Fluid Mechanics For 3rd Semester(B. E. Mechanical)
LIST OF EXPERIMENTS:
1. CALLIBRATION OF WATER METER
2. PIPE FRICTION
3. CALIBRATION OF VENTURIMETER
4. CALIBRATION OF V-NOTCH
5. FRICTION LOSSES IN PIPE
6. ORIFICEMETER
PIPE FRICTION
Object: To determine Darcy friction coefficient and to investigate the relationship
between (1) The hydraulic gradient h/f and velocity v, (2) The Darcy friction coefficient
‘f ‘and Reynolds number Re for laminar, transition and turbulent flow in a smooth pipe.
Apparatus:
1. A small diameter pipe line.
2. U-tube manometer to measure the pressure difference across the tapping, one at other
end of the pipeline.
3. A constant steady supply of water with a means of varying the flow rate
4. Measuring tank and stop watch to measure the flow rate.
Theory: A closed conduit of any cross section used for flow of liquid is known as a pipe.
In hydraulics, generally, pipes are assumed to be running full and of circular cross
section. Liquids flowing through pipes are encountered with resistance in loss of head or
energy of liquids. This resistance is of two types; depending upon the velocity of flow.
(1) Viscous resistance and (2) Frictional resistance.
The viscous resistance is due to the molecular attraction between the molecules of
the fluid. At low velocities, the fluid appeared to move in layers or lamina, and hence
the nature of this flow is termed laminar flow or streamline. If the velocity of the liquid
is steadily increased, at certain velocity termed the lower critical velocity, the parallel
bands of liquid will become wavy. On further increase in the velocity these instabilities
will increase in intensity until a velocity corresponding to the upper critical velocity is
attained. The region of flow founded by the lower and upper critical velocities is termed
the transition zone. For all further increase in velocity of flow, the streamline remains in
a diffused state and the nature of this type of flow is termed turbulent. IN this case the
flow is restricted by the friction between the liquid and the pipe surface which is known
frictional resistance. Reynold found that if Reynolds’s number Re is less than 2000, the
flow in the pipe is laminar and if Re is greater than 4000, the flow is turbulent. If Re is
between 2000 to 4000, the flow is turbulent. If Re is between 2000 to 4000, the flow is
transition. Let p represents the density of the liquid passing through the pipe, d the
internal diameter of the pipe, and v the average velocity in the pipe and n the dynamic
viscosity of the liquid, then Re = ρvd/μ
4 fl v 2
Darcy’s formula for finding the loss of head in pipeline h 
d 2g
Where h is the loss of head due to friction, l is the length of the pipe and f is friction
factor or coefficient.
For Reynolds number below about 2000, f = 16/Re and the length of the pipe and
f is friction coefficient is independent of the pipe surface. Therefore for laminar flow,
pipes of different surface roughness have the same friction coefficient for the same
Reynolds number. For Reynolds number above about 4000 for smooth pipe, the friction
1
coefficient can be determined by the equation
 2 log10 Re 4 f  0.8
4f


Experimental procedure: Measure the length I between the tapping and the diameter d
of the pipeline. Connect the pressure tapping to the U-tube manometer and expel any air
trapped in the system. Adjust the flow control valve to give the maximum possible flow
through the pipe. Record the difference in mercury level D within the manometer limbs.
Collect the water discharging from the pipe in a measuring tank of known dimensions
and measure the rise of water level R in the measuring tank for certain period of time t
sec. Reduce the discharge in steps by adjusting the flow and valve and record the series
of readings D, t and R at each stage. Repeat the above procedure for pipes of different
diameters.
Observations and Tabulation: Measuring tank dimension: Length L (m) =
Breadth B (m) =
Area A (m2) = BL =
Length of the pipe (m) =
Diameter of the pipe d (m)
d 2
Area of the pipe A (m2) =
4
Diff. In
manometer
(mm of Hg)
Rise of water
level R (m)
Discharge Qa = AR/t
Q
Velocity V = a
a
Time taken t
(sec)
m3/sec
2 gdh
4lv 2
Hydraulic gradient = h/l
vd
Reynolds number Re =
Friction coefficient f =

