H215 Reynolds Number and Transitional Flow User Guide

8/16/2019 H215 Reynolds Number and Transitional Flow User Guide

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i

CONTENTS

Section Page

LIST OF SYMBOLS ii

1 INTRODUCTION 1

2 DESCRIPTION OF THE APPARATUS 3

General Descript io n 3

Temp erature Control Module 4

Instal lat ion and Sett ing Up 4

Assembly Instructions 4

3 THEORY 7

4 EXPERIMENTAL PROCEDURE AND TYPICAL TEST RESULTS 9

General Test Proc edures 9

Effect of Varying Viscosi ty 9



TecQuipment Reynolds Number and Transitional Flow

ii

LIST OF SYMBOLS

d Pipe diameter

Re Reynolds number

u Velocity

y Distances from surface

Fluid density Coefficient of viscosity

v Kinematic viscosity

Shear stress



Page 1

SECTION 1 INTRODUCTION

Figure 1 Reynolds number and transitional flow

When a fluid flows next to a solid boundary the nature

of the flow depends on the velocity relative to that

boundary. At low velocities the layers of fluid move

smoothly over one another and this is termed ‘laminar’

flow. However, as the velocity is increased small

disturbances cause eddies which ‘mix-up’ the layers of

fluid and produces a different pattern of flow, which is

termed ‘turbulent’. This change has a marked effect on

the forces acting between the fluid and the solid boundary and an understanding of the behaviour is of

fundamental importance in the study of hydraulics and

fluid mechanics. The nature of flow over an aircraft

wing affects the drag and hence determines the power

required to propel the aircraft forwards. Similarly, when

fluid flows along a pipe the nature of the flow

determines the pressure loss and hence the power

required to pump the fluid along the pipe.

Before the advent of high speed transport, the most

important application of fluid mechanics was in the

study of flow in pipes. Many engineers and scientists

investigated the behaviour of flow in pipes but it was aBritish physicist named Osborne Reynolds (1842 -

1912) who first identified the variables controlling the

flow and produced a rational means of predicting the

nature of flow. Reynolds showed that the behaviour

depends on the balance between inertia and viscous

forces in the fluid. This led to the definition of a non-

dimensional parameter, now called Reynolds number,

which expresses the ratio of inertia to viscous forces and

can be used to identify the conditions under which the

flow changes from laminar to turbulent. By experiment

it was found that the change always occurred at asimilar value of Reynolds number irrespective of the

fluid and the size of pipe.

The Reynolds Number and Transitional Flow

demonstrates the kind of experiment conducted to show

the dependence of flow on Reynolds number. The

apparatus enables the nature of the flow in a pipe to be

studied by observing the behaviour of a filament of dye

injected into the fluid. The flow rate can be varied and

the change, or ‘transition’, between laminar and

turbulent flow can be clearly demonstrated. The effect

of viscosity on the behaviour can be demonstrated by

varying the temperature using an optional temperaturecontrol module, or by using different fluids.




Page 2



Page 3

SECTION 2 DESCRIPTION OF THE APPARATUS

General Descript io n

Figure 2 show the Reynolds Number and Transitional

Flow apparatus with the Temperature Control Module

(H215a). It should be noted that the TemperatureControl Module is an optional ancillary, which is not

supplied with the equipment as standard.

The basic apparatus consists of a precision bore

glass tube of 12 mm internal diameter which is

supported in a large shroud of rust-proof material. The

shroud is open at the front and the inside surface is a

light colour to assist flow visualisation. At the top of the

shroud is a constant head tank from which water can

pass into the tube via a specially shaped bell-mouth

entry. Water is supplied to the tank via a diffuser

located below the bell-mouth. This provides a nearly

uniform supply of water to all sides of the bell-mouth.Further smoothing of the flow is achieved by passing

the water through a stilling bed consisting of glass beads

packed above the diffuser. In this way steady uniform

flow conditions are obtained at entry to the bell-mouth.

The supply pipe to the tank is at the rear of the

apparatus and can connect either directly to a tap or to

the outlet of the temperature control module. A fixed

overflow pipe is also fitted to the tank to ensure a

constant head of water. Connect this pipe to a drainusing a length of flexible hose supplied.

A valve at the outlet from the tube controls the flow

through the glass tube. The outlet should be connected

via a loose hose to convenient drain. Flow is measured

by timing the collection of a known quantity of water in

a suitable measuring vessel.

The behaviour of the flow in the tube can be

observed by injecting a fine filament of dye into the

tube using the special dye injector provided. This

consists of a fine injector tube connected via a valve to a

dye reservoir. The assembly mounts onto a plate, which

fits on the top of the constant head tank. The injector

tube is positioned such that its outlet is in the centre of

the bell-mouth entry.

The complete apparatus is supported on a triangular

base with adjustable feet.

