EXPERIMENT NO 01
NAME OF THE EXPERIMENT: - Determination of performance characteristics of Pelton wheel
APARATUS: - Pelton wheel turbine, spring balance, weight, manometer.
FIGURE:
FORMULA: 1. Discharge, Q = 1.84 Lh3/2
Where,
L = Length of weir
h = Head of the weir.
2. Shaft power developed (S.P.)
P = (W-S)  D/2 X 2πN
= (W-S) πDN watts

Where,
(W  S )DN
kW
60  1000
W = Load applied on the brake drum (N)
S = Spring balance reading (N)
D = Mean diameter of the brake drum (m), and
N = Speed in r. p. m.
3.
Water power (W.P.) =
Where,
wQH
kW
1000
W = Specific weight of water (= 9810 N/m3)
Q = Discharge in m3 /s (as calculated at 1), and
H = Head (of water) acting on Pelton wheel
4. Overall efficiency,  o` =
S .P.
W .P.
1
THEORY: This is the only impulse type of hydrodynamic turbine now in common use.. It is well suited
for operating under high heads. Figure shows the elements of a typical pelton wheel installation.
The runner consists of a circular disc with a number of buckets evenly spaced round its
periphery. The bucket has a shape of double hemispherical cup. Each bucket is divided into two
symmetrical parts by a sharp edged ridge known as splitter. One or more nozzles are mounted so
that each directs a jet along a tangent to the circle through the centers of buckets called pitch
circle. The jet of water impinges on the splitter which divides the jet into two equal positions,
each of which after flowing round the smooth inner surface of the bucket leaves it at its outer
edge. The buckets are so shaped that angle at the outlet tip varies from 10º to 20 º so that the jet
of water gets deflected through 160 º to 170 º. The advantages of having a double cup shaped
bucket is that axial thrust neutralize each other, being equal and opposite and hence the bearing
supports the wheel shaft are not subjected to any axial or end thrust. Further at the lower tip of
the bucket, a notch is cut which prevents the jet striking the preceding the bucket being
intercepted by the next bucket very soon, and it also avoids the deflection of water toward the
centre of the wheel as the bucket firsts meets the jet. For low heads the buckets are made of cast
iron, but for higher heads they are made of cast steel, bronze or stainless steel. In order to control
the quantity of water striking the runner, the nozzle fitted or needle having a penstock, provided
with a spear or needle having a streamlined head which is fixed to the end of a rod .The spear
may be operated into either by a wheel in case of very small units or automatically by a governor
in case of almost all the bigger units. When shaft of pelton wheel is horizontal then not more than
two jets are used. But if the wheel is mounted on a vertical shaft then larger number of jet is
possible.
2
PROCEDURE: i)
Note down the internal diameter of initial pipe and throat
ii)
Keeps the gate opening at 20 % initially.
iii)
The setup is then started and the initial weight is kept zero kg.
iv)
The corresponding values of spring balance weight, speed in rpm, manometric head and
present gauge reading were noted down.
v)
Increase the weight successively at 1, 2, 3 and 4 kgs and take the corresponding all the
above mentioned reading
vi)
vii)
viii)
Stop the set up and keep opening at 40 %.
Repeat step no. 3, 4, 5
Repeat the same procedure for gate opening at 50 %
OBSERVATIONS:
1. Diameter of pipe =
2. Diameter of throat of venturimeter =
3. Perpendicular distance d =
OBSERVATION TABLE
Pressure
gauge
reading
Speed(rpm)
N
Spring Manometer
reading
balance
reading h1 h2 h3
FOR GATE OPENING 20%
Break
weight
FOR GATE OPENING 30%
FOR GATE OPENING 40%
3
Net eight= (W1W2)
CALCULATION:Torqu
Head
Discharge
e
(H)
(Q)
(T)
Input
(KW)
power
Output
Unit
Efficien
power
speed
cy(ή)
(KW)
(N)
For 20%gate openings
Unit
discharge
(Qu)
Unit
power
(Pu)
H
(m)
For 30%gate openings
For 40% gate openings
RESULT: - The working of pelton wheel turbine has been studied. The average efficiency of the
turbine for different gate openings is found to be
1. For 20 % gate opening =
2. For 30 % gate opening =
3. For 40 % gate opening =
4
EXPERIMENT NO. 02
NAME OF THE EXPERIMENT: Determination of performance characteristics of Francis
Turbine.
