laboratory scedule on fluid mechanics summer semester 2014 ... · on "fluid mechanics"...

LABORATORY SCEDULE

on "Fluid Mechanics"

summer semester 2014/2015

¹ of LW Date TITLES OF LABORATORY WORKS

1. 25.02.2015 Introduction. Fluid flow visualization – streamlines.

2. 11.03.2015 Fluid flow visualization – basic methods.

3. 25.03.2015 Flow velocity measurement in a wind tunnel.

4. 15.04.2015 Volume flow rate measurement by a horizontal Venturi meter

5. 29.04.2015 Jet impact force measurement on a flat plate

6. 13.05.2015 Jet impact force measurement on a hemispherical plate

7. 27.05.2015 Critical Reynolds number measurement in a pipe

8. 10.06.2015 Report final presentation

February 2015 Prof. S. TabakovaAssist. E. Toshkov

1

Laboratory Exercise № 1

FLUID FLOW VISUALIZATION: STREAMLINES, BASIC

METHODS

Purpose: Demonstration of different streamlines patterns: a circular

cylinder and an airfoil in a flow.

I. Theory:

1.Basic concepts: The streamline is defined as a

space line, such that at each instant is

tangential to the velocity vector of the

fluid particle passing through a space

point at the same instant.

Fig.1. A stream line

A bundle of neighbouring streamlines

may be imagined which form a passage

through which the fluid flows, and this

passage (not necessarily circular) is

known as a stream-tube. A stream-tube

with a cross-section small enough for

the variation of velocity over it to be

negligible is sometimes termed a stream

filament.

df

Fig. 2. A stream-tube.

An individual particle of fluid does not necessarily follow a streamline, but traces out a

path-line. In distinction to a streamline, a path-line may be likened, not to an

instantaneous photograph of a procession of particles, but to a time exposure showing

the direction taken by the same particle at successive instants of time.

In experimental work a dye or some other indicator is often injected into the flow, and

the resulting stream of colour is known as a streak-line or filament line. It gives an

instantaneous picture of the positions of all particles which have passed through the

point of injection.

In general, the patterns of streamlines, path-lines and streak-lines for a given flow differ;

apart from a few special cases it is only for steady flow that all three patterns coincide.

V

V

V

2

2. Eulerian and Lagrangian description: − The Eulerian method concerns the flow field in space composed of fixed points

and time;

− The Lagrangian method follows an individual particle (similarly to solid

mechanics) ;

According to the coordinate system, the streamlines patterns are: absolute at a fixed

coordinate system, or a coordinate system connected with the flow and relative at a

moving coordinate system or a system connected with the moving body.

Fig. 3

а) absolute flow pattern of a sphere

moving with a constant velocity

b) relative flow pattern of a sphere

3. Methods of experimental flow visualization include the following:

− Dye, smoke, or bubble discharges

− Surface powder or flakes of liquid flows

− Floating or neutral-density particles

− Optical techniques which detect density changes in gas flows: shadowgraph,

Schlieren, and interferometer

− Tufts of yarn attached to boundary surfaces

− Luminescent fluids or additives

− Fast cameras

3

II. Experimental scheme 1. Hele-Shaw cell

1- 2 flat plates

- (transparent) at a distance ≈ 1mm

2- 2 tanks separated by a screen

2а – a tank for water with perforated

holes

2b - a tank for dye with perforated holes

3 - body ( circle)

4 - tap

Fig. 4

2. Smoke tunnel

1- smoke generator

2- fan

3- lattice with parallel smoke

pipes

4- body ( airfoil)

Fig.5

Experimental procedure: for (1)

а) Fill the tank 2а with water, and 2b – with dye at fully closed tap and screen, such that the holes to

be tightly closed. The fluid level in both tanks must be the same;

b) Open continuously and slowly the tap till getting a streamlines pattern with two stagnation points

– front and rear being symmetrical;

c) Increase the flow velocity (at fully open tap) till the rear stagnation point disappears and a small

vortex is observed on its place.

Experimental procedure: for (2)

а) Switch on the smoke tunnel and the smoke generator. Fix the fluid paraffin flow on the heater to

be a drop-wise one. Wait till enough smoke quantity is generated.

b) Switch on slowly the fan 2. Increase continuously the fluid flow velocity till a vortex wake is

generated after the body in the smoke tunnel.

