1. 1
AKSUM UNIVERSITY
COLLEGE OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
THERMO FLUIDS LAB MANUAL
Compiled by
A.Syed Bava Bakrudeen,
Associate Professor,
Mechanical Department,
Aksum University, Ethiopia.
LIST OF EXPERIMENTS FOR THERMO FLUIDS LAB
1. Forced vortex flow
2. Free vortex flow
3. Hydraulic ram pump
4. Orifice discharge
5. Rectangular weir
6. Triangular weir
7. Stability of the floating body
8. Flow visualization Apparatus
9. Darcy’s friction factor (Friction Loss – Major loss)
10. Velocity distribution in aerodynamic trainer kit
11. Drag model of aero foil section
12. Tubular heat exchanger (Parallel flow)
13. Tubular heat exchanger (Counter flow)
2. 2
1. FORCED VORTEX FLOW
THEORY:
Forced vortex flow: Flow of fluid along a curved path is called vortex flow, in
forced vortex flow some external torque is required to rotate the fluid mass.
AIM:
To determine radius and height of the given forced vortex flow.
APPARATUS REQUIRED:
1. Impeller vortex setup.
2. Collecting tank
3. Stop watch
4. Meter scale
FORMULA:
1. Angular Velocity of Vane ωvane = 2 π n in 1/s
When n= Revolution/Seconds.
2. The Angular vortex velocity ω = 0.8x ωvane
3. Height of the vortex h= ω2
r2
/(2xg)
PROCEDURE:
A. Set Up:
1. Position test set up on HM150 such that drain and overflow route water into
drainage channel or volumetric tank.
2. Insert fittings in base plate in line with desired experiment (Forced vortex-
Vane with cover plate and shaft).
3. Position selector ball cocks such that mark faces vertically upwards the two
outlets are closed.
4. Make hose connection between HM150 and unit open drain of HM150.
5. Close main cock of HM 150 and switch on pump of HM 150.
6. Slowly turn selector ball cock to desired positions
3. 3
Anti clock wise : Tangential inlet for Forced vortex
7. The water volume can be exactly regulated with the slanted seat valve in the
outlet.
B. Height and Radius Measurement:
1. Insert combined radius and height gauge in mount from underneath and secure
using star type nut.
2. For measurement, loosen the star type nut and set new height; then use knurled
nut on cross member to move gauges to surface of vortex.
Height: Shoulder of rotating rod; this indicates the height of the gauges above
the bottom.
Radius: Left and right edges of notch of slider; this indicates radius.
C. Velocity Measurement:
1. For the forced vortex, a stop watch can be used to measure the time for the
vane revolutions. As however the friction between liquid and vessel wall
decelerates the vortex, the real vortex velocity is 20% lower than the vane
velocity ( Vvane).
GRAPHS:
i Velocity (v) Vs Radius (r) (Ordinary Graph)
RESULT:
1. The average value of height is = __________m.
2. The average value of radius is =___________m.
4. 4
TABULATION:
S.
No
No of
revolu
tions
(R)
Time
(S)
Rev/
Sec
(n)
Radius
(r)
in mm
Angular
Velocity of
vane (ω vane)
in r/s
Angular
Velocity
of vortex
(ω) in r/s
Height of
vortex (h)
(mm)
1 30 14.5 2.069 30 13 10.4 5
MODEL CALCULATIONS:
1. n=Revolutions/Second = 30/14.5 = 2.069 rev/s
2. ω = 2π n = 2xπx2.069 =13 r/s
3. ω = 0.8x ωvane = 0.8x8.6 =10.4 r/s
4. h= ω2
r2
/(2xg) = 10.42
x(30x10-3
)2
/(2x9.81) = 5 m m
Fig 1 Forced Vortex Flow
5. 5
2. FREE VORTEX FLOW
THEORY:
Free vortex flow: Flow of fluid along a curved path is called vortex flow, in free
vortex flow no external torque is required to rotate the fluid mass, it is imparted to
the fluid previously.
AIM:
To determine radius and height of the given free vortex flow.
APPARATUS REQUIRED:
1. Impeller vortex setup.
2. Collecting tank
3. Stop watch
4. Meter scale
FORMULA:
1. Angular Velocity ω = 2 π n in 1/s
When n= Revolution/Seconds.
2. The Velocity v=ω r in m/s
When r= Radius of revolution in meter
3. Height of the vortex h= hmax - (k 2
/(2xg.r2
))
When hmax= height of the water level in meter
k = v r
PROCEDURE:
A. Set Up:
1. Position test set up on HM150 such that drain and overflow route water into
drainage channel or volumetric tank.
2. Insert fittings in base plate in line with desired experiment (Free vortex-
Outlet of differing diameter and inlet ring for smoothing the flow).
6. 6
3. Position selector ball cocks such that mark faces vertically upwards the two
outlets are closed.
4. Make hose connection between HM150 and unit open drain of HM150.
5. Close main cock of HM 150 and switch on pump of HM 150.
6. Slowly turn selector ball cock to desired positions
Clock wise : Radial inlet for free vortex
7. The water volume can be exactly regulated with the slanted seat valve in the
outlet.
B. Height and Radius Measurement
1. Insert combined radius and height gauge in mount from underneath and secure
using star type nut.
2. For measurement, loosen the star type nut and set new height; then use knurled
nut on cross member to move gauges to surface of vortex.
Height: Shoulder of rotating rod; this indicates the height of the gauges above
the bottom.
Radius: Left and right edges of notch of slider; this indicates radius.
C. Velocity Measurement
1. To take small piece of paper or polystyrene to drop on to the water surface.
Then stop watch use to determine the time taken for the piece of paper to
perform 10 revolutions with the vortex. The radius on which the paper
revolves must also be known.
