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Fluid Mechanics Lab Report
Prepared By: Muhammad Bilal
Civil Engineering Department, Uet Peshawar
Fluid Mechanics Lab Report
Prepared By: Muhammad Bilal
Civil Engineering Department, Uet Peshawar
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Table of Contents
Demonstration of various parts of hydraulic bench Lab 1
To determine the discharge and coefficient of Discharge over
rectangular and triangular Notch
Lab 2 and 3
Investigation of different types of flows using Osborne
Reynolds’s apparatus (by visual observation)
Lab 4
Investigation of different types of flows using Osborne
Reynolds’s apparatus (by Reynolds’s number formula)
Lab 5
To determine the theoretical and actual center of pressure on
partially submerged body.
Lab 6
To determine hydraulic co-efficient and to study jet profile of
a small circular orifice provided at side of tank
Lab 7
To determine the hydraulic coefficients for a circular orifice at the
bottom of tank
Lab 8
To investigate the velocity of Bernoulli’s theorem as applied to the
flow of water by Bernoulli’s theorem demonstration
Lab 9
To determine the relationship between head loss due to friction and
velocity for flow of water through smooth bore pipe
Lab 10
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Experiment # 1
DEMONSTRATION OF VARIOUS PARTS OF HYDRAULIC BENCH
Hydraulic bench is a very useful apparatus in hydraulics and fluid mechanics.
It is involved in majority of experiments to be conducted e.g. to find the value of
the co-efficient of velocity, CV, coefficient of discharge ' Cd, to study the
characteristics of flow over notches, to, to find head losses through pipes, to verify
Bernoulli's theorem etc.
Various Parts of hydraulic Bench
SUMP TANK
It stores water for Hydraulic bench. It is located in the bottom portion of Hydraulic bench.
Water from here is transported to other parts by using a pump. It has a capacity of 160 liters
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
VOLUMETRIC TANK
It stores water coming from channel. This tank is stepped to accommodate low or high flow rates.
It has a capacity of 46 liters
DUMP VALVE
It is used for emptying volumetric tank. It is located in the bottom of the volumetric tank.
CHANNEL
It is used in number of experiments it provides passage for water for different experiments. A
valve is also attached to the channel to measure the depth of water in channel.
SIDE CHANNELS
They are the upper sides of the channel. They are used to attach accessories on test
CENTRIFUGAL PUMP
It draws water from sump tank and supplies it for performing experiments Vertical pipe it supplies
water to the upper part of hydraulic bench from sump tank through a pump
CONTROL VALVE
It is used to regulate the flow in the pipe i.e. to increase or decrease the inflow of water in the
hydraulic bench
STILLING BAFFLE
It decreases the turbulence of water coming from channel. It is located in the volumetric tank.
OVER FLOW
It is an opening in the upper portion of the volumetric tank. It sends the water level above 46 liters
to the sump tank
STARTER
It on / off the hydraulic bench.
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
SCALE & TAPPING
A sight tube and scale is connected to a tapping in the base of the volumetric tank and gives an
instantaneous indication of water level.
ACTUATOR : Dump valve is operated by a remote actuator, lifting actuator opens the
dump valve, when it is given a turn of 90' it will turn the dump valve in the open
position
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Experiment # 2 and 3
TO DETERMINE THE DISCHARGE AND COEFFICIENT OF
DISCHARGE OVER RECTANGULAR AND TRIANGULAR NOTCH.
Objectives of the Experiment:
1. To demonstrate the flow over different weir types.
2. To calculate the coefficient of discharge for different notch types.
Theory
For the rectangular Notch:
And for triangular Notch
Where
Cd = Coefficient of discharge
B or L = width of the rectangular weir (3
cm) H = head above the Notch apex θ =
angle of the triangular weir g =
acceleration of gravity
Apparatus
• Hydraulic bench
• Stop watch
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
• Hook and point gauge
• Notch plates
Experimental Setup
Procedures and Readings
1. Make sure that the Hydraulic Bench is levelled.
2. Consider the zeros in point gauge. Take enough care not Damage the weir plate
and the point gauge
3. Put the point gauge half way between the stilling baffle plate and the Notch plate.
4. Allow water to flow into the experimental setup and adjust the Minimum flow
rate by means of the control valve to have atmospheric Pressure all around water
flowing over the Notch. Increase the flow rate incrementally such that the head
above the weir crest increases around 1 cm for each flow rate increment. 5. For
each flow rate, wait until steady condition is attained then measure and record
the head (H) above the weir
5. For each flow rate, measure and record the initial and final volumes in the
Collecting tank and the time required to collect that volume. For each Flow Rate,
take 3 different readings of the volumes and time and record the average
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
For the rectangular Notch:
Where b=width of notch
𝑸 = 𝒌 × 𝑯 𝟑/𝟐 Equating
both equations and taking log on both sides
This log equation is the equation of a line where logk is y intercept and slope n=3/2 Finally
equation for Cd
V(dm^3) time(sec) Q(dm^3/sec) H1 H2 H(dm) logQ LogH
10 8.37 1.19474313 85 156 0.71 0.077275
-
0.14874
10 10.21 0.979431929 85 146 0.61 -0.00903
-
0.21467
5 11.31 0.442086649 85 122 0.37 -0.35449 -0.4318
After plotting we get the coefficient of x=1.525 which should be 1.5,
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
For triangular notch:
Equating both equations and taking long on both sides
Finally equation becomes
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
time(s) Q(dm^3/
s)
H1 H2 H(dm) LogQ LogH
29.2 0.3425 125 158 0.33 -0.4654 -0.4815
36.98 0.2704 125 154 0.29 -0.5680 -0.5376
30.33 0.1649 125 150 0.25 -0.7829 -0.6021
Logk=0.8026
Fluid Mechanics Lab report
Experiment # 04:
Investigation of different types of flows using Osborne Reynolds’s
apparatus (by visual observation).
OBJECTIVE:
The objective of this experiment is to determine different types of flows under different
conditions visually.
Types of flows:
There are three types of flows.
S
No.
Types of
flow
Reynolds’s
number
Remarks
1
Laminar
flow
R<2000
When stream line follows parallel path. The dye
remains easily identifiable as solid core.
2
Transition
flow
2000<R>4000
When stream line interact and partial mixing of flow
occur. Dye form eddies which flow through water.
3
Turbulent
flow
R>4000
When stream line interact and complete mixing of
flow occur. Dye stream completely disappear in flow
of water.
APPRATUS:
1. Hydraulic bench
2. Osborne Reynolds’s apparatus
3. Dye
4. Thermometer
COMPONENTS OF OSBORNE
REYNOLD’S APPRATUS.
