate the driving force needed to maintain the specified flow rate. Express

the driving force in terms of pressure drop per unit length of the pipe.

(e) From the dye injection experiment, estimate the critical Reynolds number for pipe flow (this

may be a range). Is this consistent with the value reported in the literature? If not, explain

why this is so.

6. Conclusion

7. Appendix

? This should include a completed Take 5 Form

5

Rubric

The breakdown of marks for the laboratory report associated with this practical is as follows:

Component Marks

Abstract 10

Aim/Methods 15

Questions - (a) 10

Questions - (b) 10

Questions - (c) 10

Questions - (d) 10

Questions - (e) 10

Conclusion 10

Take 5 Form 5

Assessor’s Discretion 10

Total 100

Full marks will be given for a complete consideration of forces and dimensionless numbers, full labelling

of schematics/diagrams, clear labelling and use of axes on plots, correct calculations, and complete

discussionsasappropriateforeachquestion. MarksassociatedwithAssessor’sDiscretionwillbeawarded

based on the overall quality of the report.