Graphs: Log l vs log v and log f v/s log Re
Loss of head H
= 12.6d
Discharge in
m3/sec
CALIBRATION OF VENTURIMETER
Aim: To determine the coefficient of discharge for a given Venturi meter.
Apparatus: Venturi meter with pressure tapping at the entrance (mouth) and the throat
installed in a horizontal pipeline.
U-tube mercury filled manometer to measure the difference across the tapping.
A constant study supply of water with a means of varying the flow rate.
Measuring tank and stop watch to measure the flow rate.
Theory: Venturimeter is an instrument for measuring the quantity of liquid flowing
through a pipe. The meter, in its form consists of a short converging section leading
through a throat and followed by a diverting section. The entrance and the exit diameter
will be the same as that of the pipe line to which it is fitted. The function of the
converging portion is to increase the velocity of the liquid and lower its pressure. A
pressure difference between inlet and throat is thus developed and this pressure is
correlated with the flow rate and U-tube manometer is connected to the tapping that are
provided at the entrance and at serves to change the area of stream back to entrance area
and to convert the velocity pressure back into static pressure.
Theoretical discharge = Qt  a 2 M 2 gH
Where M = velocity of approach factor or coefficient of
1
Venturi meter =
2
 a2 
1   
 a1 
a1 =
Area of mouth
a2 =
g =
Sm
=
Sw
=
D
=
Area of throat
acceleration due to gravity
specific gravity of mercury = 13.6
specific gravity of water = 1.0
difference of pressure Head in mercury column
H
difference of pressure head in water column =
=
S m  S w 
Sw
*D
The above equation is based on the assumption of perfect transformation of static
pressure into velocity pressure. Because of friction and turbulence, this is never true.
The actual velocities and volume rates of flow are less than those predicted by this
equation. The ratio of actual to theoretical volume rates of flow is termed the coefficient
of discharge Cd
Therefore, actual discharge Qa  C d * Qt  C d * a 2 * M * 2 gH
The above equation can be written as Qa  K H
, where K = C d a 2 2 g
The coefficient of discharge Cd lies between 0.96 to 0.98. The C d will not be a truly a
constant for all velocities, but the variation is slight. The venturimeter is not accurate for
low velocities on account of the variation of Cd.
Experimental Procedure:
Measure the diameter of the venturimeter at the mouth d1 and at the throat d2.
Connect the pressure tapping to the U-tube manometer and expel any air trapped in the
system. Adjust the flow control valve to give the maximum possible flow through the
venturimeter. Record the difference in mercury level within the manometer limbs.
Collect the water discharging from the venturimeter in a measuring tank of known
dimensions and measure the rise of water level in the measuring tank for certain period
of time ‘t’ seconds. Reduce the discharge in steps by adjusting the flow control valve
and record the series of reading D: t & R at each stage.
Where D is difference in the mercury level,
R is the rise in water level in the measuring tank
T is the time taken to measure the rise in water level
Observations:
Measuring tank dimensions: L length (m) =
Mouth dia d1 (m)
Throat dia d2 (m)
Breadth B (m)
Area A (m2) = BL =
d12
2
Area at the mouth a1 (m ) =
4
d 2
Area at the throat a2 (m2) = 2
4
Velocity of approach factor M =
1
a
1   2
 a1



2
Trial No.
Diff. in
mercury level
in manometer
D (m. of Hg)
Rise of water
level in M.T.R
(m)
Time taken t
(sec)
Discharge Qa =
AR/t (m3/sec)
Coefficient of
discharge Cd
Q
=
a 2 M 2 gh
Log Qa
Log H
Graphs: Draw the following graphs:
Head in water
column H=12.6
D (m)
H v/s Qa and logQa v/s log H
Analysis: By plotting the graph from experimental results Qa as base and as ordinate, a
straight line is obtained from which the slope can be found
Cd =
1
a2 M 2 g
*
Qa
H