APPARATUS: - Francis turbine set up, weights, manometer.
FIGURE:
THEORY: Francis turbine is mixed flow type of reaction turbine. It is named in ward radial flow type of
reaction turbine in 1849. later on it was modified and the modern Francis is a mixed flow type, in
which water enters the runner radically at its outer periphery and leaves axially at its centre. The
water from the penstock enters a scroll casing which completely surround sterner. The purpose of the
casing is to provide an even distribution of water around the circumference of the turbine runner,
maintaining an approximately constant velocity for the water so distributed. From the scroll casing
the water passes through a speed ring on stay ring. From the speed ring, the water passes through a
series of guide vanes or wicket gate provided all around the periphery of the turbine runner. The
function of guide vanes is to regulate the quantity of water supplied to the runner and to direct water
on to the runner to an angle Appropriate to the design The main purpose of the components is to lead
the water to the runner with minimum loss of energy. The runner of francis turbine Consists of series
of curved vanes evenly arranged around the circumference in the annular transmitted to the generator
through the shaft space between two plates. The torque produced by the runner is which is usually
connected to the generator shaft by bolted flanged Connection. The water after passing through
runner flows to the tail race through a draft tube
PROCEDURE:i)
Initially before starting the startup of Francis turbine priming process was completed.
ii)
Keep the gate opening initially at 50%.
iii)
Start the setup and keep the initial weight to zero.
iv)
Note down the corresponding values of spring balance weight, speed in rpm, manometer
head and pressure gauge .
v)
Increase the weight successively as 1,2,3,4 and 5 kgs and take reading of corresponding
values of all the above mentioned readings
vi)
Stop the setup and keep the gate openings at 60%.
vii)
Repeat the same procedure for 60% and 70% gate opening.
5
OBSERVATION TABLE:
Sr.No
PRESURE
GAUGE(p)
KG/CM2
VACCUM
GAUGE
SPEED
(RPM)
BREAK
BALANCE
SPRING
BALANCE
MANOMETER
READING
h1
h 2 h
50% GATE OPENING
60% GATE OPENING
70% GATE OPENING
CALCULATION:H’(m)
V’(M)
T(M)
Q(lpm)
H(m)
Input
power
Output
power
η%
50%GATE OPENING
60%GATE OPENING
70%GATE OPENING
RESULT:
The Working of Francis Turbine Has Been Studied.
The average efficiency of the Turbine at different gate openings is found as follows:
a. For 50%gate openings (η)=
b. For 60% gate openings(η)=
c. For 70%gate openings(η)=
6
NET
WEIGHT
EXPERIMENT NO :03
NAME OF THE EXPERIMENT: Determination of performance characteristics of Centrifugal
Pump
APPARATUS: Centrifugal Pump (Constant Speed), Scale, Stop Watch, etc.
FIGURE:
THEORY:
The hydraulic machines, which convert the mechanical energy into hydraulic energy, are
called pumps. The hydraulic energy is in the form of pressure energy. If the mechanical energy
is converted into pressure energy by means of centrifugal force acting on the fluid, the
hydraulic machine is called as centrifugal Pump. The centrifugal pump act as a reversed of an
inward radial form reaction turbine. This means that the flow in the centrifugal pumps is in the
radial outward direction. The centrifugal pump works on the principle of forced vortex flow
which means that when a certain mass of liquid is rotated by an external tongue, the rise in
pressure head of rotating liquid takes place. The rise of pressure head at any point of rotating
liquid in proportional to square of tangential velocity of the liquid at that point.
Main Parts of Centrifugal Pump.
The following are the main parts of the centrifugal pum
1. Impeller : The rotating part of a centrifugal pump is called impeller. It consists of a series of
backward curved vanes. The impeller is mounted on shaft which is connected to the shaft of
an electric motor.
2. Casing: The casing of centrifugal pump is an air tight passage surrounding the impeller and is
designed in such a way that the kinetic energy of the water discharged at the outlet of the
impeller is converted into pressure energy before the water leaves the casing and enters the
delivery pipe. The following 3 types of casings are a). Volute casing b). Voter casing c).