GRAPHS:
i Velocity (v) Vs Radius (r) (Ordinary Graph)
RESULT:
1. The average value of height is = __________m.
2. The average value of radius is =___________m.
8. 8
3. HYDRUALIC RAM PUMP
THEORY:
Using this type of pump it is possible to pump water to a higher level without
provision of additional mechanical energy. In this process, the kinetic energy in the
flowing water is converted into potential pressure energy by very sudden retardation.
AIM:
To determine mass flow ratio and efficiency of the given hydraulic ram
pump.
APPARATUS REQUIRED:
1. Hydraulic ram pump setup.
2. Collecting tank
3. Stop watch
4. Meter scale
FORMULA:
1. Pump Head (H) = h1 – h2 (m)
h1= First raised container (m)
h2 = Second raised container (m)
2. Amount of water raised in the first raised level (m2)= m1 + mv (l/s)
m1= Amount of water pumped (l/s)
mv = Amount of water lost (l/s)
3. Flow ratio (µ)
Practical = m2/m1
Theoretical= h1/h2
Percentage = (Practical/Theoretical)x100
4. Efficiency of the pump = P1/P2
P1= m1gh1; P1= Energy of the water pumped
P2= m2gH; P2= Energy of the water used.
9. 9
PROCEDURE:
1. The unit is first to be connected to the water supply (HM 150).
2. Closed the bleed valve and out let valve.
3. Completely open the regulating valve.
4. Switch on HM 150 pump and open main valve.
5. Open inlet valve and fill fist raised vessel.
6. Once the overflow has been reached, reduce the feed a little to avoid the water
level increasing further.
7. Normally the hydraulic ram pump now starts working. If does not work, step
the action valve can be triggered by operating the valve spindle manually.
8. After pumping is finished the volumetric flow rate of the pump can be
measured using a stop watch and a measuring container on the outlet with use
of stop watch.
GRAPHS:
i Practical mass flow ratio Vs efficiency (Ordinary Graph)
RESULT :
1. The average value of flow ratio is = ________.
2. The average value of efficiency =___________.
10. 10
TABULATION:
S.
N
o
First
rai
sed
cont
aine
r
h1
in m
Sec
o
nd
rai
sed
cont
aine
r
h2
in
m
Pump
Head
(H =
h1-h2)
in
m
Amoun
t of
water
pumpe
d
(liter
/sec)
(m2)
Amout
of
water
last
(liter/
sec)
(mv )
Amo
unt of
water
in
first
raised
level
(m1=
m2+m
v)
(L/s)
Flow ratio (µ)
Ener
gy of
the
wate
r
pum
ped
(P1)
(W)
Ener
gy of
the
wate
r
used
(P2)
(W)
Efficie
ncy of
the
pump
=
P1/P2
(W)
Prac
tical
The
orit
cal
In
per
cen
tag
e
1 0.88 1.15 0.27 1/40
=0.025
1/14.5
=0.069
0.094 .266 .765 35 0.81 .066 8.1
Average = Average =
MODEL CAL CULATION:
h1= 0.88m, h2= 1.15m, H= h1-h2 = 0.27m
m2=1/40 = 0.025 kg/s; mv= 1/14.5= 0.069 kg/s
m1=m2+mv=0.094 kg/s
Practical flow ratio = m2/m1= 0.025/0.094 =0.266
Theoretical flow ratio = h1/h2 = 0.88/1.15 =0.765
% of flow ratio = 0.266/0.765 =0.347=35%
Efficiency Pin = m1g h1 =0.094x9.81x0.88 = 0.81W
Pout =m2gh2= 0.025x9.81x0.27 = 0.066 W
Efficiency = Pout/Pin = (0.066/0.81)x100 =8.1%
11. 11
Fig 3 Principal of Hydraulic Ram
………………………………………………………………………………………
Fig 4 Orifice discharge
12. 12
4.ORIFICE DISCHARGE
THEORY:
Orifice is a small opening of any cross section (such as circular, rectangular or
triangular etc) on the side or bottom of the tank, through which a fluid is flowing.
AIM:
To determine jet diameter and coefficient of discharge of the given orifice
APPARATUS REQUIRED:
1. Orifice discharge setup.
2. Collecting tank fitted with piezo meter
3. Stop watch
4. Meter scale
FORMULA:
1. Radius of jet = (10 –Value read on micrometer )x103
2. Jet contraction or contraction coefficient α = ( Ajet/Ainlet) = (d2
jet/ d2
inlet)
djet - Dia of jet in „m‟
dinlet – Dia of inlet in „m‟
3. Velocity coefficient φ = ( Wjet/Wtheor)=(√ 2 g hstat)/ (√ 2 g htotal)
hstat = Height calculated in manometer in „ m‟.
htotal = Height calculated in pitot tube in „ m‟.
4. Discharge coefficient µ = φ α
PROCEDURE:
1. Screw the adjusting aid into the base of the tank from underneath.
2. Using the height adjusting screw, adjust the spindle so that the tip is at the height
of the adjusting aid.
3. Loose the knurled nut.
4. Set the micrometer 4.00mm.
5. Hold the piece of paper between the tip of the spindle and the adjusting aid and
using star screw, adjust the tip so that the sheet of paper is lightly clamped.
6. Hold the micrometer and securely tighten the knurled nut.
13. 13
7. Using the star screw, turn back the spindle so that the tip of the spindle is no
longer touching the adjusting aid
8. Unscrew the adjusting aid.
9. Screw the relevant nozzle and sealing ring into the base of the tank from
underneath.
10. Position test setup on HM 150 such that drain and overflow route of the later into
outlet.
11. Make hose connection between HM 150 and unit, open drain of HM150 and unit
and switch on pump of HM150.
12. Slowly open the main cock and adjust discharge height, the water level should be
below the over flow.
13. Adjust the height of the inlet basket so that it is not immersed in the water.
14. Read off head of water column in tank on left pressure gauge.
15. Rotate pitot tube into centre of jet and read off height of water column on right
pressure gauge.