1. Dye reservoir. 5. Bell mouth inlet
2. Control valve. 6. Marbles.
3. Over flow pipe. 7. Water supply pipe.
4. Head tank. 8. Flow visualization pipe.
9. Velocity control valve.
Figure 1 Reynolds’sOsborne Apparatus
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
PROCEDURE:
• Fill the reservoir with dye.
• Fix the apparatus on the bench and connect the inlet water supply pipe with the bench
feet.
• Lower the dye injector until it’s just above the bell mouth inlet.
• Open the bench inlet valve and slowly fill the head tank up to the overflow level. And
then close it.
• Open the velocity control valve to enter water to the flow visualization pipe.
• Open the control valve slightly and adjust the dye control valve until slow flow with
thin dye line is obtained (laminar flow).
• Increase the flow rate till the dye takes a wave form (transition flow).
• Further increase of flow rate will completely disappear the dye and form eddies
(turbulent flow).
Control
Dye Reservoir
Head Over flow
Needle
Marble pieces
Flow visualization pipe
Velocity control valve
Water supply pipe
Osborne Reynolds' Apparatus
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Different Flows
OBSERVATION AND CALCULATIONS
S.NO OBSERVATION TYPE OF FLOW
1
DYE CANNOT MIX WITH WATER
AND MOVE PARRALLEL
LAMINAR
2
DYE PARTIALLY MIX WITH
WATER
TRANSITION
3
DYE COMPLETELY DISAPPEAR
IN WATER
TURBULANT
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Experiment # 05
Investigation of different types of flows using
Osborne Reynolds’s apparatus (by Reynolds’s number formula)
OBJECTIVE:
The objective of this experiment is to determine different types of flows under different
conditions by Reynolds’s number formula.
Where:
R=Reynolds number V=velocity of fluid ϑ =Kinematic
viscosity at observed temperature of water.
APPRATUS:
1. Hydraulic bench
2. Osborne Reynolds’s apparatus
3. Dye
4. Thermometer
PROCEDURE:
• Fill the reservoir with dye.
• Fix the apparatus on the bench and connect the inlet water supply pipe with the bench
feet.
• Lower the dye injector until it’s just above the bell mouth inlet.
• Open the bench inlet valve and slowly fill the head tank up to the overflow level. And
then close it.
• Open the velocity control valve to enter water to the flow visualization pipe.
• Open the control valve slightly and adjust the dye control valve until slow flow with
thin dye line is obtained (laminar flow).
• Note down the volume and time using graduated cylinder and stop watch.
• Increase the flow rate till the dye takes a wave form (transition flow).and record
volume and time.
• Further increase of flow rate will completely disappear the dye and form eddies
(turbulent flow).again calculate volume and time for this flow.
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
OBSERVATION AND CALCULATION
VOLUME
(M3)
TIME
(S)
TEMP
(C)
Q(m3
/s)
Velocity
=Q/A
(m/s)
ϑ R Type of flow
2x10-4 110.54 20°
C 1.809x10-6
0.023 1.003x10-6
229.3 laminar
3x10-4
70.6 20°
C 4.249 x10-6
0.054 1.003x10-6
538.4 laminar
8x10-4
31.7 20°
C 2.525 x10-5
0.322 1.003x10-6
3210 transition
4x10-4
77.57 20°
C 5.157 x10-5
0.657 1.003x10-6
6550 turbulent
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Experiment No 06:
To determine the theoretical and actual center of pressure on
partially submerged body.
Objective:
The objective of this experiment is to determine the hydrostatic thrust acting on a plane
surface immersed in water.
Theory:
Thrust force is given by.
Theoretical center is given by.
Actual center is given by.
Where:
W=weight
P=moment arm (p=27.5cm)
𝐹 𝑟=resultant force
R=depth of water
Q=depth of water from pivot point (q=20-r)
B=width of plane area (B=7.5cm)
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Apparatus:
1. Hydraulic pressure apparatus
2. Weights
3. Water
Hydraulic pressure device.
Different Parts of Apparatus
Q
R
P
W
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Procedure:
1. Position the empty hydrostatic apparatus on a plane table or hydrostatic bench and adjust
the leveling screw until the circular spirit level shows that the base in horizontal and
balance.
2. Then concede share edge of beam and y-line.by moving the counter balance weight.
3. Ensure that the drain valve is closed and the plastic pipe is connected to the drain valve.
4. Add 50g weight to the weight hanger.
5. Add water until the hydrostatic thrust on the end face of quadrant causes the balance arm to
rise.
6. Continue adding water until balance arm is horizontal, measuring this by aligning the base
of balance arm with the central marking on the balance rest.
7. If the tank is over filled then the equilibrium can be obtained by slightly opening the
drained valve and allow some water to flow.
8. Read the depth of the immersion from the scale on the face of the quadrant.
9. Repeat the same procedure and increase the load by 50g each time. And take four readings.
Observation and calculation
S No
Weight
(g)
Weight
(n)
Depth of
water
R(m)
Q(m)
Q=0.2-
r 𝐹 𝑟(n)
𝐻 𝑝
Actual
𝐻 𝑝
Theoretical
(m)
(m) (cm) (m) (cm)
1 50 0.49 0.046 0.154 0.778 0.173 17.3 0.184 18.4
2 100 0.98 0.066 0.134 1.602 0.168 16.8 0.178 17.8
3 150 1.47 0.083 0.117 2.534 0.159 15.9 0.172 17.2
4 200 1.96 0.097 0.103 3.461 0.156 15.6 0.168 16.8
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Experiment # 7
To determine hydraulic co-efficient (𝐶 𝑑 , 𝐶 𝑣, 𝐶𝑐) and to study jet profile
of a small circular orifice provided at side of tank
Theory
• An orifice is an opening in a vessel through which water flows out, in case of orifice
the upstream level of water is above the top edge of opening
• Co-efficient of contraction is the ratio of area of jet at vena contracta to the area of
orifice
Mathematically
• Co-efficient of velocity is the ratio of actual velocity to the theoretical velocity of jet
from orifice
Mathematically
Where ℎ 𝑜 is depth of water over orifice (from center) and ℎ𝑐 is velocity head of jet at
vena contracta. In this experiment we will find 𝐶 𝑣 with the help of jet profile
i.e.
• Co-efficient of discharge is the ratio of actual discharge to theoretical discharge
Mathematically
• Vena contracta is the portion of jet with least diameter
• Diameter of orifice used in experiment is 6mm
• A jet is a stream of fluid that is projected into a surrounding medium, usually from some
kind of a nozzle or orifice. Jets can travel long distances without dissipating, Jet profile
refers to the trajectory followed by jet during the experiment.