Figure 2 Schematic diagram of Reynolds number and transitional flow demonstration apparatus with

optional temperature control module




Page 4

Temp erature Control Mo dule

The Temperature Control Module is a separate free-

standing unit which can connect into the supply to the

apparatus to heat the water and control the temperature,

and thus to vary the viscosity of the water. The heated

water passes via a ‘T’ to the outlet connection. If

required, excess water can bypass the apparatus to drain

via the second flow control valve fitted on the module

base. This valve is for fine control of the flow to the

apparatus without affecting the water temperature.

Electr ical Supp ly

Connect the electrical supply for

this apparatus through a switch

or circuit-breaker.

This apparatus must beconnected to earth.

The heater unit is rated at 32 A,

only connect the apparatus with

the cable supplied.

Connect the apparatus to the electrical supply with the

cable supplied. Use the following colour-code:

Green – and – Yellow - Earth (E or )

Brown: - Live (L)

Blue: - Neutral (N)

Water Supp ly

The cold water supply for the heater must have a pressure of greater than 1 bar or the apparatus will notfunction.

The unit MUST NOT be used with any liquid other

than water.

Instal lat ion an d Sett ing Up

The apparatus is free-standing and can mount onto any

suitable bench or working surface. A water supply and

drain are required so choose a convenient siting positionwhere these services are available. A suitable electrical

supply is required for the temperature control module.

Notes:

1) Water will not flow through the heater

unless the electrical supply is connected.

2) Water will not heat up if the pressure is too

low.

Assembly Inst ruct ion s (Refer to Figu res 2to 2e)

1. Put the main assembly on the floor.

2. Fit the dye bottle bracket and lightly tighten the

nylon locating screws, as you may need to adjust

them later (see Figures 2a-2b).

3. Fill the lower part of the constant head tank with

the glass beads supplied. Fill the tank with beads to

a level 10 - 15 mm below the top of the bell-mouth.

Do not let beads fall into the bell-mouth. After

filling make sure that the surface of the bell-mouth

is free of beads and any other obstructions, such as

loose packing material.

4. Fit the injector tube to the dye reservoir (see

Figures 2c-2d. Adjust the dye bottle bracket so that

the injector tube is in the centre of the bell-mouth.

5. The apparatus is quite tall, so you may need to use

steps when making adjustments to the dye injector

system.6. Remove any packing from around the tank.

7. Stand the thermometer such that the bulb is resting

on the stilling bed.

8. Stand the apparatus in the desired position and

connect up the supply and drainpipes as shown in

Figure 2 using the flexible hoses and clips provided

with the apparatus. Note that all drain and overflow

pipes must be free draining and that access to the

discharge pipe from the experimental tube will be

required for measurement of flow.

9. Turn the dye control valve to off and pour the dye

into the dye reservoir.10. If required, connect the temperature control module

to a suitable electrical supply. Do not switch on

until water is available. Make sure that all pipe

connections to the units are firmly secured with

hose clips.

11. Adjust the feet on the base to make sure the tube is

perfectly vertical (see Figure 2e).




Page 5

Figure 2a Unscrew Bracket

Figure 2b Refit Bracket

Figure 2c Fit Injector

Figure 2d Fit Injector

Figure 2e Make Sure Tube is Vertical




Page 6



Page 7

SECTION 3 THEORY

Consider the case of a fluid moving along a fixed

surface such as the wall of a pipe. At some distance y

from the surface the fluid has a velocity u relative to the

surface. The relative movement causes a shear stress

which tends to slow down the motion so that thevelocity close to the wall is reduced below u. It can be

shown that the shear stress produces a velocity gradient

du/dy which is proportional to the applied stress. The

constant of proportionality is the coefficient of viscosity

and the equation is usually written:

dy

du

(1)

Equation (1) is derived in most textbooks and represents

a model of a situation in which layers of fluid move

smoothly over one another. This is termed ‘viscous’ or‘laminar’ flow. For such conditions experiments show

that Equation (1) is valid and that is a constant for a

given fluid at a given temperature.

It may be noted that the shear stress and the velocity

gradient have a fixed relationship, which is determined

only by the viscosity of the fluid. However, experiments

also show that this only applies at low viscosities. If the

velocity increases above a certain value, small

disturbances produce eddies in the flow causing mixing

between the high energy and low energy layers of fluid.

This is called turbulent flow and under these conditions

it is found that the relationship between shear stress and

velocity gradient varies depending on many factors in

addition to the viscosity of the fluid. The nature of the

flow is entirely different since the interchange of energy

between the layers now depends on the strength of the

eddies (and thus on the inertia of the fluid) rather than

simply on the viscosity. Equation (1) still applies but the

coefficient no longer represents the viscosity of the

fluid. It is now called the ‘Eddy Viscosity’ and is no

longer constant for a given fluid and temperature. Its

value depends on the upstream conditions in the flow

and is much greater than the coefficient of viscosity for

the fluid. It may be noted that this implies an increase in

shear stress for a given velocity and so the losses in theflow are much greater than for laminar conditions.