4

c) Turn the body (airfoil) to an angle towards the flow (an angle of attack α). Increase continuously

the fluid flow velocity, in order to observe the separation process from the body surface and the

further vortices in the whole flow after the body.

III. Experimental photos and movies

www.efluids.com

http://css.engineering.uiowa.edu/fluidslab/gallery/index.html

http://css.engineering.uiowa.edu/fluidslab/referenc/processes.html

1. For a circular cylinder

Fig. 6 Oil flow around a circular

cylinder at different Reynolds

numbers Re

The flow around a cylinder is a fundamental problem of fluid mechanics with practical application. At

small Reynolds numbers (µ

ρdV=Re ), the flow is symmetrical, but with the increase of Re the flow begins

to separates at the cylinder rear and a vortex wake is observed, which is an unsteady phenomenon.

5

b) for an airfoil

http://media.efluids.com/galleries/all

IV. Computer visualization

The visualization is obtained on the basis of the Computer Fluid Dynamics (CFD) methods.

• CFD софтуер

FLUENT: http://www.fluent.com

ANSYS: http://www.ansys.com

http://css.engineering.uiowa.edu/fluidslab/gallery/ani-num-sim.html

V. Analysis:

а) Draw schematically the two streamlines patterns observed by the Hele-Shaw cell.

b) Draw schematically the streamlines pattern around a circular cylinder (for different Rе) according to

the photos and sketches in the references.

c) Draw schematically the streamlines pattern around an airfoil (for different angles of attack), observed

in the smoke tunnel.

d) Draw schematically the streamlines pattern around an airfoil according to the photos and sketches in

the references.

e) Give examples for computer visualization using materials from Internet.

of 3


FLOW VELOCITY MEASUREMENT IN A WIND TUNNEL

Purpose: Introduction to the measurement methods of fluid flow velocity

1. Theory:

A. Devices for velocity measurement: anemometers

• Mechanical anemometer

Fig. 1

• Hot-wire anemometer

Fig. 2

• Ultrasonic and laser anemometer

Fig. 3

B. Pitot-static tube

Fig. 4

∞ 0 Bernoulli equation for sections ( ∞ ) and (0)

V∝ ρρV

p pV2

0

0

2

2 2

∞

∞+ = +.

Р∞ = Рst – static pressure

р0 – stagnation pressure

Р∝ V0=0

Fig. 5 р0 рst

of 3

( )stppp −=∆ 0

2

. 2

∞=∆=V

PPd

ρ dynamic pressure

( ) ( )sttheorppV −=∞ 0

2

ρ

( )

tubestatic-Pitot theoft coefficien2.1...8.0

220

−=

∆=−=∞

ξ

ρξρ

ρξ

ppV st

2. Experimental scheme 4

1 3 z

Fig. 6

1. Nozzle of the wind tunnel

2. Standard Pitot-static tube

3. Pitot-static tube

4. Diffuser of the wind tunnel

5. Coordinator in z

6. Sloping micro-manometer

7. Sloping micro-manometer

3. Experimental data and result treatment:

3.1. Standardization of the Pitot-static tube (3) by the Pitot-static tube (2).

The sloping micro-manometer reading, correspondent to the standard Pitot-tube, is l10, while the

reading of the sloping micro-manometer, correspondent to the Pitot-tube (3), is l20. Since the

velocities measured by the two Pitot-static tubes must be equal, i.e., Vst = V, the following

relation is obtained:

airair

stst

pp

ρξ

ρξ

∆=

∆ 22,

where 1=stξ , [ ] mmlgklpst ==∆ 1010 ; ; [ ] mmllkgp ==∆ 2020 ;.. ;

...........;.........................;.................. 2010 == kmmlmml

7

2

5

6

of 3

Then 20

10

l

l=ξ =.........

3.2. Velocity measurement by the Pitot-static tube (3). Determination of the velocity

field in the working part of the wind tunnel.

pat= ............... Pa ; R = 287,14 J/kg.0K; T=273,15+t

0 C = ........

0K

....==RT

patairρ kg/m

3;

The readings of the sloping micro-manometer, connected to the Pitot-static tube (3) at different

values of z, are l2. These values are filled in the following table. The coordinate beginning z=0

corresponds to the middle plane that intersects the working part of the wind tunnel into two

symmetric parts. The coordinator is moved vertically downwards till going out of the air jet, i.e.,

when atpp = and l2 = 0.