16. Using the star screw, unscrew the spindle until the tip of the spindle just touches
the water jet. Read off the value on the micrometer.
GRAPHS
i hstat Vs µ (Ordinary Graph)
ii. htotal Vs µ (Ordinary Graph)
OBSERVATION
Dia of the Orifice (Dia of inlet) =……12x10-3
…………… m
RESULT:
1. The average value of jet diameter is = ______________ m
2. The average value of velocity coefficient =___________.
14. 14
TABULATION:
S.
N
o
Static
Head
hstat in
mm of
w.c
(x10-3
)
in m
Total
Head
htotal in
mm of
w.c
(x10-3
)
in m
Value
read
in
micro
meter
in mm
Jet
radiu
s
in
m
Jet
diamet
er
in
m
Veloc
ity of
the
jet
Wjet
in
m/s
Calcula
ted
velocit
y Wtheo
in m/s
Contrac
tion
coeffici
ent
α
Velocity
coefficient
φ
Discharg
e
coefficie
nt
µ
1 250 249 5.1 4.9 9.8 2.21 2.215 0.66 0.997 0.65
Average = Average =
MODEL CALCULATION:
1. Wjet = √(2ghtotal)=√(2x9.81x249x10-3
)=2.210 m/s
2. Wtheo = √(2ghstat)=√(2x9.81x250x10-3
)=2.215 m/s
3. φ = Wjet/Wtheo = 0.997
4. α= (djet)2
/(dinlet)2
= (9.8x10-3
)2
/( 12x10-3
)2
=0.667
15. 15
5.RECTANGULAR WEIR
THEORY:
A notch or weir is an opening in the side of a tank or a channel in such a way
that the liquid surface in the tank or channel is below the top edge of the opening. A
notch is smaller in size, it‟s made by metallic structure and commonly constructed in
the tank. A weir is bigger in size, it‟s made of concrete or masonary structure and
commonly constructed in channel.
Nappe or Vein: The sheet of water flowing through a notch or over weir is
called Nappe or Vein.
Crest or Sill: The bottom edge of the notch or weir which the water flows is
known a sill or crest.
AIM:
To determine the Coefficient of discharge for the given rectangular notch.
APPARATUS REQUIRED:
1. Notch tank
2. Rectangular Notch
3. Hook Gauge
4. Collecting tank fitted with piezo meter
5. Stop watch
6. Meter scale
FORMULA:
1. Head Over the Sill H = H1 – H2 (cm)
H1 - Sill Level of the tank in „cm‟
H2 – Final Hook Gauge Reading in „cm‟
2. Actual Discharge Qa = y / t (cm3
/ s)
Qa = Actual discharge in cm3
/ s
y = Discharge of water in liter
t = time taken for y cm rise in the collection tank in „sec‟
(1 Liter = 1000 cm3
)
16. 16
3. Theoretical Discharge Qt = (2/3) x L x (√2g) H 3/2
(cm3
/ s)
Qt = Theoretical Discharge in cm3
/Sec
L = Length of the notch in „cm‟
H = Head over the sill in „cm‟
4. Co-efficient of discharge Cd = Qa /Qt
Qa = Actual discharge in cm3
/ s
Qt = Theoretical Discharge in cm3
/s
PROCEDURE:
1. The internal plan dimensions of the collecting tank and the length of the notch are
measured.
2. The supply valve is opened and water is allowed to rise only up to the sill of the
notch and the supply valve is closed tightly.
3. The tip of the points of the hook gauges is adjusted such that the tip coincides
with free water surface.
4. The sill level of the notch is noted from the hook gauge reading (H1)
5. The supply valve is opened and water is allowed to flow through the notch. When
the flow becomes steady, the reading in the hook gauge (H2) is noted.
6. The outlet valve of the collection tank is tightly closed and the time taken for „y‟
cm rise in the collection tank is noted.
7. The experiment is repeated by varying the discharge through the channel by
adjusting the control valve and thus for various heads over the notch.
8. The observations are tabulated and the co-efficient of discharge is calculated.
GRAPHS:
i. H Vs Cd (Ordinary Graph)
ii. H Vs Qa (Ordinary Graph)
OBSERVATION:
Breadth of the Notch b =………6………… cm
RESULT:
1. The value of co-efficient of discharge of rectangular notch Cd =
17. 17
TABULATION:
S.
No
Hook Gauge
Reading in m Head
over the
sill H=
H1-H2
in m
Water
lever
rise in
collect
ing
tank
‘y’in
liter
Time taken
for ‘y’ liter
rise in the
tank in sec
Actual
discha
rge
Qa
Theo
retic
al
disch
arge
Qt
Coefficie
nt of
discharg
e
Sill
Level
(H1)
Final
hook
gauge
readin
g (H2)
1. 9.7 7.2 2.5 10 22 2200 2215 0.99
Average =
MODEL CALCULATIONS:
Qa = y / t = 22/10 =2.2 =2200 cm3
/s
Qt = (2/3) x L x (√2g) H 3/2
= (2/3)x6x √(2x9810)x (2.5)3/2
=2215 cm3
/s
Cd=Qa/Qt= 2200/2215=0.99
18. 18
6.TRAINGULAR WEIR
THEORY:
A notch or weir is an opening in the side of a tank or a channel in such a way
that the liquid surface in the tank or channel is below the top edge of the opening. A
notch is smaller in size, it‟s made by metallic structure and commonly constructed in
the tank. A weir is bigger in size, it‟s made of concrete or masonary structure and
commonly constructed in channel.
Nappe or Vein: The sheet of water flowing through a notch or over weir is
called Nappe or Vein.
Crest or Sill: The bottom edge of the notch or weir which the water flows is
known a sill or crest.
AIM:
To determine the Coefficient of discharge for the given triangular notch.