𝐶𝑣 = √
𝑥2
4 𝑦ℎ 𝑜
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Apparatus Used in experiment
Fig 1- Labeled diagram of orifice and Jet apparatus
Fig 2- Actual apparatus (It is fitted over hydraulic bench and then the
experiment is Performed)
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Procedure
• Adjust the orifice and jet apparatus over hydraulic bench, through control valve start
flow and wait till there is reasonable amount of water in head tank
• Adjust the overflow accordingly and note the reading of overflow as ℎ 𝑜
• Water will comes out of orifice, Screw up the needles according to the path of the flow
of water
• Mark the points of top of needle accurately by pencil on A3 size paper sheet.
• For specific volume of water that is been driven to volumetric tank find the time with
help of stopwatch
• Remove the paper and find x and y distances with respect to a reference line/first point
• Plot y on x-axis and 𝑥2 on y-axis in Excel and calculate slope for 𝐶 𝑣 From the data
collected find the other co-efficient
Fig 3- Experimental setup over hydraulic bench and marking of points on A3
size paper
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Observations and calculations
x (cm) y (cm) 𝑥2 (cm)
0 0 0
5 0.6 25
10 1.6 100
15 2.9 225
20 5 400
25 7.4 625
30 10.2 900
35 13 1225
We get 93.916cm and we have, ℎ0=31cm
After plotting y and 𝑥2 Values
y = 93.916x - 40.297
-200
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12 14
Y values
X^2/y plot
𝐶𝑣 = √
𝑥2
4 𝑦ℎ 𝑜
𝐶𝑣=√
99.916
4(31)
𝐶𝑣= 0.87
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
For 𝐶 𝑑
From Experiment
Diameter d of orifice=0.6cm, Area of orifice=0.283𝑐𝑚2
Take g=980cm/𝑠𝑒𝑐2
Volume=3litre=3000𝑐𝑚3
ℎ0=31cm Time=82.37sec
Now to calculate 𝐶 𝑐 we know that
𝐶𝑑=
3000 82.37⁄
0.283√2(980)(31)
𝐶𝑑 =0.52
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Experiment # 8
To determine the hydraulic coefficients (𝐶 𝑑 , 𝐶 𝑣, 𝐶𝑐) for a circular orifice
at the bottom of tank
Theory
• An Orifice is an opening in the side or base of tank or reservoir through which fluid is
discharge in the form of a jet. The discharge will depend up on the head of the fluid (H)
above the level of the orifice. The term small orifice means that the diameter of the
orifice is small compared with the head producing flow
• The equations for hydraulic coefficients are
•
•
•
Apparatus used in experiment
Fig 1- orifice at bottom of tank
The apparatus used in this experiment are hydraulic bench, tank having circular orifice at the
bottom and Pitot tube which is installed near bottom orifice to measure the velocity head of jet
and diameter at vena contracta.
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
𝐶𝑣=0.98, 𝐶𝑐=0.73, 𝐶𝑑=0.65𝑐 ,
Procedure
• Adjust the orifice and jet apparatus over hydraulic bench, through control valve start
flow and wait till there is reasonable amount of water in head tank
• When the water in the tank becomes constant note down depth of water in tank ℎ 𝑜 and
also note down the velocity head of jet ℎ𝑐 which is on the scale, the pitot tube that is
installed actually gives us the velocity head
• To find the diameter of vena contracta 𝐷 𝑐 note the number of revolutions of pitot tube
from one end of jet to another end of jet such that 1rev=1mm
• Take the diameter of orifice as 14mm
• For specific volume of water that is been driven to volumetric tank find the time with
help of stopwatch
Observations and calculations
S.no 𝐷 𝑜(mm) 𝐷 𝑐(mm) ℎ 𝑜(mm) ℎ𝑐(mm) vol(lit) time(sec) 𝐶 𝑣 𝐶 𝑐 𝐶 𝑑
1 14 12 323 318 15 58.64 0.98 0.73 0.66
2 14 12 251 249 10 43.07 0.99 0.73 0.67
3 14 12 258 255 10 45.21 0.97 0.73 0.63
Average values
Calculations for 𝐶 𝑣
• When ℎ𝑐=318 and ℎ 𝑜=323
• When ℎ𝑐=249 and ℎ 𝑜=251
• When ℎ𝑐=255 and ℎ 𝑜=258
Fluid Mechanics Lab report
CED, UET-P Muhammad Bilal
Calculations for 𝐶 𝑐
𝐴𝑐=113.097𝑚𝑚2
𝐴 𝑜=153.93𝑚𝑚2
𝐶 𝑐=0.73
Calculations for 𝐶 𝑑
• 𝐴 𝑜 is constant, ℎ 𝑜=323mm, volume=15lit=15x108 𝑚𝑚3 and t=58,64
𝐶 𝑑=0.66
• 𝐴 𝑜 is constant, ℎ 𝑜=251mm, volume=10lit=1x107 𝑚𝑚3 and t=43.07
𝐶 𝑑=0.67 𝐴 𝑜 is constant,
ℎ 𝑜=258mm, volume=10lit=1x107 𝑚𝑚3 and t=45.21
𝐶 𝑑=0.63
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Experiment # 9
To investigate the velocity of Bernoulli’s theorem as applied to the flow of water
by Bernoulli’s theorem demonstration
Theory
• The statement of the Bernoulli’s theorem is stated as the total head of a liquid flowing
between two points remains constant provided that there is no loss due to friction and no
gain due to an application of outside work between these two points
• Mathematically H =
• Where
𝑃
ϒ
is called static or pressure head,
𝑉2
2𝑔
we call it velocity head and is datum or
elevation head which is considered zero in horizontal pipe.
• To find pressure head at various points manometer is fixed at each of these points and for
total head we use hypodermic probe which is installed in the apparatus.
• For theoretical velocity head this equation will be used
• For theoretical pressure head use
Apparatus used in experiment
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Inside the test section of the apparatus we have a venture meter which has a converging and
diverging section
Procedure
• The apparatus is located on the flat top of the hydraulic bench and the instrument is
properly levelled with the help of spirit level.
• The water is allowed to fill in the manometer tubes until all trapped air is removed
• All manometer tubes are checked properly connected to the corresponding pressure
taps are air-bubble free
• The discharged valve is adjusted to a high measureable flow rate.
• After the level is stabilized, the water flow rate is measured using volumetric
method.
• The pressure head for each point(total six) is observed by the reading shown in
monometer tube similarly the total head at each point is observed with the help of
hypodermic probe
Observations and calculations
tapping
point
actual
static
head(mm)
actual
velocity
head(mm)
actual
total head
H(mm)
theoretical
statichead
(mm)
theoretical
velocity
head (mm)
theoretical
total head
H (mm)
head loss
between
two points
(mm)
total head
loss up to
point(mm)
A 232 3 235 232 2.04 234.04 ~ ~
B 213 21 234 212.65 21.04 233.69 1 1
C 178 55 233 192.85 41.23 234.08 1 2
D 173 57 230 173.11 60.98 234.09 3 5
E 135 94 229 154.18 80 234.18 1 6
F 152 30 182 232 2.04 234.04 47 53
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Tapping position and diameter of test section
A B C D E F
25mm 13.9mm 11.8mm 10.7mm 10mm 25mm
It is important to note that for the theoretical static and velocity head the equations that were
discussed in the theory section were used.