What, then, determines whether the flow will be

laminar or turbulent in a given situation? We have seen

that laminar flow is the result of viscous forces and that

turbulent flow is in some way related to inertia forces.

This was realised by Reynolds who postulated that the

nature of flow depended on the ratio of inertia to

viscous forces. This led to the derivation of a non-

dimensional variable, now called Reynolds number Re

which expresses this ratio.

On physical grounds we may say that the inertia

forces are proportional to mass multiplied by velocitychange divided by time. Since mass divided by time is

the mass flow rate and this is equal to density

multiplied by cross sectional area multiplied by velocity

u we may write:

Inertia forces 2

d u u.

(2)where d is the diameter of the pipe.

Similarly the viscous forces are given by shear stress

multiplied by area so, using Equation (1), we may write:

Viscous forces 2d d

u

(3)

Dividing the inertia forces by the viscous forces we

obtain Reynolds number as:

μ

ρ

μ

ρ

22

duud

ud Re

(4)

The term / is called the kinematic viscosity, , and it

is often convenient to write Equation (4) as:

ud Re

(5)

Note that the previous equations can also be derived by

dimensional analysis but in either case it should be

remembered that Re represents the ratio of inertia toviscous forces.

The important discovery made by Reynolds was that

for normal flow in a pipe, the transition between laminar

and turbulent flow always occurs at approximately the

same value of Re, irrespective of the fluid and the size

of the pipe. This, therefore, enables prediction of flow

conditions in pipes of any size carrying the fluid. It must

be appreciated, however, that there is never a precise

point at which transition between laminar and turbulent

flow occurs.

Consider the case of increasing velocity in a pipe.

Initially the viscous forces dominate and the flow is

laminar. As velocity increases occasional eddies form but these are quite quickly damped out by viscous

effects. Further increase in velocity is accompanied by

an increase in the number of eddies until a point is

reached where the complete flow is subject to turbulent

mixing and can be considered fully turbulent. Transition

from fully laminar to fully turbulent flow may occur

interspersed with periods of quite steady laminar flow.

The final transition to fully turbulent flow tends to be

more well-defined since above a certain level of

turbulence becomes self-generating and a few

disturbances will set the whole flow into turbulent

motion. Now consider the case of reducing velocity. In this

case the turbulent motions tend to continue until the

velocity is below that at which turbulent flow originally




Page 8

started. Eventually, however, a point is reached when

the viscous forces damp out the eddies and the flow

reverts quite quickly to laminar. This behaviour can be

demonstrated by flow visualisation and also by

measuring head losses along pipes.

As an example, Figure 3 shows the variation in head

loss with velocity for a smooth pipe. On increasing the

velocity, transition occurs between points A and B, andfor decreasing flow it occurs between points C and D.

There is a ‘reluctance’ of the flow to change from one

condition to the other and this causes the hysteresis

shown in Figure 3. Generally point D is the most well-

defined and it is normally accepted that this transition

from turbulent back to laminar flow occurs at a

Reynolds number between 2000 and 2300. The

Reynolds numbers at points A, B and C depend on the

entry conditions and roughness of the pipe. Typically,

point A may represent a Reynolds number between

2000 and 2500 but if the entry is carefully controlled

and the pipe very smooth, laminar flow may continue up

to much higher values. The range over which laminar

flow occurs may be extended by eliminating sources of

turbulence but the reverse in not true: irrespective of the

level of turbulence at entry, the flow always returns to

laminar below a Reynolds number of about 2000. Thus

it may be said that below this value turbulent flow

cannot exist, but above it the flow may be either laminar

or turbulent depending on the entry conditions.

Figure 3 Variation of head loss with velocity forflow along a pipe

This behaviour is demonstrated and observed using the

Reynolds Number and Turbulent Flow apparatus. In

considering the results it must be remembered that the

transition points are not always clearly defined and that

values of Reynolds number must be expected to vary

somewhat from one test to another.



Page 9

SECTION 4 EXPERIMENTAL PROCEDURE AND TYPICAL TEST RESULTS

General Test Proc edures

For normal demonstrations a controlled supply of cold

water from the laboratory can be used. Details of how to

use the temperature control module are given later inthis section.

The basic procedure, which can be used for all tests,

demonstrates how the conditions in the pipe vary with

flow velocity and that the changes occur over a range of

velocity (and therefore of Reynolds number). The

Reynolds number can be calculated for each condition

from the pipe diameter, velocity and the viscosity of

water for the particular temperature of test. Sample

calculations are given later in this section. The basic

procedure is as follows:

1. Set up the apparatus as previously described, turn

on the water supply, and partially open the

discharge valve at the base of the apparatus.