APPARATUS REQUIRED :
1. Notch tank
2. Traingular Notch
3. Hook Gauge
4. Collecting tank fitted with piezo meter
5. Stop watch
6. Meter scale
FORMULA:
1. Head Over the Sill H = H1 – H2 (m)
H1 - Sill Level of the tank in „cm‟
H2 – Final Hook Gauge Reading in „cm‟
2. 2. Actual Discharge Qa = y / t (cm3
/ s)
Qa = Actual discharge in cm3
/ s
y = Discharge of water in liter
t = time taken for y cm rise in the collection tank in „sec‟
(1 Liter = 1000 cm3
)
19. 19
3. Theoretical Discharge Qt = (8/15) (√2g) H 5/2
tan (ϴ/2) (m3
/ s)
Qt = Theoretical Discharge in m3
/Sec
H = Head over the sill in „m‟
ϴ = Angle of inclination of v notch in degrees
4. Co-efficient of discharge Cd = Qa /Qt
Qa = Actual discharge in m3
/ s
Qt = Theoretical Discharge in m3
/s
PROCEDURE:
1. The internal plan dimensions of the collecting tank and the length of the notch are
measured.
2. The supply valve is opened and water is allowed to rise only up to the sill of the
notch and the supply valve is closed tightly.
3. The tip of the points of the hook gauges is adjusted such that the tip coincides
with free water surface.
4. The sill level of the notch is noted from the hook gauge reading (H1)
5. The supply valve is opened and water is allowed to flow through the notch. When
the flow becomes steady, the reading in the hook gauge (H2) is noted.
6. The outlet valve of the collection tank is tightly closed and the time taken for „y‟
cm rise in the collection tank is noted.
7. The experiment is repeated by varying the discharge through the channel by
adjusting the control valve and thus for various heads over the notch.
8. The observations are tabulated and the co-efficient of discharge is calculated.
GRAPHS:
i. H Vs Cd (Ordinary Graph)
ii. H Vs Qa (Ordinary Graph)
OBSERVATION:
Angle of the Notch =……900
……
RESULT:
1. The value of co-efficient of discharge of triangular notch Cd =
20. 20
TABULATION:
S.
No
Hook Gauge
Reading in m Head
over the
sill H=
H1-H2
in m
Water
lever
rise in
collect
ing
tank
‘y’ in
liter
Time taken
for ‘y’liter
rise in the
tank in sec
Actual
discha
rge
Theor
etical
discha
rge
Coefficie
nt of
discharg
e
Sill
Level
(H1)
Final
hook
gauge
readin
g (H2)
1 10.7 5.5 5.2 10 41 4,100 4,606 0.89
Average =
MODEL CALCULATIONS:
Qa = y / t = 41/10 =4.1L/S =4100 cm3
/s
Qt = (8/15) x (√2g) H 5/2
x tan(ϴ/2)= (8/15)√(2x9810)x (5.2)5/2
=4606 cm3
/s
Cd=Qa/Qt= 4100/4606=0.89.
21. 21
7.STABILITY OF THE FLOWTING BODY
THEORY:
a.Buoyancy: A body is immersed in the fluid, a upward force is exerted by
the fluid on the body. This upward force is equal to weight of the fluid displaced by
the body. This force is called buoyancy. The point at which the force of buoyancy
act is called centre of buoyancy.
b. Metacentre: It is defined as point at which the line of action of the force of
the buoyancy will meet normal axis of the body, when the body is given a small
angular displacement.
c. Metacentric height: The distance between the meta centre of the body to
the centre of gravity of the body is called metacentric height.
AIM:
To determine the stability of the floating body using metacentric height and
also to find the buoyancy of it.
APPARATUS REQUIRED:
1. Floating body apparatus.
2. Meter scale.
FORMULA:
1. Flowting conditions
A. If Zs-M is positive – Steady floating condition.
B. If Zs-M is negative – Unsteady floating condition- It is submerged.
Where Zs = Vertical position centroidal axis in meter
M = Metacentre in meter.
2. Centre line of the floating body Xs= (MhxX) / (M+ Mh+ Mv)
Where Mh = 194g, Mv = 576g, M=2636g.
X= Distance of centre line of horizontal mass from bottom line.
3. The vertical position is referenced to the underside of the floating body
Zs = (MvxZ)+ ((M+Mh)xZg) / (M+ Mh+ Mv)
Zg = Centre gravithy of floating body without central weight = 7.13cm.
4. Stability gradient (dXs/dα) = Xs/α
22. 22
5. Buyonancy FA= FG= BxLxTxρxg
B= Width of the floating body in m
L= Length of the floating body in m
T= Depth of immersion of a floating body in m
PROCEDURE:
1. Set horizontal sliding weight to position X cm
2. Move vertical sliding weight at bottom position.
3. Fill the tank with necessary water and insert the whole body to float.
4. Gradually raise vertical sliding weight and read off angle on heel indicator.
5. Read off height of sliding weight at top edge of weight and enter in table
together with angle.
6. A further experiment can be performed to determine buoyancy. As the
floating body is block-shaped, the volume of water displaced can easily be
calculated from the width, length and immersion depth. The immersion depth
can be read off the vertical scale. A horizontal floating position is a
prerequisite for this.
GRAPHS:
Vertical centre of gravity (Zs) Vs Stability gradient (dXs/dα)
OBSERVATION:
B= Width of the floating body = -----200 mm-----
L= Length of the floating body = ------300mm-----
T= Depth of immersion of a floating body =---80mm----
RESULT:
1. The value of metacentric height is in between ___ to ___cm.
2. The average buyonancy is =___________m.
23. 23
TABULATION:
Horizontal sliding weight distance X= _______8_______ cm
Horizontal sliding weight distance Xs= ______0.0456________ cm
S.No 1
Height of vertical
sliding weight
Z cm
3
Centre of gravity
position Zs cm
6.431
Angle α 12.50
dXs/dα 0.0365
MODEL CALCUALTIONS:
1. Centre line of the floating body Xs= (MhxX) / (M+ Mh+ Mv)
Where Mh = 194g, Mv = 576g, M=2636g. at X= 8cm
Xs = 0.0456 cm.