Casing with guide blades.
3. Suction Pipe with a foot valve and strainer: A pipe whose one end is connected to the inlet of
the pump and other end dips into water in a sump is known as suction pump. A foot valve
which is non-return valve or one way type of valve is fitted at the lower end of suction pipe.
The foot valve is open only in the upward direction. A strainer is also fitted at the lower end
of the suction pipe.
7
4. Delivery Pipe : A pipe whose one end is connected to the outlet of the pump and other end
delivers the water at required height is known as delivery pipe
Head and efficiencies of Centrifugal Pump
1. Suction Head: It is the vertical height of the center line of a centrifugal pump above the
water. This is called the suction head, denoted by “hs
2. Delivery Head : The vertical distance between the center line of the pump and water surface
in the tank to which water is delivered is known a delivery head denoted by hd.
3. Static Head : The sum of suction head and delivery heads is known as static head. This is
represented by Hs and given by Hs = hx + hd
4. Manometer Head : The manometric head is defined as the head against which a centrifugal
pump has to work and is denoted by “Hm”.
Efficiencies of Centrifugal Pump
In case of centrifugal pump, the power is transmitted from the shaft of the electric motor to the
shaft of the pump and then the water. The following are the efficiencies of centrifugal pump
A. Manometer Efficiency (  Man) : The ratio of the manometric head to the head imparted by
impeller to the water in m as manometric efficiency.
Man 
9 Hm
vw  H 2
B. Mechanical Efficiency (  m) : The power of the shaft of the centrifugal pump is more than
the power available to the impeller of the pump. The ratio of power at the centrifugal pump
is known as mechanical efficiency  m = Power at the impeller.
C. Overall Efficiency( 0) : It is defined as the ratio of power output of the pumnp to the power
input to the pump. The power output of the pump
Weight of water lifted x Hm
1000
0 =
S.P.
WHm
[
]
1000
0 =
S.P
0 = mano x m x v
8
PROCEDUR:
1. Open the suction valve in the inlet pipe
2. Prime the pump by pouring water into collecting tank and suction pipe till it get full
3. Close the outlet valve of the delivery pipe
4. Open the delivery valve fully for maximum discharge
5. Note the pressure guage reading on the delivery side and record
6. Record the time in seconds for 10 revolutions of the energy meter
7. Note the vaccum guage reading on the suction side and not
8. Measure the internal dimensions of the collecting tank
OBSERVATION:
Pressure gauge readings
Sr.No
Discharge
Pd
(m3/s)
(kg
Pd
Hd (m)
/cm2)
(kg
Hd (m)
/cm2)
Wattmeter
Manometric
readings
Head Hm
X (watts)
(m)
Output
Input Pi
P0 (H.P.)
(H.P.)
0
CALCULATION: Perform the Following Calculation for each opening of the delivery Valve
1. Vd =
2. Hd =
Q
( / 4)d s
2
; Vs =
Q
( / 4)d s
2
P
Pd
; Hs = s
w
w
3. Hm Form eqn. (1)
4. P0 =
wQHm
H .P
75
5. Pi =
P0
 100
Pi
RESULT: The efficiency of the centrifugal pump is found to be ------------.
9
EXPERIMENT NO 04
NAME OF THE EXPERIMENT: Determination of performance characteristics reciprocating
pump .
APPARATUS: Reciprocating pump setup, collecting tank, suction gauge, delivery
gauge, stopwatch.
FIGURE:
THEORY :
The theoretical discharge can be calculated by formula:
Qth 
Where,
ALN
60
Qth = Theoretical discharge
A = area of cylinder
L=length of piston rod
N=speed of motor
Percentage of slip can be calculated as
% slip = ( Oth - Qact )/ Qth
%η =
Input X100
Output
PROCEDURE:i)
Open fully the gate valve in the delivery pipe
ii)
Keep the field resistance of the rheostats in the minimum resist position (i.e. for minimum
speed) start the motor.
iii)
Adjust core shaft by varying the field rheostat.
iv)
Adjust the gate valve to get the required head.