Table 1

N z

mm

l2

mm

∆p g k l= . . 2

Pa air

pV

ρξ

∆=

2

m /s

1 0 l20

2

3

4

5

6

7

8

9

10 0

4. Graphical representation of the results

Plot the graph of V as a function of z according to the data presented in the table and plot its

mirror image in the upper semi-plane of z.

z

V

Fig. 7

5. Analysis

5.1. Analyze the errors during the experiment.

5.2. Discuss the form of the curve V = f(z): for what values of z it is possible to assume

that V= const and give approximately the precision of this assumption.

1


FLOW RATE MEASUREMENT BY A VENTURI-METER

Purpose: The mean discharge coefficient is to be determined for a Venturi-meter

1. Theory. Devices for measuring flow rate.

Fig. 1

2

2

221

2

11 gz+

2

.gz+

2

.ρ

ρρ

ρ Vp

Vp +=+ - Bernoulli’s equation

where p1 is the static pressure in section (1), and p2 – in section (2);

V1 is the mean velocity in section (1), and V2 – in section (2);

z1 is the vertical location of section (1), and z2 – of section (2).

For a horizontal Venturi-meter, z1 = z2.

V1.f1 = V2 .f2 - the continuity equation

where f1 is the cross-sectional area of section (1), and f2 – of section (2) and fd

=π. 2

4.

Q = V2 . f2 - the ideal volume flow rate

( )

( )Q fp

f

f

fp

f

f

fg h h

f

f

k h h=

−

=

−

=−

−

= −2

2

1

2 2

2

1

2 2

1 2

2

1

2 1 2

2

1

2

1

2

1

∆ ∆

ρ ρ

where p1 - p2 = ∆Ρ =ρg(h1-h2); k fg

f

f

=

−

2

2

1

2

2

1

The actual volume flow rate, Qd is less than the theoretically predicted value, Q due to energy

losses between sections (1) and (2) and the lack of uniform velocity across the flow section.

2

This discrepancy is accommodated by introducing the empirical factor known as the discharge

coefficient µ (or Cd), i.e., QQ ..εϕ=a

=µ Q, where ϕ - velocity coefficient, ε - contraction

coefficient and µ µ ϕ ε=

Re, ,

f

f

2

1

at Re.

=V d2 2

ν.

1.1. Orifice

1.2. Nozzle meter

1.3. Venturi-meter

(Please, give the schemes of the devices 1.1 and 1.2 using the lectures or the given references)

2. Experimental scheme

Fig. 2

3. Experimental procedure:

(i) Close all valves and start the pump.

(ii) Slowly open the supply valve until fully open.

(iii) Slowly open the control valve downstream of the Venturi-meter to release any air trapped

in the supply pipe to the Venturi-meter.

(iv) With the control valve closed, adjust the height of the water in the manometer tubes to give

a reading of approximately 200 mm by either “bleeding off” air from the manifold or by

adding air with a hand pump.

(v) Level the Venturi-meter by adjusting the supporting legs so that the manometer tubes each

read the same value.

3

(vi) Open the control valve slowly until the maximum difference in water levels is achieved in

the tubes at sections (1) and (2) (say, 250 mm).

(vii) Record the water levels in the tubes at sections (1) and (2) and, by use of the volumetric

bench, measure the volume flow rate (initially, collect 35 liters of water).

(viii) By closing the control valve, reduce the flow rate so that the difference in water levels in

the tubes at sections (1) and (2) is decreased, in 30 mm increments, to zero.

(ix) For each flow setting, record the water levels in the tubes at sections (1) and (2) and

measure the volume flow rate.

(x) For low flow rates, the collected water volume may be reduced provided that the time

period remains greater than 100 sec.

(xi) Close the supply valve and stop the pump.

4. Experimental data:

Fig. 3

Diameter at inlet, at section (1), D1 = 26.mm

Diameter at throat, section (2), D2 = 16.mm

Cross sectional area at throat, section (2), f2=4

2

2Dπ = 0.201.10

-3 m

2

Area ratio, throat to inlet, f2/f1 = 2

1

2

2

D

D = 0.379

Manometer Readings

Volume Flow Rate Readings, Q=W/t

h1

(mm)

h2

(mm)

h1 - h2

(mm)

Volume of water, W

(l)

Collection time, t

(s)

4

5. Result treatment

k fg

f

f

=

−

2

2

1

2

2

1

= …………m5/2

/s

h1 - h2

(m)

Theoretical Volume Flow

Rate, 21 hhkQ −=

(m3/s)

Actual Volume Flow Rate,

Qd=W/t

(m3/s)

6. Graphical representation of the results:

Plot a graph of the actual, Qd against theoretical, Q volume flow rate so that the slope of the graph

gives the mean value of the discharge coefficient, µ of the Venturi-meter.