2. The vertical position is referenced to the underside of the floating body
Zs = (MvxZ)+ ((M+Mh)xZg) / (M+ Mh+ Mv) ; Zg = 7.13cm.
Zs = 6.431cm
3. Stability gradient (dXs/dα) = Xs/α =0.0456/12.5 =0.0365 cm/0
4. Buyonancy FA= FG= BxLxTxρxg=0.2x0.3x0.08x9810 = 47.088 N
M –Meta centre
G – Centre of gravity
M- Metacentre
FB – Buoyancy force
MG- Metacentric height
24. 24
8. FLOW VISUVALISATION APPARATUS
THEORY:
Path lines are the trajectories that individual fluid particles follow. These can
be thought of as "recording" the path of a fluid element in the flow over a certain
period.
AIM:
To visualize the flow path of a liquid with subjected to various shapes of
obstacles.
APPARATUS REQUIRED:
1. Flow visualization apparatus setup
2. Collecting tank
3. Ink
PROCEDURE:
A. Venting of Apparatus:
1. Before tests or experiments can be performed , all the hoses and valves must
be vented.
2. Install and position of flat gasket and install glass pane and fasten it using 10
knurled head screw.
3. Connect the reservoir tank to the flow chamber, supply water and open all the
valves of the apparatus. The hoses and valves will be rinsed out by a strong
water flow.
4. When no more air bubbles can be seen, close all the valves again and maintain
the water supply.
5. Carefully remove the glass pane. If necessary push it out to the side in order to
prevent adhesion.
B. Assembly of the glass pane:
1. Position the flat gasket exactly onto the bore holes on the flow chamber.
2. If desired, install obstacle models and press firmly on to the plastic plate.
3. Lay the glass pane onto the gasket on one side at the supply side. Ensure the
water supply via the supply valve and slowly lower the glass pane down on
25. 25
the other side. Make sure that there are no air bubbles. If necessary, repeat
this procedure.
4. Install all of the knurled-head screws and tighten them by hand.
C. Filling and injecting the ink:
1. For good results, it is sufficient to dilute the provided ink in a ratio of 1:5.
2. Make sure that valve (B) is closed and that the pump of the HM 150 is
switched on.
3. Slightly open valve (9a). Water will flow through the flow chamber.
4. Fill the reservoir tank to the 2/3 with diluted ink.
5. Open valve (C) and slightly open valve (B). Ink will now flow through the
thin hose to the injection bore holes.
6. When the water at valve (C) has a bluish colour, close valves (B) and (C).
7. The apparatus is now ready to perform experiments.
8. In order to avoid the formation of air bubbles, make sure that there is
always enough ink in the reservoir tank!
RESULT:
Thus the fluid flow path of the liquid is shown according to the
obstacle.
Fig 8. Flow Visualization
26. 26
9. DARCY’S FRICTION FACTOR (FRICTION LOSS –MAJOR LOSS)
THEORY: When a liquid is flowing through a pipe with high velocity a shear stress
is produced in the whole liquid due to viscosity. The viscous action causes loss of
energy which usually known as friction loss. This is major loss of energy when a
liquid flow through pipe. The minor losses are loss due to sudden contraction, loss
due to bending and loss due to sudden enlargement etc.
AIM:
To determine the Darcy‟s friction factor for a material of the given pipe and to
study the variation of Reynolds number under varying flow conditions (laminar or
turbulent flow).
APPARATUS REQUIRED:
1. Darcy‟s friction apparatus
2. Collecting tank
3. Stop watch
4. Meter scale
FORMULA:
1. Difference in Head H = H1 – H2 (m)
H1 - Sill Level of the tank in „m‟
H2 – Final Hook Gauge Reading in „m‟
3. Actual Discharge Qa = y / t (m3
/s)
y = Depth of changes of water in collecting tank in “liter”
t = time taken for rise of water in the collecting tank in „sec‟
4. Velocity v= Qa/A
Qa is in m3
/sec (1 liter/Sec = 0.001 m3
/Sec)
A= Area of pipe at diameter = 3mm
5. Actual friction factor fa = 2 g d H/(4xlxv2
)
g- Specific gravity in m/s2
.
d- Dia of pipe = 3 mm
l = Length of pipe = 400 mm.
27. 27
6. Reynolds number Re = v x d/υ .
v = Velocity of water in m/s
υ = Viscosity of water =0.0107x10-4
m2
/Sec.
If Re < 2300 Laminar flow
Re > 2300 Turbulent flow
7. Theoretical Friction factor fth
fth = 16/Re for laminar flow
fth = 0.0791/(Re)0.25
for turbulent flow
8. Percentage of deviation % = (fa- fth)x100/fa
PROCEDURE:
1. The supply valve is opened and water is allowed to flow in the pipe.
2. Different in monometer readings are noted (H1, H2)
3. The outlet valve of the collection tank is tightly closed and the time taken for „y‟
liter rise in the collection tank is noted.
4. The experiment is repeated by varying the discharge through the channel by
adjusting the control valve.
GRAPHS
i. Velocity Vs Head loss (Ordinary Graph)
OBSERVATION
Diameter of the pipe =………………… m
Length of the pipe = …………………...m
Kinematic viscosity =…………………. m2
/Sec
RESULT
The average coefficient of friction (practical) f =
The average coefficient of friction (Theortical) f =
28. 28
TABULATION:
S.