Plotting
We will be plotting here the hydraulic and energy grade line. The length of the test section is
approximately 130.68cm=1306.8mm, starting from point A which has zero length
A B C D E F
0mm 400mm 600.8mm 800.8mm 900.8mm 1308.8mm
Hydraulic grade line for this experimental data
120
140
160
180
200
220
240
0 200 400 600 800 1000 1200 1400
lenght of test section (mm)
Hydraulic grade line
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Energy grade line for this experimental data
RECOMMENDATIONS
• Make sure there is no air bubbles trapped before and during running the experiment.
• The eye level must be perpendicular to the reading when recording the data to avoid
parallax error
• The control valve should be maintained at a constant flow so that each at every readings of
each manometer has the same value of pressure
• The experiment should be repeated for a few times so that an average value could be
obtained
233.6
233.7
233.8
233.9
234
234.1
234.2
234.3
0 200 400 600 800 1000 1200 1400
lenght of test section(mm)
Energy grade line
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Experiment # 10
To determine the relationship between head loss due to friction and velocity for
flow of water through smooth bore pipe
Objectives
• To study and develop laminar flow
• To study and develop turbulent flow
• To study head losses in pipes at different velocities
Theory
• A flow where we can say head losses are proportional to velocity is termed as laminar flow
while for turbulent flow the head losses are proportional to some power of velocity For
laminar H α V and for turbulent H α 𝑉 𝑛 where n can be any number
• It should be noted that for turbulent flow the head losses becomes more sensitive to velocity
• The circled section is transition stage where there is no proper relationship between H and
V
• Here we will be using Darcy weisbach equation to calculate theoretical head loss
• where f is Darcy friction factor which can be observed from Moody chart
• Also Reynolds number can be calculated from R=
𝑉𝐷
ϒ
where ϒ is kinematic viscosity ϒ
• L is the length of the pipe between tapings, D is the internal diameter of the pipe, v is the
mean velocity of water through the pipe in m/s, g is the acceleration due to gravity in m/s2
and f is the pipe friction coefficient.
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Apparatus Used in Experiment
Fig 1- Hydraulic bench and fluid friction apparatus
Labeled Diagram of apparatus
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Parts
• Water is fed in from the hydraulics bench via the barbed connector (1)
• An in-line strainer (2)
• A sudden contraction (3)
• A 45° "Y" (4)
• A 45° elbow (5)
• A long radius 90° bend (6)
• An artificially roughened pipe (7)
• Smooth bore pipes of 4 different diameters (8), (9), (10) and (11)
• A 90° "T" (13)
• A 90° miter (14)
• A short radius 90° bend (15)
• A sudden enlargement (16)
• A pipe section made of clear acrylic with a Pitot static tube (17)
• A Venturi meter made of clear acrylic (18)
• An orifice meter made of clear acrylic (19)
• Ball valve (20), (21)
• A 90° elbow (22)
• exit tube (23)
• Short samples of each size test pipe (24) are provided loose so that you can measure the
exact diameter
• isolating valves (25)
Procedure
• Water is pumped through the Fluid Friction Apparatus using a centrifugal pump mounted
on the inside of the hydraulics bench.
• Water flows through the connector in the channel on the bench top, through the flexible
connecting hose shown in the diagram. It will then flow through whichever of the test pipes
is selected
• Flow rates through the apparatus may be adjusted by operation of the Control Valve on the
hydraulics bench.
• The flow path through the pipe friction network is controlled using the system of isolating
valves shown in the diagram above. By opening and closing these valves as appropriate, it
is possible to select flow through any combination of pipes.
• When test conditions have stabilized, the dump valve is lowered, retaining the water in the
tank. Timings are taken as the water level rises in the tank and volume is recorded
• The head loss due to pipe friction is measured by taking pressure readings at different
tapping points on the pipe network. In order to measure the pressure loss along a pipe, the
pressure measurement device is connected
• It is important to expel any air which may be trapped in the pipes of the pressure meter
before taking readings..
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
Observations and calculations
1liter=106 𝑚𝑚3 , all units are in mm, ϒ kinematic viscosity is 0.8721 𝑚𝑚2/sec
S.no 1 2 3 1 2 3 1 2 3
diameter(mm) 6 6 6 10 10 10 17 17 17
Volume
(mm^3)
106 106 106 107 107 107 107 107 2×
107
time(sec) 74.56
sec
35.02
sec
24.87
sec
79.54
sec
60.07
sec
44.03
sec
33.25
sec
17.11
sec
25.70
sec
Discharge
(mm^3/sec)
1341
2
3123
0.4
4020
9
125250.
5
1664
72.4
2271
17.8
3007
51.9
5844
53.5
7782
10.1
Velocity
(mm/sec)
474.3
5
1104.
56
1422.
11
1594.75 2119.
61
2891.
78
1325.
01
2574.
91
3428.
54
Reynolds No 3263.
502
7599.
312
9784.
039
18286.3
2038
2430
4.67
3315
8.81
2582
8.65
5019
3.18
6683
3.14
friction factor f 0.042 0.034 0.031 0.024 0.023 0.023 0.027 0.021 0.019
Measured head
loss(mm H20)
1201.
5
2268 3888 1512 2146.
5
3739.
5
1161 2416.
5
2713.
5
Calculated
Head loss
(mm H20)
80.27 352.3
7
546.3
1
321.46 538.1
2
980.3
0
142.1
2
417.4
41
697.8
0
Velocity vs head loss relationships for different pipes
For 6mm pipe
y = 2.6734x - 221.79
1000
1400
1800
2200
2600
3000
3400
3800
400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
Velocity(mm/sec)
Velocity vs head loss (for 6mm pipe)
Fluid Mechanics Lab Report
CED, UET-P Muhammad Bilal
From the table if we look at Reynolds number Row for 6mm pipe it ranges from 3000-9000
which clarifies the shape of the plot. It shows turbulent flow H α 𝑉 𝑛 where n=2.6734
The flow is turbulent (from Reynolds number as well as shape of graph) value of n=1.7423
Comment: The flow is turbulent (from Reynolds number as well as shape of graph) value of
n=0.7577 Here if we increase V head losses will decrease.