v)
Note the following
a) Pressure and vacuum gauge reading
b) Voltmeter and ammeter reading
c) Height of pressure gauge (m) above vacuum gauge
vi)
Take some more sets of reading by varying the head
10
OBSERVATIONS:



Dia Of Cylinder =
length of piston rod=
speed of motor =N=
area of collecting tank=
OBSERVATION TABLE:SR.NO
t
Qa
Qth
Cd
T
OBSERVATION TABLE
HS
Hd
Po
ηo
%Slip
Pi
CALCULATIONS:volume
1. Qa=
Time
2. Qth 
ALN
Qth - Qact
= % slip =
60
Qth
RESULT: The following results are obtained
a. coefficient of discharge
=
b. overall efficiency of pump =
c. percentage slip =
11
EXPERIMENT NO.05
NAME OF THE EXPERIMENT: Study of flow around immersed bodies by Hele Shaw Apparatus
APPARATUS:
1. Hele-Shaw apparatus
2. The object around which the flow pattern is to be determined.
3. Dye, tracing paper and water supply.
The Hele-shaw apparatus consists of two closely spaced parallel, transparent flat plates. The
narrow gap is of the order of 1.5 mm. They are connected to small transparent reservoirs at two
opposite ends one being the unlit reservoir and the other out reservoir. At the other two sides the
gap is sealed at the edges by means of clamps to prevent outflow. The level of liquid in both the
inlet and outlet reservoirs is maintained as steady during the experiment. An arrangement for
injection of dye is provided at various equally spaced points on the inlet side. The object around
which the flow pattern is to be determined is placed centrally in the gap between the plates. When
the dye is injected in the flow between the plants, the dye filaments form streamlines depicting the
flow pattern around the object.
FIGURE:
THEORY:
In order to understand flow of complex nature it is often necessary to have a mental picture of
the qualitative pattern of the flow this can be obtained by means of flow visualization techniques.
One such technique, developed by Hele shaw, stimulates the streamline patterns of two
dimensional flow based on the principle of viscous flow between parallel plates. It is well known
that any acting forces. The apparatus developed by Hele Shaw takes advantage of this fact to trace
streamlines in two dimensional flows.
12
PROCEDURE:
1. Insert the object between the plates centrally.
2. Put water in the inlet reservoir and let it flow through the gap between the parallel plates unlit
the inlet and outlet reservoirs attain steady levels.
3. Introduce dye into the flow and wait until a well defined pattern of streamlines is observed
4. Fix a tracing paper over the glass plate, between the inlet and outlet reservoir and trace the
pattern of the streamlines and the geometry of the given object.
RESULT The flow around immersed bodies by Hele Shaw Apparatus is studied
PRECAUTIONS
1. Ensure that the levels of the liquid in the inlet and outlet reservoirs remain steady while plotting
the flow of pattern.
2. Keep the rate of flow between the plates very low
13
EXPERIMENT NO :06
NAME OF THE EXPERIMENT: Determine of the Darcy-Weisbach Friction Factor for a given
pipe.
APPARATUS:
U – tube manometer connected across a pipe line, Stop Watch, Collecting tank
.
FIGURE:
FORMULA: Head loss due to friction in pipe
4flv 2
Flv 2
OR
hf 
2gd
2gd
Where,
F = friction factor = (4f)
l = length of pipe
V = Velocity of flow through pipe.
d = Diameter of pipe.
g = Acceleration due to gravity.
f = Coefficient. of friction
THEORY:
The experimental set up consists of a large number of pipes of different diameters. The pipes
have tapping at certain distance so that a U – Tube manometer is connected in between them. The
flow of water through a pipeline is regulated by operating a control valve which is provided in
main supply line, for measuring the head loss. The length of the pipe is considered as a distance
between the two pressure tapping, to which a U – Tube mercury manometer is fitted. Actual
discharge through pipeline is calculated by collecting the water in collecting tank and by noting
the time for collection.
 Velocity of flow = V 
Q ( A / t)
=
a
a
Where,
A = Area of tank.
H = Depth of water collected in tank.
t = Time required to collect the water up to a height “H” in the tank.
a = Area of pipe.
Q = Discharge through pipe.
Now applying Bernoulli’s equation between two pressures tapping, we have.