No
Manomete
r Reading
in m
Loss
of
head
H=
H1-H2
in
x10-2
m
Water
lever
rise in
collect
ing
tank
‘y’lite
r
Time
taken
for ‘y’
liter
rise in
the
tank
in sec
Actual
discharge
Qa
m3
/Sec
Velocity
(V)
in m/sec
Actual
friction
factor
(fa)
Renol
ds
numbe
r (Re)
Theoriti
cal
friction
factor
(fth)
% of
Devia
tion
H1 H2
1 30 28 2 0.2 230 0.00087 0.123 0.0486 345 0.0463 4.7
Average =
MODEL CALCULATION:
1. H= 30 -28 = 2 cm.
2. Qa = 0.2/230 = 0.00087l/s = 0.00087x10-3
m3
/s.
3. V = Qa/A = 0.00087x10-3
/7.07x10-6
= 0.123 m/s.
4. A= (π/4)xd2
= (π/4)x(3x10-3
)2
= 7.07x10-6
m2
.
5. fa = 2 g d H/(4xlxv2
) = 2x9.81x0.003x0.02/(4x0.4x0.1232
) = 0.0486
6. Re = v x d/υ = 0.123x 0.003/ 0.0107x10-4
= 344.85
7. fth = 16/Re = 16/ 344.85 = 0.0463
8. % = (fa- fth) x100/fa = (0.0486- 0.0463)x100/0.0486
Fig 9. Friction loss through pipe
29. 29
10. VELOCITY DISTRIBUTION IN AERODYNAMIC TRAINER
THEORY: Aerodynamics Trainer can be used to carry out extensive experiments
on the subject of aerodynamics.
The experiments from the field of flow around bodies are 1.velocity measurement of
flows with Pitot tube. 2. Boundary layer analysis on a flat plate with incident flow
3.Visualisation of streamlines
AIM:
To determine the velocity distribution on a plate using aerodynamic trainer kit.
APPARATUS REQUIRED
1. Aerodynamic trainer kit
2. Plate.
3. Vaporization chamber.
FORMULA:
1. Pdyn = Ptotal- Pstat.
Pdyn = Dynmic pressure in Pa.
Ptotal = Total pressure in Pa.
Pstat = Static pressure in Pa.
2. Velocity (v) = √(2xPdyn/ρ)
ρ=1.204 kg/m3
.
PROCEDURE:
1. Install necessary arrangements
2. Measure ambient temperature and air pressure and use these to determine the
current air density.
3. Push the plate to the vertical position x = 0 mm (distance from the leading
edge of the plate) and secure with knurled screw.
4. Read the atmospheric pressure off a manometer tube not connected to a
measuring point.
5. Read the measured values for Ptotal and Pstat off the manometer tubes.
6. Use the micrometer screw to increase the horizontal position y (horizontal
distance from the plate) and read the measured values for Ptotal and Pstat off the
manometer tubes.
30. 30
7. Repeat this step several times to obtain a series of measurements.
GRAPHS
i Vertical position (x) Vs Flow velocity n (Ordinary Graph)
ii. Horizontal position (y) Vs Flow velocity (Ordinary Graph)
OBSERVATION
Density of vapour ρ=1.204 kg/m3
.
RESULT:
Thus the velocities are calculated and velocity gradients are generated.
31. 31
TABULATION:
S.No
Horizontal y Axis=10mm Horizontal y Axis
Ptotal in
Pa
Pstat in
Pa
Velocity
in m/s
Ptotal in
Pa
Pstat in
Pa
Velocity
in m/s
Verti
cal
X-
axis
0.35 142 202 31.6
MODEL CALCULATIONS:
1. Pdyn = Ptotal- Pstat. = 1420-2020 =600 Pa.
2. Velocity (v) = √2xPdyn/ρ. = √(2x600/1.204) =31.6 m/s.
Fig 10.Velocity distribution in plate
32. 32
11. DRAG MODEL OF AERO FOIL SECTION
THEORY:
A. Coefficient of lift (CA) is a dimensionless coefficient that relates
the lift generated by a lifting body to the fluid density around the body,
the fluid velocity and an associated reference area. A lifting body is
a foil or a complete foil-bearing body such as a fixed-wing aircraft. CA is a
function of the angle of the body to the flow, its Reynold number and
its Mach number. The lift coefficient cl refers to the dynamic lift
characteristics of a two-dimensional foil section, with the reference area of
the foil.
B. Coefficient of drag (Cw) is a dimensionless quantity that is used to
quantify the drag or resistance of an object in a fluid environment, such as
air or water.
AIM:
To determine the coefficient of drag and coefficient of lift for the given aero
foil section with use of wind tunnel.
APPARATUS REQUIRED
1. Wind tunnel.
2. Aerofoil section.
3. Computer system.
FORMULA:
1. Holder resistance FH =0.5 x ρ CwAHOLDER x V2
.
ρ= Density of air = 1.225 Kg/m3
.
CwAHOLDER = 0.000125 m2
.
V = Velocity of air in m/s.
2. Area of the aero foil A = C x L
C – Chord length in mm
L – Chord width in mm
3. Drag force Fw= Fwgem – FH.
Fwgem - Drag force in Newton.
4. Coefficient of lift (CA) = 2FA / (ρ A V2
).
FA = Lift force in newton.
33. 33
5. Coefficient of drag (CW) = 2FW / (ρ A V2
).
FW = Drag force in Newton.
6. Re = Vx Lx ρ/μ
μ = Dynamic viscosity = 18.1x10-6
kg/ms.
PROCEDURE:
1. Install the aero foil section in the wind tunnel and close the tunnel
2. Apply the necessary speed to the fan.
3. Note down the velocity of air, lift and drag force.
4. Repeat the process with higher speeds.
5. Note down the value and tabulate the record.
GRAPHS:
1. Coefficient of lift Vs Coefficient of Drag
2. Coefficient of Drag Vs Angle of inclination
3. Coefficient of lift Vs Angle of inclination.
OBSERVATION:
i. Chord Length L = 100 mm
ii. Chord Width W= 7.5mm
RESULT:
Thus the average coefficient of lift= ____________.