For 10mm pipe
Comment:
y = 1.7432x - 1372.7
1400
1900
2400
2900
3400
3900
1500 1700 1900 2100 2300 2500 2700 2900
Velocity(mm/sec)
Velocity vs head loss (for 10mm pipe)
For 17mm pipe
y = 0.7577x + 246.09
1000
1300
1600
1900
2200
2500
2800
3100
1200 1600 2000 2400 2800 3200 3600
Velocity(mm/sec)
Velocity vs head loss (for 17mm pipe)

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Fluid mechanics Lab Report

  • 1. Fluid Mechanics Lab Report Prepared By: Muhammad Bilal Civil Engineering Department, Uet Peshawar Fluid Mechanics Lab Report Prepared By: Muhammad Bilal Civil Engineering Department, Uet Peshawar
  • 2. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Table of Contents Demonstration of various parts of hydraulic bench Lab 1 To determine the discharge and coefficient of Discharge over rectangular and triangular Notch Lab 2 and 3 Investigation of different types of flows using Osborne Reynolds’s apparatus (by visual observation) Lab 4 Investigation of different types of flows using Osborne Reynolds’s apparatus (by Reynolds’s number formula) Lab 5 To determine the theoretical and actual center of pressure on partially submerged body. Lab 6 To determine hydraulic co-efficient and to study jet profile of a small circular orifice provided at side of tank Lab 7 To determine the hydraulic coefficients for a circular orifice at the bottom of tank Lab 8 To investigate the velocity of Bernoulli’s theorem as applied to the flow of water by Bernoulli’s theorem demonstration Lab 9 To determine the relationship between head loss due to friction and velocity for flow of water through smooth bore pipe Lab 10
  • 3. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Experiment # 1 DEMONSTRATION OF VARIOUS PARTS OF HYDRAULIC BENCH Hydraulic bench is a very useful apparatus in hydraulics and fluid mechanics. It is involved in majority of experiments to be conducted e.g. to find the value of the co-efficient of velocity, CV, coefficient of discharge ' Cd, to study the characteristics of flow over notches, to, to find head losses through pipes, to verify Bernoulli's theorem etc. Various Parts of hydraulic Bench SUMP TANK It stores water for Hydraulic bench. It is located in the bottom portion of Hydraulic bench. Water from here is transported to other parts by using a pump. It has a capacity of 160 liters
  • 4. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal VOLUMETRIC TANK It stores water coming from channel. This tank is stepped to accommodate low or high flow rates. It has a capacity of 46 liters DUMP VALVE It is used for emptying volumetric tank. It is located in the bottom of the volumetric tank. CHANNEL It is used in number of experiments it provides passage for water for different experiments. A valve is also attached to the channel to measure the depth of water in channel. SIDE CHANNELS They are the upper sides of the channel. They are used to attach accessories on test CENTRIFUGAL PUMP It draws water from sump tank and supplies it for performing experiments Vertical pipe it supplies water to the upper part of hydraulic bench from sump tank through a pump CONTROL VALVE It is used to regulate the flow in the pipe i.e. to increase or decrease the inflow of water in the hydraulic bench STILLING BAFFLE It decreases the turbulence of water coming from channel. It is located in the volumetric tank. OVER FLOW It is an opening in the upper portion of the volumetric tank. It sends the water level above 46 liters to the sump tank STARTER It on / off the hydraulic bench.
  • 5. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal SCALE & TAPPING A sight tube and scale is connected to a tapping in the base of the volumetric tank and gives an instantaneous indication of water level. ACTUATOR : Dump valve is operated by a remote actuator, lifting actuator opens the dump valve, when it is given a turn of 90' it will turn the dump valve in the open position
  • 6. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Experiment # 2 and 3 TO DETERMINE THE DISCHARGE AND COEFFICIENT OF DISCHARGE OVER RECTANGULAR AND TRIANGULAR NOTCH. Objectives of the Experiment: 1. To demonstrate the flow over different weir types. 2. To calculate the coefficient of discharge for different notch types. Theory For the rectangular Notch: And for triangular Notch Where Cd = Coefficient of discharge B or L = width of the rectangular weir (3 cm) H = head above the Notch apex θ = angle of the triangular weir g = acceleration of gravity Apparatus • Hydraulic bench • Stop watch
  • 7. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal • Hook and point gauge • Notch plates Experimental Setup Procedures and Readings 1. Make sure that the Hydraulic Bench is levelled. 2. Consider the zeros in point gauge. Take enough care not Damage the weir plate and the point gauge 3. Put the point gauge half way between the stilling baffle plate and the Notch plate. 4. Allow water to flow into the experimental setup and adjust the Minimum flow rate by means of the control valve to have atmospheric Pressure all around water flowing over the Notch. Increase the flow rate incrementally such that the head above the weir crest increases around 1 cm for each flow rate increment. 5. For each flow rate, wait until steady condition is attained then measure and record the head (H) above the weir 5. For each flow rate, measure and record the initial and final volumes in the Collecting tank and the time required to collect that volume. For each Flow Rate, take 3 different readings of the volumes and time and record the average
  • 8. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal For the rectangular Notch: Where b=width of notch 𝑸 = 𝒌 × 𝑯 𝟑/𝟐 Equating both equations and taking log on both sides This log equation is the equation of a line where logk is y intercept and slope n=3/2 Finally equation for Cd V(dm^3) time(sec) Q(dm^3/sec) H1 H2 H(dm) logQ LogH 10 8.37 1.19474313 85 156 0.71 0.077275 - 0.14874 10 10.21 0.979431929 85 146 0.61 -0.00903 - 0.21467 5 11.31 0.442086649 85 122 0.37 -0.35449 -0.4318 After plotting we get the coefficient of x=1.525 which should be 1.5,
  • 9. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal For triangular notch: Equating both equations and taking long on both sides Finally equation becomes
  • 10. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal time(s) Q(dm^3/ s) H1 H2 H(dm) LogQ LogH 29.2 0.3425 125 158 0.33 -0.4654 -0.4815 36.98 0.2704 125 154 0.29 -0.5680 -0.5376 30.33 0.1649 125 150 0.25 -0.7829 -0.6021 Logk=0.8026