7. Analysis

On the basis of the plotted graph, analyze the following:

• whether the graph is linear;

• whether the graph passes through the origin of the coordinate system;

• whether the graph has any appreciable scatter, i.e., what are the discharge coefficient variations

for different flow rates with respect to the mean value of the discharge coefficient µ ;

• what is the expected arnge of the discharge coefficient µ and whether the experimentally

obtained value of µ falls within this range;

• what are the reasons for the discharge coefficient µ to be less than unity;

• what are the possible experimental errors and state their effect upon the obtained results.

1


JET IMPACT FORCE MEASUREMENT ON A FLAT PLATE AND

ON A HEMISPHERICAL CUP

Purpose: The experimental values of impact force are to be compared with

values predicted by the momentum equation, when a jet of water impinges

on either a flat plate or a hemispherical cup.

1. Theory.

The momentum equation of a jet impinging a solid surface has the following form:

( )r r rR q v v= −1 2 ,

where rR is the reactive force of the jet exerted on the на струята onto the surface,

rv1 and

rv2 are

respectively the jet velocities, before and after its impact with the surface.

Two cases will be considered: a flat plate and a hemispherical cup.

i) flat plate

rv1 =(V, 0),

( )222122

vvq

vqrrr

+= ,

rv21 =(0, V),

rv22 =(0, -V)

Therefore

Rx=qV and Ry=0 (1)

ii) hemispherical cup

rv1 =(V, 0),

( )222122

vvq

vqrrr

+= ,

rv21 =(- V, 0),

rv22 =(- V, 0)

Therefore

Rx=2qV and Ry=0 (2)

iii) Determine q and V

Applying the Bernoulli equation for sections

(0) and (1), the following expression for the

velocity V is obtained:

V U gs= −2 2

The mass flow rate q is determined by dividing the mass of collected water ρ W (here W is the

collected volume and ρ is the water density) by the timing period t, i.e., q= ρ W /t .

2

The volume flow rate is Q=q/ρ.

The velocity of water leaving the nozzle is U=Q/A, where А is the nozzle area.

iv) determination of the experimental impact force

T – spring force when the beam is horizontal

F – experimental impact force of the water jet on the vane

M – mass of beam assembly (excluding jockey)

m – mass of the jockey weight

• If no impact force, F = 0, the jockey is positioned at zero location on the scale and the

beam is horizontal. Then the moment about the pivot is:

Mg mg Tl l l1 2 3 0+ − = (3)

• If impact force is acting, F ≠ 0, the jockey weight is at x location on the scale and make

the beam horizontal. Then the moment about the pivot is:

( ) 0321 =−−++ lFlTxlmglMg (4)

Subtracting equation (3) from (4): 0=− lFmgx and consequently:

Fmg

x=l

(5)

2. Experimental scheme

3

3. Experimental procedure:

(i) Check that the apparatus stands vertically and that, when the tally is correctly positioned, the

beam is horizontal.

(ii) Fit the flat plate to the beam.

(iii) Place the jockey weight on the zero of the scale and set the beam horizontal by adjusting the

nut.

(iv) Close the supply valve and start the pump.

(v) Open the supply valve to achieve a layer of water on top of the flat plate.

(vi) Open fully the supply valve and set the beam horizontal by adjusting the position of the jockey

weight.

(vii) Note the position of the jockey weight on the scale and choose convenient settings for eight

jockey weight positions, equally spaced, using the full available range of the scale.

(viii) Place the jockey weight on the first setting and set the beam horizontal by adjusting the supply

valve.

(ix) Record the jockey weight position and measure the volume flow rate by timing the period for

35 liters of water to flow through the apparatus.

(x) Repeat steps (viii) and (ix) for the eight jockey weight positions. For the lower flow rates, the

collected water volume may be reduced, provided that the timing period does not become less

than 60 sec.

(xi) Close the supply valve and replace the flat plate with the hemispherical cup.

(xii) Open the supply valve to give a moderate flow rate; keeping the beam horizontal, adjust the

orientation of the nozzle to give a symmetrical flow from the plate (if possible).

(xiii) Repeat steps (iii) and (vi) to (x).

(xiv) Close the supply valve and stop the pump.