2. Adjust the water supply until the level in the

constant head tank is just above the overflow pipe

and is maintained at this level by a small flow down

the overflow pipe. This is the condition required for

all tests and at different flow rates through the tube;

the supply will need to be adjusted to maintain it.

At any given condition the overflow should only be

just sufficient to maintain a constant head in the

tank.

3. Open and adjust the dye injector valve to obtain a

fine filament of dye in the flow down the glasstube. If the dye is dispersed in the tube reduced the

water flow rate by closing the discharge valve and

adjusting the supply as necessary to maintain the

constant head. A laminar flow condition should be

achieved in which the filament of dye passes down

the complete length of the tube without disturbance.

4. Slowly increase the flow rate by opening the

discharge valve until disturbances of the dye

filament are noted (see Figure 4b). This can be

regarded as the starting point of transition to

turbulent flow. Increase the water supply as

required to maintain constant head conditions.5. Record the temperature of the water using the

thermometer, then measure the flow rate by timing

the collection of a known quantity of water from

the discharge pipe.

6. Further increase the flow rate as described above

until the disturbances increase such that the dye

filament becomes rapidly diffused as shown in

Figure 4c. Small eddies will be noted just above the

point where the dye filament completely breaks

down. This can be regarded as the onset of fully

turbulent flow. Record the temperature and flow

rate as in step (5).

7. Now decrease the flow rate slowly until the dye justreturns to a steady filament representing laminar

flow and again record the temperature and flow

rate.

Figure 4 Typical flow patterns at various flow

conditions

Effect of Varying Viscosi ty

The viscosity of water varies with the temperature as

shown in Figure 5. The variations are quite large over

the range 10 - 40C and this can be used to demonstrate

the effect of viscosity on the velocities at which

transition occurs.

The temperature may be varied either by using the

Temperature Control Module, or by using an existing

hot water supply. The following procedure relates to use

of the temperature control module:

1. Connect the unit as shown in Figure 2. Switch on theelectrical supply. Set the temperature control to

MAX. Turn on the water supply. Adjust the flow

control valve on the left of the unit, and the

discharge valve on the apparatus, to achieve

turbulent flow conditions in the pipe and a consistent

head in the tank. Adjust the water supply to the unit

as necessary to achieve these conditions. This

procedure will ensure that there is adequate flow to

cover the required range of flow rates at any

temperature.

2. Adjust the temperature control to obtain the required

temperature of water in the apparatus. Note that the

temperature control affects the flow rate. Once the

temperature has been set, the temperature control




Page 10

should not be adjusted; control of flow rate is

achieved by using the flow control valve.

3. When the temperature has stabilised, follow the

procedure in the previous section for determining the

flow rate at each transition point. Use the flow

control valve on the temperature control module to

control the supply flow to the apparatus as

necessary.4. The procedure can be repeated for different

temperatures by adjusting the temperature control.

Figure 5 Kinematic viscosity of water at various

temperatures

Table 1 shows a typical set of results for four different

temperatures. Sample calculations for the first set of

results are as follows:

Velocity u = sm172.03.10106

10200

62

6

From Figure 5 the kinematic viscosity of water at 18C

is 1.06 106

m2/s, hence from Equation (5):

1947

1006.1

1012172.0

6

3

Re

This value and the value of 1822 for return to laminar

flow for decreasing velocity, is in reasonable agreement

with the value of 2000 usually quoted.

The results in Table 1 are plotted in Figure 6 to show

the variation in transition Reynolds number with

kinematic viscosity. Generally it can be seen that the

value of Re for each transition point is roughly constant

and there is no definite variation with viscosity. There isa fairly high level of scatter due to the variable nature of

the flow and the difficulty in determining transition

points by flow visualisation.

However, the results demonstrate that Re is

approximately constant for a range of viscosities.

Comparison of the velocities in Table 1 shows that at

any given condition the velocity decreases as the

viscosity decreases. The results demonstrate quite well

that the nature of flow depends on Reynolds number

and not simply on the flow velocity. Transition from

laminar to turbulent flow is seen to take place over a

range of Re from about 1900 to 2500, which is in

agreement with that expected from the data shown in

Figure 3.

Figure 6 Typical transition numbers for various

viscosities

Temp (

C) Condition Time for 200 ml (s) u (m/s)

106 (m

2 /s) Re

18 Just turbulent (up) 10.3 0.172 1.06 1947

18 Fully turbulent (up) 8.0 0.225 1.06 2547

18 Fully laminar (down) 11.0 0.161 1.06 1822










Table 1 Typical results for varying temperature and viscosity

H215 Reynolds Number and Transitional Flow User Guide

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