  • 11. Fluid Mechanics Lab report Experiment # 04: Investigation of different types of flows using Osborne Reynolds’s apparatus (by visual observation). OBJECTIVE: The objective of this experiment is to determine different types of flows under different conditions visually. Types of flows: There are three types of flows. S No. Types of flow Reynolds’s number Remarks 1 Laminar flow R<2000 When stream line follows parallel path. The dye remains easily identifiable as solid core. 2 Transition flow 2000<R>4000 When stream line interact and partial mixing of flow occur. Dye form eddies which flow through water. 3 Turbulent flow R>4000 When stream line interact and complete mixing of flow occur. Dye stream completely disappear in flow of water. APPRATUS: 1. Hydraulic bench 2. Osborne Reynolds’s apparatus 3. Dye 4. Thermometer COMPONENTS OF OSBORNE REYNOLD’S APPRATUS. 1. Dye reservoir. 5. Bell mouth inlet 2. Control valve. 6. Marbles. 3. Over flow pipe. 7. Water supply pipe. 4. Head tank. 8. Flow visualization pipe. 9. Velocity control valve. Figure 1 Reynolds’sOsborne Apparatus
  • 12. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal PROCEDURE: • Fill the reservoir with dye. • Fix the apparatus on the bench and connect the inlet water supply pipe with the bench feet. • Lower the dye injector until it’s just above the bell mouth inlet. • Open the bench inlet valve and slowly fill the head tank up to the overflow level. And then close it. • Open the velocity control valve to enter water to the flow visualization pipe. • Open the control valve slightly and adjust the dye control valve until slow flow with thin dye line is obtained (laminar flow). • Increase the flow rate till the dye takes a wave form (transition flow). • Further increase of flow rate will completely disappear the dye and form eddies (turbulent flow). Control Dye Reservoir Head Over flow Needle Marble pieces Flow visualization pipe Velocity control valve Water supply pipe Osborne Reynolds' Apparatus
  • 13. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Different Flows OBSERVATION AND CALCULATIONS S.NO OBSERVATION TYPE OF FLOW 1 DYE CANNOT MIX WITH WATER AND MOVE PARRALLEL LAMINAR 2 DYE PARTIALLY MIX WITH WATER TRANSITION 3 DYE COMPLETELY DISAPPEAR IN WATER TURBULANT
  • 14. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Experiment # 05 Investigation of different types of flows using Osborne Reynolds’s apparatus (by Reynolds’s number formula) OBJECTIVE: The objective of this experiment is to determine different types of flows under different conditions by Reynolds’s number formula. Where: R=Reynolds number V=velocity of fluid ϑ =Kinematic viscosity at observed temperature of water. APPRATUS: 1. Hydraulic bench 2. Osborne Reynolds’s apparatus 3. Dye 4. Thermometer PROCEDURE: • Fill the reservoir with dye. • Fix the apparatus on the bench and connect the inlet water supply pipe with the bench feet. • Lower the dye injector until it’s just above the bell mouth inlet. • Open the bench inlet valve and slowly fill the head tank up to the overflow level. And then close it. • Open the velocity control valve to enter water to the flow visualization pipe. • Open the control valve slightly and adjust the dye control valve until slow flow with thin dye line is obtained (laminar flow). • Note down the volume and time using graduated cylinder and stop watch. • Increase the flow rate till the dye takes a wave form (transition flow).and record volume and time. • Further increase of flow rate will completely disappear the dye and form eddies (turbulent flow).again calculate volume and time for this flow.
  • 15. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal OBSERVATION AND CALCULATION VOLUME (M3) TIME (S) TEMP (C) Q(m3 /s) Velocity =Q/A (m/s) ϑ R Type of flow 2x10-4 110.54 20° C 1.809x10-6 0.023 1.003x10-6 229.3 laminar 3x10-4 70.6 20° C 4.249 x10-6 0.054 1.003x10-6 538.4 laminar 8x10-4 31.7 20° C 2.525 x10-5 0.322 1.003x10-6 3210 transition 4x10-4 77.57 20° C 5.157 x10-5 0.657 1.003x10-6 6550 turbulent
  • 16. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Experiment No 06: To determine the theoretical and actual center of pressure on partially submerged body. Objective: The objective of this experiment is to determine the hydrostatic thrust acting on a plane surface immersed in water. Theory: Thrust force is given by. Theoretical center is given by. Actual center is given by. Where: W=weight P=moment arm (p=27.5cm) 𝐹 𝑟=resultant force R=depth of water Q=depth of water from pivot point (q=20-r) B=width of plane area (B=7.5cm)
  • 17. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Apparatus: 1. Hydraulic pressure apparatus 2. Weights 3. Water Hydraulic pressure device. Different Parts of Apparatus Q R P W
  • 18. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Procedure: 1. Position the empty hydrostatic apparatus on a plane table or hydrostatic bench and adjust the leveling screw until the circular spirit level shows that the base in horizontal and balance. 2. Then concede share edge of beam and y-line.by moving the counter balance weight. 3. Ensure that the drain valve is closed and the plastic pipe is connected to the drain valve. 4. Add 50g weight to the weight hanger. 5. Add water until the hydrostatic thrust on the end face of quadrant causes the balance arm to rise. 6. Continue adding water until balance arm is horizontal, measuring this by aligning the base of balance arm with the central marking on the balance rest. 7. If the tank is over filled then the equilibrium can be obtained by slightly opening the drained valve and allow some water to flow. 8. Read the depth of the immersion from the scale on the face of the quadrant. 9. Repeat the same procedure and increase the load by 50g each time. And take four readings. Observation and calculation S No Weight (g) Weight (n) Depth of water R(m) Q(m) Q=0.2- r 𝐹 𝑟(n) 𝐻 𝑝 Actual 𝐻 𝑝 Theoretical (m) (m) (cm) (m) (cm) 1 50 0.49 0.046 0.154 0.778 0.173 17.3 0.184 18.4 2 100 0.98 0.066 0.134 1.602 0.168 16.8 0.178 17.8 3 150 1.47 0.083 0.117 2.534 0.159 15.9 0.172 17.2 4 200 1.96 0.097 0.103 3.461 0.156 15.6 0.168 16.8
  • 19. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Experiment # 7 To determine hydraulic co-efficient (𝐶 𝑑 , 𝐶 𝑣, 𝐶𝑐) and to study jet profile of a small circular orifice provided at side of tank Theory • An orifice is an opening in a vessel through which water flows out, in case of orifice the upstream level of water is above the top edge of opening • Co-efficient of contraction is the ratio of area of jet at vena contracta to the area of orifice Mathematically • Co-efficient of velocity is the ratio of actual velocity to the theoretical velocity of jet from orifice Mathematically Where ℎ 𝑜 is depth of water over orifice (from center) and ℎ𝑐 is velocity head of jet at vena contracta. In this experiment we will find 𝐶 𝑣 with the help of jet profile i.e. • Co-efficient of discharge is the ratio of actual discharge to theoretical discharge Mathematically • Vena contracta is the portion of jet with least diameter • Diameter of orifice used in experiment is 6mm • A jet is a stream of fluid that is projected into a surrounding medium, usually from some kind of a nozzle or orifice. Jets can travel long distances without dissipating, Jet profile refers to the trajectory followed by jet during the experiment. 𝐶𝑣 = √ 𝑥2 4 𝑦ℎ 𝑜