Thus the average coefficient of Drag= ____________.
34. 34
TABULATION:
S.
No
Angle
of
inclina
tion in
Degree
Veloc
ity
(S)
Drag
force in
Newton
(Fwgem)
Lift
force in
Newton
(FA)
Holder
resistance
(FH) in
Newton
Drag
force
(Fw) in
Newton
Coeffici
ent of
lift (CA)
Coefficie
nt of
drag in
(CW)
Renol
d‟s
Numb
er
1 10 25 2.23 2 0.05 2.18
MODEL CALCULATIONS:
1. FH =0.5 x ρ CwAHOLDER x V2
= 0.5 x 1.225x0.000125x252
= 0.04785=0.05 N.
2. A = C x L = 0.1x0.0075 = 7.5x10-4
m2
.
3. Fw= Fwgem – FH.= 2.23 – 0.05 =2.18 N.
4. CA = 2FA / (ρ A V2
) = 2x2/(1.225x 7.5x10-4
x252
) = 6.96
5. CW = 2FW / (ρ A V2
) = 2.18x2/(1.225x 7.5x10-4
x252
) = 7.6.
6. Re = Vx Lx ρ/μ = 25x0.0075x1.225/1.8x10-6
= 127604 s/m2
.
Fig 11. Drag model of aerofoil section
35. 35
12. TUBULAR HEAT EXCHANGER (PARRALLEL FLOW)
THEORY: A heat exchanger is a device used to transfer heat between one or more
fluids. The fluids may be separated by a solid wall to prevent mixing or they may be
in direct contact.[1]
They are widely used in space heating, refrigeration, air
conditioning, power stations, chemical plants, petrochemical plants, petroleum
refineries, natural-gas processing, and sewage treatment. The classic example of a
heat exchanger is found in an internal combustion engine in which a circulating fluid
known as engine coolant flows through radiator coils and air flows past the coils,
which cools the coolant and heats the incoming air. There are several types heat
exchanger shell and tube heat exchanger and plate type heat exchanger etc.
AIM: Parameter determination of the tubular heat exchanger in parallel flow of
water.
APPARATUS REQUIRED:
1. Tubular heat exchanger setup.
2. Water tank.
FORMULA:
1. LMTD = Logarithmic Mean Temperature Difference.
LMTD = [Thi –Tci]- [Tho – Tco] / {ln [(Thi- Tci)/(Tho- Tco)]}
Where Tci = T6 = Entry temperature of cold fluid in Kelvin.
Thi = T1 = Entry temperature of hot fluid in Kelvin.
Tco = T4 = Exit temperature of cold fluid in Kelvin.
Tho = T3 = Exit temperature of hot fluid in Kelvin.
2. Qh = Heat transfer rate from hot water in KJ = mh x Cph [Thi – Tho]
Where mh = Mass flow rate of hot water [Kg/s]
Cph = Specific heat of hot water [KJ/KgK] = 4.187 KJ/KgK
3. Qc = Heat Transfer rate to the cold water = mc x Cpc [Tco- Tci]
Where mc = Mass flow rate of cold water [Kg/s]
Cpc = Specific heat of cold water [KJ/KgK] =4.187 KJ/KgK
4. Q = Heat transfer rate in Watts = [Qh + Qc] / 2
5. U = Overall Heat transfer co-efficient W/m2K = Q/(A x[ΔT]M)
Where [ΔT]M = LMTD
36. 36
A = Area = πdl
6. Cr = Cmin/ Cmax
Ch = Cph x mh
Cc = Cpc x mc
In Cc , Ch which is minimum called Cmin and which is maximum called Cmax.
7. NTU = No of transfer units = Ux A/ Cmin
1- exp [ - NTU x (1+ Cr)]
8. Effectiveness E = ------------------------------------
1+ Cr
PROCEDURE:
1. Give the necessary connection to the set up.
2. Heat the water in the setup using heater.
3. Give the flow of hot water and cold water using the valve according to the
diagram. Note down the flow rate of hot and cold water.
4. Now the change in temperatures take place, note down the temperatures after
the change in temperatures reaches a steady value
5. Repeat the process of for other flow rates.
6. Tabulate the value and plot the graph.
GRAPHS: Heat transfer rate Vs Effectiveness.
Observation:
Overall length (L) = ……..560…….. mm.
Diameter (D) = ………..7…….. mm.
RESULT:
1. Heat transfer rate (Q)= _______________ W
2. Overall heat transfer coefficient (U)= _____________ W/m2
k.
3. Effectiveness (E) = ___________ .
37. 37
TABULATION:
S
.
N
o
Flow rate
of Hot
water
Flow rate
of Cold
water
Inlet
temp of
hot
water
(Thi)
(T1)
outlet
temp of
hot water
(Tho) (T3)
Inlet
temp of
cold
water
(Tci)
(T6)
Outlet
temp of
hot water
(Tco)
(T4) LMT
D
Hea
t
tran
sfer
rate
(Q)
Ove
r all
heat
tran
sfer
coef
ficie
nt
(U)
Effe
ctiv
enes
s
(E)
L/hr Kg /s
L/mi
n
Kg /s 0
C K 0
C K 0
C K 0
C K
1 144 .04 120 .0333 56 329 45 318 34 307 39 312 12.31 1.27 8.4 .403
MODEL CALCULATIONS:
LMTD = [Thi – Tci] - [Tho – Tco] / ln [Thi – Tci/Tho – Tco]
= [329 – 307] – [318 – 312] / ln [(329 – 307) / (318 – 312)]= 12.31 K.
Qh = mh x Cph [Thi – Tho] = 0.04 x 4.187 x [329 – 318] = 1.842 KJ/sec.
Qc = mc x cpc [Tco –Tci]= 0.0333 x 4.187 [312 – 307] = 0.691 KJ/sec.