(xv) Record: mass of the jockey weight; diameter of the nozzle; distance between the beam pivot

and the vane; vertical distance between the nozzle and the vane.

4. Experimental data: Density of water, ρ =1000 kg/m

3

Mass of the jockey weight, m=………..kg

Diameter of the nozzle, d=………..m

Distance between the beam pivot and the vane, l = ………m

Vertical distance between the nozzle and the vane, s = ………m

Nozzle area, А=………………m2

(i) Flat plate

Position of jockey weight,

x

Volume flow rate readings,

Q=W/t

(mm)

Volume of water, W

(l)

Collection time, t

(s)

4

(ii) Hemispherical cup

Position of jockey weight,

x

Volume flow rate readings,

Q=W/t

(mm)

Volume of water, W

(l)

Collection time, t

(s)

5. Result treatment

(i) Flat plate

Position of

jockey

weight, x,

(m)

Experimental

impact force

Fmg

x=l

,

(N)

Volume

flow rate,

Q=W/t

(m3/s)

Mass

flow rate,

q=ρW/t

(kg/s)

Velocity of

water leaving

nozzle,

U=Q/A

(m/s)

Velocity of

water

impacting

vane

V U gs= −2

2

(m/s)

qV

(N)

Rx=qV

(N)

(ii) Hemispherical cup

Position of

jockey

weight, x,

(m)

Experimental

impact force

Fmg

x=l

,

(N)

Volume

flow rate,

Q=W/t

(m3/s)

Mass

flow rate,

q=ρW/t

(kg/s)

Velocity of

water leaving

nozzle,

U=Q/A

(m/s)

Velocity of

water

impacting

vane

V U gs= −2

2

(m/s)

qV

(N)

Rx=2qV

(N)

5

6. Graphical representation of the results:

Plot on two different graphs the experimental impact force F, as well as the theoretical reactive

force Rx as a function of qV for both the flat plate and hemispherical cup cases. Find the slope

F/qV of both graphs.

7. Analysis

On the basis of the plotted graph, analyze the following:

• whether the graphs are linear;

• whether the graph do not pass through the origin of the coordinate system and point out the

reasons for that;

• whether the slopes of the graphs are smaller than the expected ones and point out the factors

responsible for that;

• what are the possible experimental errors and state their effect upon the obtained results.

F F

R x Rx

F lat p late qV H em ispherical cup qV


MEASUREMENT OF THE CRITICAL VALUE OF THE

REYNOLDS NUMBER

Purpose: The different types of flow are to be demonstrated using the

apparatus of Reynolds and the critical Reynolds number is to be

determined

1. Theory:

A. Flow types:

A.1. Laminar – at low velocities, the fluid

particles move along straight lines.

A.2. Unstable or transitional

A.3 Turbulent – at high velocities, the

fluid particles move in an irregular,

chaotic manner, which leads to their full

mixing.

B. Critical Reynolds number:

Re =Vd

ν, for circular pipes, d – pipe diameter, V – mean velocity, V

Q

d=

42

π ., ν -

kinematic viscosity coefficient

Recr – corresponds to the transition from laminar to turbulent flow, i.e., when the flow is

unstable, wavy:

ν

dVcr

cr

.Re = , where

2.

4

d

QV cr

crπ

=

The experiments are performed at normal engineering conditions that occur at some

disturbances and then: 4000Re2000 ≤≤ cr . The lower bound is usually taken as a

theoretical value of Recr: (Recr)theor = 2000.

2. Experimental scheme: Apparatus of Reynolds – Osborne Reynolds (1842–1912), Professor of Engineering

at Manchester University.

.

d =0.022m 1

4 3

5 2

2 7

6 entrance

exit exit

1- reservoir filled with a dye

2 - valve

3 - overflow

4 – reservoir filled with water

5 – transparent pipe

6 - rotameter

7 - needle

3. Experimental data:

t 0

water = ............. С0

ν water(t 0) = ........... using reference data

Q V

Q

d=

42

π . Re

.=

V d

ν

Flow type

m.l/s m3/s m/s

4. Analysis of the experimental data: а) Determine Recr.

b) Explain the nature of disturbances during the experiment.

c) Determine the relative discrepancy between the experimental and theoretical

value of Recr. What are the reasons for it?

d) Draw schematically the flow observations correspondent to each measurement.

laboratory scedule on fluid mechanics summer semester 2014 ... · on "fluid mechanics"...

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