1
a2 M 2 g
*
1
slopeoftheline
Calibration: Actual discharge = Qa = C d a 2 M 2 gH
Where the constant K = C d a 2 M 2 g and n=1/2
Taking logarithms on both sides of the equation, log Qa = log K + n log H.
Which is an equation of a straight line. By plotting the graph from experimental results
log H as base and log Qa as ordinate, a straight line is obtained from which K and n can
be determined. The value of log K is the intercept on the ordinate and n is the gradient
of the straight line.
Form the graph:
Log k
K
Gradient n =
Qa = K Hn
Precaution: 1. Venturi meter should horizontal.
2. The air bubbles in the manometer tubes should be removed.
CALIBRATION OF V-NOTCH
Aim: To calibrate the given V-notch by establishing the relationship between the flow
rate and the head over V-notch.
Apparatus: Triangular notch, hook gauge, stop watch etc.
Theory: A notch may be defined as a sharp edged obstruction over which flow of a
liquid occurs. The sheet of water discharged by a notch is called vein. Notches are used
for measuring the flow of water from a reservoir and are generally rectangular,
trapezoidal or triangular in shape. The most common shape is triangular, since it has the
advantage of greater accuracy at reduced flow rates compared with other shapes. The coefficient of contraction will be constant for all heads. A triangular notch is called Vnotch.
Theoretical discharge through the V-notch
8

Qth 
2 g . tan
H 5/ 2
15
2
Actual discharge through the V-notch
8

Q Act  C d 2 g tan
H 5/ 2
15
2
Where H is the height of water surface above the apex of the notch is the half the
notch angle and Cd is the co-efficient of discharge. The value of Cd with different heads
will be more nearly constant. The value of Cd varies from 0.59 to 0.62 depending upon
the dimensions of the notch. The above equation can be written as
Qact = KH5/2 where the constant K 
8

C d 2 g tan
15
2
Procedure:
1. Fix the notch under test at the end of approach channel in a vertical plane with the
sharp-edge on the upstream side.
2. Fill the channel with water up to the crust level and note the initial reading ‘h’ on the
height gauge.
3. Adjust the flow control valve to give the maximum possible discharge without
flooding the notch. Note the final height gauge readings given the head over the
notch i.e. H.
4. Collect the water discharging from the notch in a measuring tank of known
dimensions and measure the rise of water level ‘h’ in the measuring tank for certain
period of time.
5. Conditions are allowed to steady state before the head and rise of water level are
recorded.
6. Lower and water level in the approach channel in stages by adjusting the flow control
valve and record the series of the readings h2 and ‘h’ at each stage.
Observation:
Area of measuring tank =
Tabular column:
Sl. No.
1.
Initial
Cd 
V-notch readings
Final
Difference
H (m)
Collecting tank readings
Initial
Final
Difference
hv (m)
Qact
5
8
2 g tan  H 2
15
2
2. Qact = Areaof tank X Ht. of water filled
60
3
Qth 
8