14
PA
P
h p .g
 Z  B  ( Z hm )  m m
w
w
w
PROCEDURE :
1. Note down the diameter of pipe (d).
2. Note the density of manometric liquid (m) and that of fluid (water) flowing through a pipe i.e.
(m).
3. Connect the U – tube manometer to the pipe in between two pressure tapings.
4. Start the flow and adjust the control valve in pipe line for required discharge.
5. Measure the pressure difference at two points A & B of a pipe by means of a U – tube
manometer.
6. By collecting the water in collecting tank for a particular period of time.
7. Determine the velocity of flow (V) and frictional head loss (hf) by using appropriate equations.
8. Determine the friction factor (f) in pipe by using Darcy – Weisbach formula.
9. Change the flow rate by adjusting the control valve & repeat the process for at least five times.
10. Find out the mean friction factor (f) mean of the pipe.
11. Plot a graph of velocity of flow (V) on y – axis verses frictional head loss (hf) on x – axis which
shows a straight line.
OBSERVATION:
1)
l = Length of Pipe = cm
2)
d = Dia of Pipe = cm
3)
Size of collecting tank = _______ x _______ cm2
4)
m = Density of mercury = 13600 kg / m3
5)
w = Density of water = 1000 kg / m3
15
OBSERVATION TABLE :
Manometic
Reading
Left Right
Sr.No Lim Lim Diff.
b
b
(hBhA)
HA
HB
Frictional Hedad
Actual
Tank Reading
Loss
Discharge
p 1
hf  hm m
Diff. Time
AH
pm
Initial Final H – Set Qac 
2
t
Height Height
PA  PB
3
H
1
M /Sec
Meter
hf 
Qw .g
1
2
3
4
5
Calculation:
 (d ) 2
1.
a = c/s area of pipe =
2.
A = Area of tank =--------------
4
=
  2
= _____ M2
4
For Reading No. 1
Frictional head loss = hf = hm
Actual Discharge Qac =
-----
M³ / sec
Velocity of flow, V = Qac / a = ------ m / Sec
F 
F
2hf .g .d
lV 2
2hf .g.d hf .gh

4l.V 2
2lv 2
Result: The friction factor “ F ” for the pipe is found to be ________.
16
Velocity
of flow
Qac
a
M/Sec
V 
Frict
on
factor
F
EXPERIMENT NO 7
NAME OF THE EXPERIMENT: Determine of Manning’s& chezy’s constant for an open
channel..
APPARATUS: Standard tilting hydraulic flume.
FIGURE
THEORY:
In 1989, Robert manning’s presented a formula according to which the mean velocity of uniform
flow in a channel is expressed in terms of a coefficient of roughness ‘n’ called manning’s “n”
hydraulic radius and channel bottom slope so .the manning’s formula expressed is in m
TYPE OF CHANNEL
BOUNDARY SURFACE
Very smooth concrete and planed
timber
Smooth concrete
Glazed brickwork
Good wood
Vitrified clay
Brick surface lined with cement
mortar
Cement concrete finish
VALUE OF ‘n’
0.01
0.011
0.012
0.013
0.013
0.014
0.014
0.015
0.015
Unified cement surface
0.017
Earth channel in best condition
Neatly excavated rock
0.017
0.02
Straight unlined earth canals in
good condition
Rubble masonary
Corrugated metal surface
0.02
0.02
0.02
Rivers and earth canals in fair
condition
Earth channel with gravel bottom
Earth channel eith dense weed
Mountain stream with rock beds
and rivers with variable section
and some vegetation
17
0.025
0.025
0.035
0.045
FORMULA :Discharge Q = A Discharge Q= AX V
Q  A  C  R  SO
V  C  R  SO
PROCEDURE:
1) Set the flume at the suitable bed slope(so)
2) Measure width B of the flume.
3) Take manometer readings for the measurement of discharge.
4) Open the inlet valve of the flume and allow water to flow through --------5) Take the manometric readings
6) Measure depth of flow at three different locations (y1,y2,y3)
7) Repeat the steps from 4 to 6 for different discharges.