Q = [Qh + Qc] / 2 = [1.842 + 0.691] / 2 = 1.27 KJ/sec.
A = π x D x L= π x 0.007 x 0.56= 0.0123 m2
.
U = Q/(A x[ΔT]M)= 1.27 / (0.0123 x 12.31)= 8.4 W/m2
K.
Cr = Cmin/ Cmax = 0.14/0.167= 0.8383
Ch = Cph x mh = 4.187 x 0.04= 0.167 = Cmax
Cc = Cpc x mc = 4.187 x 0,0333= 0.140 = Cmin
NTU = Ux A/ Cmin = 8.4x0.0123/ 0.14 = 0.737.
39. 39
13. TUBULAR HEAT EXCHANGER (COUNTER FLOW)
THEORY: A heat exchangers are classified parallel flow and counter flow based on
the direction of both the fluids flow. In parallel flow heat exchanger both the fluids
(hot and cold) are flowing in the same direction. But in counter flow heat exchanger
both the fluids are flowing in the opposite direction.
AIM: Parameter determination of the tubular heat exchanger in counter flow of
water.
APPARATUS REQUIRED:
1. Tubular heat exchanger setup.
2. Water tank.
FORMULA:
1. LMTD = Logarithmic Mean Temperature Difference.
LMTD = [Thi –Tci]- [Tho – Tco] / {ln [(Thi- Tci)/(Tho- Tco)]}
Where Tci = T4 = Entry temperature of cold fluid in Kelvin.
Thi = T1 = Entry temperature of hot fluid in Kelvin.
Tco = T6 = Exit temperature of cold fluid in Kelvin.
Tho = T3 = Exit temperature of hot fluid in Kelvin.
2. Qh = Heat transfer rate from hot water in KJ = mh x Cph [Thi – Tho]
Where mh = Mass flow rate of hot water [Kg/s]
Cph = Specific heat of hot water [KJ/KgK] = 4.187 KJ/KgK
3. Qc = Heat Transfer rate to the cold water = mc x Cpc [Tco- Tci]
Where mc = Mass flow rate of cold water [Kg/s]
Cpc = Specific heat of cold water [KJ/KgK] =4.187 KJ/KgK
4. Q = Heat transfer rate in Watts = [Qh + Qc] / 2
5. U = Overall Heat transfer co-efficient W/m2K = Q/(A x[ΔT]M)
Where [ΔT]M = LMTD
A = Area = πdl
6. Cr = Cmin/ Cmax
Ch = Cph x mh
Cc = Cpc x mc
40. 40
In Cc , Ch which is minimum called Cmin and which is maximum called Cmax.
7. NTU = No of transfer units = Ux A/ Cmin
1- exp [ - NTU x (1- Cr)]
8. Effectiveness E = -------------------------------------------
1- {Cr xexp [ - NTU x (1- Cr)]}
PROCEDURE:
1. Give the necessary connection to the set up.
2. Heat the water in the setup using heater.
3. Give the flow of hot water and cold water using the valve according to the
diagram. Note down the flow rate of hot and cold water.
4. Now the change in temperatures take place, note down the temperatures after
the change in temperatures reaches a steady value
5. Repeat the process of for other flow rates.
6. Tabulate the value and plot the graph.
GRAPHS: Heat transfer rate Vs Effectiveness.
Observation:
Overall length (L) = ……..560…….. mm.
Diameter (D) = ………..7…….. mm.
RESULT:
1. Heat transfer rate (Q)= _______________ W
2. Overall heat transfer coefficient (U)= _____________ W/m2
k.
3. Effectiveness (E) = ___________ .
41. 41
TABULATION:
S.
N
o
Flow rate
of Hot
water
Flow rate
of Cold
water
Inlet
temp of
hot
water
(Thi)
(T1)
outlet
temp of
hot
water
(Tho)
(T3)
Inlet
temp of
cold
water
(Tci)
(T4)
Outlet
temp of
hot
water
(Tco)
(T6)
LMT
D
Hea
t
tran
sfer
rate
(Q)
Over
all
heat
trans
fer
coeff
icien
t (U)
Effe
ctiv
enes
s
L/h
r
Kg /s L/hr Kg /s 0
C K 0
C K 0
C K 0
C K
1 288 .08 191 .053 82 355 57 330 35 308 51 324 26.24 5.95 18.43 0.44
MODEL CALCULATIONS:
LMTD = [Thi – Tci] - [Tho – Tco] / ln [Thi – Tci/Tho – Tco]
= [355 – 324] – [330 – 308] / ln [(355 – 324) / (330 – 308)]= 26.24 K.
Qh = mh x Cph [Thi – Tho] = 800 x 10-4
x 4.187 x [355 – 330] = 8.347 KJ/sec.
Qc = mc x cpc [Tco –Tci]= 0.053 x 10-4
x 4.187 [32 4 – 308] = 3.551 KJ/sec.
Q = [Qh + Qc] / 2 = [8.347 + 3.551] / 2 = 5.95 KJ/sec.
A = π x D x L= π x 0.007 x 0.56= 0.0123 m2
.
U = Q/(A x[ΔT]M)= 5.95 / (0.0123 x 26.24)= 18.4352 W/m2
K.
Cr = Cmin/ Cmax = 0.335/0.222 = 1.51
Ch = Cph x mh = 4.187 x 0.08 = 0.335 = Cmax
Cc = Cpc x mc = 4.187 x 0.053 = 0.222 = Cmin
NTU = Ux A/ Cmin = 18.4352x0.0123/ 0.222 = 1.02.
42. 42
1- exp [ - NTU x (1- Cr)] 1- exp [- 1.02 x -0.51]
E = ------------------------------------ = --------------------------------------- = 0.44
1- {Cr xexp [ - NTU x (1- Cr)]} 1- {1.51xexp [- 1.02 x -0.51]}
Fig 13. Counter Flow Tubular Heat Exchanger