2 g . tan
15
2
H 5/ 2
FRICTION LOSSES IN PIPE
Aim: To find the friction factor ‘f’ for the given pipes
Equipments: A set of pipes with closing and opening mechanism at both ends to let in
water or let out, mounting stands, collecting tank, manometer, piezometer, scale, stop
watch etc.,
Theory: When water or any other fluid flows through closed pipes under pressure, the
fluid flowing in the pipe is subjected to resistance due to shear forces between fluid
particles and boundary walls of pipe and the fluid particles themselves resulting from the
viscosity of the fluid. The resistance to the flow of fluid is in general known as frictional
resistance. Since certain amount of energy is possessed by the fluid flowing in a
direction and a portion at this energy is used to overcome the frictional forces, there will
always be some drop or loss of energy that however depends upon the type of flow.
Procedure:
i)
In initial steps see that the overhead tank overflows so as to maintain uniform
head throughout the coarse of experiment.
ii)
Check for scale or stop watch correction if any in the respective instruments.
iii)
Open the inlet & outlet valve of the respective pipe under consideration at
maximum.
iv)
Read the differential manometer device the difference in height in equal no. of
divisions approximately to take different separate readings.
v)
For every set of reading in manometer see that actual discharge-using tank for
collecting water.
vi)
Proceed for different sets of pipe
Calculations:
hL 
4 fL v 2
d 2g
hL
4f 2
i
.v
L
2 gd
 i  Kv n
log i  log K  n log v
Where ‘f’ is friction factor, i = head lost per meter, h l is head loss, v is velocity of flowing
fluid.
Results: The values obtained from the graph are, n =
k=
f=
The graph between log v & log i is a straight line.
Conclusion: The values obtained from the graph are well within the acceptable limit,
and (log v & log i)
Observations:
Dia of pipe =
Length of pipe (L)
=
Length of collecting tank
=
Width of collecting tank
=
Area of collecting tank (A) =
Area of pipe (A) =
Sl.
No.
Mercury
hL
Manometer
(12.
Reading
6)
L.L R.L Diff of
(cm (cm . (h) wat
er
)
)
d 2
4
Collecting
tank
H
cm
T
Sec
Q
act
cm3
/sec
V= F
Q/A
cms
./se
c
I
HL/l
From graph
F = 2gd x K
4
There is no consistency b/w equation you have used & results obtained.
ORIFICEMETER
Aim: To determine the co-efficient of discharge Cd of an orifice meter.
Apparatus:
(i)
Orifice fitted with a pipe of known diameter.
(ii)
Manometer
(iii)
Collecting tank
From graph
K
n
f
(iv)
Stop watch
Theory: Orifice is a simple device to measure the flow in a pipe by reducing the flow
passage in one section. The pressure difference between 2 sections is created. The
measurement of pr.difference between 2 sections enables us to determine the discharge,
which is taking place in the pipe.
Since the diameter of the passage at the orifice meter is less than that of the pipe,
the flowing stream converges to a minimum cross-section known as vena-contracta. As
the fluid flows through it the velocity of the flow of fluid reaches maximum value & the
pressure becomes minimum. A pressure tap is provided at this section. Another pressure
tap is provided at a distance of 0.9 to 01.1 times the diameter of pipe from orifice plate
where the pressure is maximum (velocity is equal to velocity of flow in the pipe). So
connecting a manometer to these pressure taps we get the pressure differences.
Now if the difference in the level of mercury in the manometer is H cm equivalent
head of water, H=12.6 H cm where density of water = 1. Now from the collecting tank
we can measure the actual discharge using the formula Qact = Ah/T where A is the area
of cross section of the tank and h is rise in water level in time t seconds.
For actual discharge we have the expression as follows:
a a 2 gh
Qth  1 2
a12  a 22
Where a1 
 d12
and a 2 
 d 22
4
4
are the diameters of the pipe and orifice respectively.
Qact =
K hn
(I)
Where n = ½
a1 a 2 2 g
K = Cd
a12  a 22
Now, taking log
Log Qact = log k + n log h
Values of Qact and h are plotted and from the graph one can the value of C d, n & K.
Procedure:
(i)
Diameter of pipe and orifice are noted down.
(ii)
Air in the manometer pipe is removed after allowing war to pass through the pipe.
(iii)
The inlet and outlet valves are brought to required position
(iv)
For a constant discharge the readings of the manometer are taken down.
(v)
Collecting tank readings are taken down.
(vi)
The above procedure is repeated for different values of discharge.
(vii) The graph of Qact V/s H is plotted value of Cd is computed.
Sl
.
N
o.
Manometer reading
Limb
A
(cm)
Lim
bB
(cm)
H=12.
6R
Diff cm
. (h)
cm
Q act
Collecting
cm3/se tank reading
c
Heigh Tim
t (x)
et
cm
(sec)
Qact =
Ax/t
(cm3/
sec)
C Qact From graph
= Qact
C
K
N
Result: The co-efficient of discharge of orifice meter is
Inference:The plot of Qact V/s h is a straight line and the value obtained from the graph
for ‘Cd’ is very close to the expected value. The value differs a title from the expected
value by a little amount because of the errors associated with the instruments or
equipments and the process itself.
Significance: The orifice meter is a flow-measuring device. It is used to measure the
discharge in a flow. An orifice meter is calibrated in the experiment.