  • 20. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Apparatus Used in experiment Fig 1- Labeled diagram of orifice and Jet apparatus Fig 2- Actual apparatus (It is fitted over hydraulic bench and then the experiment is Performed)
  • 21. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Procedure • Adjust the orifice and jet apparatus over hydraulic bench, through control valve start flow and wait till there is reasonable amount of water in head tank • Adjust the overflow accordingly and note the reading of overflow as ℎ 𝑜 • Water will comes out of orifice, Screw up the needles according to the path of the flow of water • Mark the points of top of needle accurately by pencil on A3 size paper sheet. • For specific volume of water that is been driven to volumetric tank find the time with help of stopwatch • Remove the paper and find x and y distances with respect to a reference line/first point • Plot y on x-axis and 𝑥2 on y-axis in Excel and calculate slope for 𝐶 𝑣 From the data collected find the other co-efficient Fig 3- Experimental setup over hydraulic bench and marking of points on A3 size paper
  • 22. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Observations and calculations x (cm) y (cm) 𝑥2 (cm) 0 0 0 5 0.6 25 10 1.6 100 15 2.9 225 20 5 400 25 7.4 625 30 10.2 900 35 13 1225 We get 93.916cm and we have, ℎ0=31cm After plotting y and 𝑥2 Values y = 93.916x - 40.297 -200 0 200 400 600 800 1000 1200 1400 0 2 4 6 8 10 12 14 Y values X^2/y plot 𝐶𝑣 = √ 𝑥2 4 𝑦ℎ 𝑜 𝐶𝑣=√ 99.916 4(31) 𝐶𝑣= 0.87
  • 23. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal For 𝐶 𝑑 From Experiment Diameter d of orifice=0.6cm, Area of orifice=0.283𝑐𝑚2 Take g=980cm/𝑠𝑒𝑐2 Volume=3litre=3000𝑐𝑚3 ℎ0=31cm Time=82.37sec Now to calculate 𝐶 𝑐 we know that 𝐶𝑑= 3000 82.37⁄ 0.283√2(980)(31) 𝐶𝑑 =0.52
  • 24. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Experiment # 8 To determine the hydraulic coefficients (𝐶 𝑑 , 𝐶 𝑣, 𝐶𝑐) for a circular orifice at the bottom of tank Theory • An Orifice is an opening in the side or base of tank or reservoir through which fluid is discharge in the form of a jet. The discharge will depend up on the head of the fluid (H) above the level of the orifice. The term small orifice means that the diameter of the orifice is small compared with the head producing flow • The equations for hydraulic coefficients are • • • Apparatus used in experiment Fig 1- orifice at bottom of tank The apparatus used in this experiment are hydraulic bench, tank having circular orifice at the bottom and Pitot tube which is installed near bottom orifice to measure the velocity head of jet and diameter at vena contracta.
  • 25. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal 𝐶𝑣=0.98, 𝐶𝑐=0.73, 𝐶𝑑=0.65𝑐 , Procedure • Adjust the orifice and jet apparatus over hydraulic bench, through control valve start flow and wait till there is reasonable amount of water in head tank • When the water in the tank becomes constant note down depth of water in tank ℎ 𝑜 and also note down the velocity head of jet ℎ𝑐 which is on the scale, the pitot tube that is installed actually gives us the velocity head • To find the diameter of vena contracta 𝐷 𝑐 note the number of revolutions of pitot tube from one end of jet to another end of jet such that 1rev=1mm • Take the diameter of orifice as 14mm • For specific volume of water that is been driven to volumetric tank find the time with help of stopwatch Observations and calculations S.no 𝐷 𝑜(mm) 𝐷 𝑐(mm) ℎ 𝑜(mm) ℎ𝑐(mm) vol(lit) time(sec) 𝐶 𝑣 𝐶 𝑐 𝐶 𝑑 1 14 12 323 318 15 58.64 0.98 0.73 0.66 2 14 12 251 249 10 43.07 0.99 0.73 0.67 3 14 12 258 255 10 45.21 0.97 0.73 0.63 Average values Calculations for 𝐶 𝑣 • When ℎ𝑐=318 and ℎ 𝑜=323 • When ℎ𝑐=249 and ℎ 𝑜=251 • When ℎ𝑐=255 and ℎ 𝑜=258
  • 26. Fluid Mechanics Lab report CED, UET-P Muhammad Bilal Calculations for 𝐶 𝑐 𝐴𝑐=113.097𝑚𝑚2 𝐴 𝑜=153.93𝑚𝑚2 𝐶 𝑐=0.73 Calculations for 𝐶 𝑑 • 𝐴 𝑜 is constant, ℎ 𝑜=323mm, volume=15lit=15x108 𝑚𝑚3 and t=58,64 𝐶 𝑑=0.66 • 𝐴 𝑜 is constant, ℎ 𝑜=251mm, volume=10lit=1x107 𝑚𝑚3 and t=43.07 𝐶 𝑑=0.67 𝐴 𝑜 is constant, ℎ 𝑜=258mm, volume=10lit=1x107 𝑚𝑚3 and t=45.21 𝐶 𝑑=0.63
  • 27. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Experiment # 9 To investigate the velocity of Bernoulli’s theorem as applied to the flow of water by Bernoulli’s theorem demonstration Theory • The statement of the Bernoulli’s theorem is stated as the total head of a liquid flowing between two points remains constant provided that there is no loss due to friction and no gain due to an application of outside work between these two points • Mathematically H = • Where 𝑃 ϒ is called static or pressure head, 𝑉2 2𝑔 we call it velocity head and is datum or elevation head which is considered zero in horizontal pipe. • To find pressure head at various points manometer is fixed at each of these points and for total head we use hypodermic probe which is installed in the apparatus. • For theoretical velocity head this equation will be used • For theoretical pressure head use Apparatus used in experiment
  • 28. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Inside the test section of the apparatus we have a venture meter which has a converging and diverging section Procedure • The apparatus is located on the flat top of the hydraulic bench and the instrument is properly levelled with the help of spirit level. • The water is allowed to fill in the manometer tubes until all trapped air is removed • All manometer tubes are checked properly connected to the corresponding pressure taps are air-bubble free • The discharged valve is adjusted to a high measureable flow rate. • After the level is stabilized, the water flow rate is measured using volumetric method. • The pressure head for each point(total six) is observed by the reading shown in monometer tube similarly the total head at each point is observed with the help of hypodermic probe Observations and calculations tapping point actual static head(mm) actual velocity head(mm) actual total head H(mm) theoretical statichead (mm) theoretical velocity head (mm) theoretical total head H (mm) head loss between two points (mm) total head loss up to point(mm) A 232 3 235 232 2.04 234.04 ~ ~ B 213 21 234 212.65 21.04 233.69 1 1 C 178 55 233 192.85 41.23 234.08 1 2 D 173 57 230 173.11 60.98 234.09 3 5 E 135 94 229 154.18 80 234.18 1 6 F 152 30 182 232 2.04 234.04 47 53
  • 29. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Tapping position and diameter of test section A B C D E F 25mm 13.9mm 11.8mm 10.7mm 10mm 25mm It is important to note that for the theoretical static and velocity head the equations that were discussed in the theory section were used. Plotting We will be plotting here the hydraulic and energy grade line. The length of the test section is approximately 130.68cm=1306.8mm, starting from point A which has zero length A B C D E F 0mm 400mm 600.8mm 800.8mm 900.8mm 1308.8mm Hydraulic grade line for this experimental data 120 140 160 180 200 220 240 0 200 400 600 800 1000 1200 1400 lenght of test section (mm) Hydraulic grade line
  • 30. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Energy grade line for this experimental data RECOMMENDATIONS • Make sure there is no air bubbles trapped before and during running the experiment. • The eye level must be perpendicular to the reading when recording the data to avoid parallax error • The control valve should be maintained at a constant flow so that each at every readings of each manometer has the same value of pressure • The experiment should be repeated for a few times so that an average value could be obtained 233.6 233.7 233.8 233.9 234 234.1 234.2 234.3 0 200 400 600 800 1000 1200 1400 lenght of test section(mm) Energy grade line
  • 31. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Experiment # 10 To determine the relationship between head loss due to friction and velocity for flow of water through smooth bore pipe Objectives • To study and develop laminar flow • To study and develop turbulent flow • To study head losses in pipes at different velocities Theory • A flow where we can say head losses are proportional to velocity is termed as laminar flow while for turbulent flow the head losses are proportional to some power of velocity For laminar H α V and for turbulent H α 𝑉 𝑛 where n can be any number • It should be noted that for turbulent flow the head losses becomes more sensitive to velocity • The circled section is transition stage where there is no proper relationship between H and V • Here we will be using Darcy weisbach equation to calculate theoretical head loss • where f is Darcy friction factor which can be observed from Moody chart • Also Reynolds number can be calculated from R= 𝑉𝐷 ϒ where ϒ is kinematic viscosity ϒ • L is the length of the pipe between tapings, D is the internal diameter of the pipe, v is the mean velocity of water through the pipe in m/s, g is the acceleration due to gravity in m/s2 and f is the pipe friction coefficient.
  • 32. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Apparatus Used in Experiment Fig 1- Hydraulic bench and fluid friction apparatus Labeled Diagram of apparatus
  • 33. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Parts • Water is fed in from the hydraulics bench via the barbed connector (1) • An in-line strainer (2) • A sudden contraction (3) • A 45° "Y" (4) • A 45° elbow (5) • A long radius 90° bend (6) • An artificially roughened pipe (7) • Smooth bore pipes of 4 different diameters (8), (9), (10) and (11) • A 90° "T" (13) • A 90° miter (14) • A short radius 90° bend (15) • A sudden enlargement (16) • A pipe section made of clear acrylic with a Pitot static tube (17) • A Venturi meter made of clear acrylic (18) • An orifice meter made of clear acrylic (19) • Ball valve (20), (21) • A 90° elbow (22) • exit tube (23) • Short samples of each size test pipe (24) are provided loose so that you can measure the exact diameter • isolating valves (25) Procedure • Water is pumped through the Fluid Friction Apparatus using a centrifugal pump mounted on the inside of the hydraulics bench. • Water flows through the connector in the channel on the bench top, through the flexible connecting hose shown in the diagram. It will then flow through whichever of the test pipes is selected • Flow rates through the apparatus may be adjusted by operation of the Control Valve on the hydraulics bench. • The flow path through the pipe friction network is controlled using the system of isolating valves shown in the diagram above. By opening and closing these valves as appropriate, it is possible to select flow through any combination of pipes. • When test conditions have stabilized, the dump valve is lowered, retaining the water in the tank. Timings are taken as the water level rises in the tank and volume is recorded • The head loss due to pipe friction is measured by taking pressure readings at different tapping points on the pipe network. In order to measure the pressure loss along a pipe, the pressure measurement device is connected • It is important to expel any air which may be trapped in the pipes of the pressure meter before taking readings..
  • 34. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal Observations and calculations 1liter=106 𝑚𝑚3 , all units are in mm, ϒ kinematic viscosity is 0.8721 𝑚𝑚2/sec S.no 1 2 3 1 2 3 1 2 3 diameter(mm) 6 6 6 10 10 10 17 17 17 Volume (mm^3) 106 106 106 107 107 107 107 107 2× 107 time(sec) 74.56 sec 35.02 sec 24.87 sec 79.54 sec 60.07 sec 44.03 sec 33.25 sec 17.11 sec 25.70 sec Discharge (mm^3/sec) 1341 2 3123 0.4 4020 9 125250. 5 1664 72.4 2271 17.8 3007 51.9 5844 53.5 7782 10.1 Velocity (mm/sec) 474.3 5 1104. 56 1422. 11 1594.75 2119. 61 2891. 78 1325. 01 2574. 91 3428. 54 Reynolds No 3263. 502 7599. 312 9784. 039 18286.3 2038 2430 4.67 3315 8.81 2582 8.65 5019 3.18 6683 3.14 friction factor f 0.042 0.034 0.031 0.024 0.023 0.023 0.027 0.021 0.019 Measured head loss(mm H20) 1201. 5 2268 3888 1512 2146. 5 3739. 5 1161 2416. 5 2713. 5 Calculated Head loss (mm H20) 80.27 352.3 7 546.3 1 321.46 538.1 2 980.3 0 142.1 2 417.4 41 697.8 0 Velocity vs head loss relationships for different pipes For 6mm pipe y = 2.6734x - 221.79 1000 1400 1800 2200 2600 3000 3400 3800 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Velocity(mm/sec) Velocity vs head loss (for 6mm pipe)
  • 35. Fluid Mechanics Lab Report CED, UET-P Muhammad Bilal From the table if we look at Reynolds number Row for 6mm pipe it ranges from 3000-9000 which clarifies the shape of the plot. It shows turbulent flow H α 𝑉 𝑛 where n=2.6734 The flow is turbulent (from Reynolds number as well as shape of graph) value of n=1.7423 Comment: The flow is turbulent (from Reynolds number as well as shape of graph) value of n=0.7577 Here if we increase V head losses will decrease. For 10mm pipe Comment: y = 1.7432x - 1372.7 1400 1900 2400 2900 3400 3900 1500 1700 1900 2100 2300 2500 2700 2900 Velocity(mm/sec) Velocity vs head loss (for 10mm pipe) For 17mm pipe y = 0.7577x + 246.09 1000 1300 1600 1900 2200 2500 2800 3100 1200 1600 2000 2400 2800 3200 3600 Velocity(mm/sec) Velocity vs head loss (for 17mm pipe)