OBSERVATIONS TABLE:
Manometer
reading
LHS RHS x
H=12.6x
Q= K√H
Y1
Y2
Y3
Yavg
Observations table:
A = Bx y
P=B+2y
R = A/P
C
n
RESULT: for the flow range of ______m3/sec to ________m3/sec through a open channel with
width B= and bed slope SO______, the Chezy’s constant “c “and Manning’s constant “‘n’ are as
follows:
‘c’=______
‘n’=_______
18
EXPERIMENT NO 08
NAME OF THE EXPERIMENT: Developing specific energy diagram for rectangular channel
APPARATUS: Venturiflume
FIGURE
THEORY:
A channel may be defined as a passage through which water flows under atmospheric pressure as
such in channels the flow of water take place with a free surface which is subjected to atmospheric
pressure. The channels without any cover at the top are known as open channels
In case of long channels often it becomes necessary to provide transitions.
A transition is the portion of a channel with varying cross sections, which connects one uniform
channel to other which may or may not have the same cross section form. The variation of channels
section may be caused either by reducing or increasing width
Or by raising or lowering bottom of channel
The critical depth of flow may be obtained at certain section in an open channel where the
channel bottom is raised by the construction of low hump or the channel is constructed by reading its
width. Since at critical state of flow, the relationship
Between depth of flow and discharge is definite and is independent of channel roughness
And other uncontrollable factors, it provides a theoretical basis for the measurement of
Discharge in open channel device which is commonly used for measurement of flow in open
channels is known as venturiflime
Venturiflume as shown in figure is a structure in a channel which has a contracted
section called throat downstream of which follow a flared transition section. Designed to restore the
stream to its original width. At the throat section there will be a drop in the water surface and this
drop may be related to discharge the velocity of flow at the throat is always less than the critical
velocity and hence the discharge passing through it will be a function of the difference between the
depth of flow upstream of the entrance section and at the throat. Since the velocity of flow at the
throat is less than critical velocity hydraulic jump will not be formed.
Where,
Q
KAa 2 g ( H  h)
A2  a 2
Where, A and a are areas & H and h are depth of flow section at entrance and throat of flume.
K=discharge coefficient of flume.
19
For rectangular channels the above eqn becomes
Qk
BH  2 g  h  h
( BH ) 2  (bh) 2
In which B and b are bottom width at entrance and throat respectively
Tilting flume can also be used to determine chezy’s constant and manning’s constant
With the help of flume velocity can be determined by knowing discharge and area
Where area is a function of B and y, R can also be determined as R=A/P and bed slope can also be
easily determined. Hence by performing various trials by varying discharge
The value of c can be determined. Similarly manning’s constant can also be determined by
V
1R 2 / 3 S 1 / 2

here too the value of V,R,S can be known and hence by experiments the value of n can be
determine Development of specific energy curve can also be done by using this experiment. Since
the free surface in case of channel flow represents the hydraulic gradient. Bernoulli’s equation can be
applied between the section 1 and 2 which are L distance apart
V 12  Y1  Z1 V 2 2  Y 2Z 2  ht

2g
2g
hf = energy loss between two sections specific energy is the sum of the depth of flow at any section
and velocity head
Y V 2
Q2
E

2g
2GA2
Since V= Q/A
E =function of depth
Thus for given channel section and discharge eqn May be represented graphically
In which specific energy is plotted along x axis and depth of flow on y axis the curve so obtained is
called specific energy curve
RESULT: The working of tilting flume is studied
20
EXPERIMENT NO. 09
NAME OF THE EXPERIMENT: Study of Gradually varied flow profiles
APPARATUS: Venturiflume
FIGURE
THEORY: Open channel flow is characterized by existence of a free surface is atmospheric and is
constant throughout the flow takes place due to gravity. Channel flow gradually varied flow:- (non
uniform flow) Gravity force produces flow with continuously increasing velocity. The frictional
resistance increases with velocity whereas gravity force is constant when there two exactly balance
each other uniform flow occurs.
CLASSIFICATION OF SURFACE PROFILES:The various water surface profiles occurring in the channel are designated with reference to
the bottom slopes of the channel viz. M curve, S curve etc. They are further classified depending
upon the relative position of actual depth (y) and the critical depth (yc) a shown below.
For mild slope channel:Zone
(i) dy/dx = +ve
Where, y = yn, dy/dx= 0
When y = ∞, dy/dx = So
Zone
(ii) dy/dx = -ve (Yn >y > Yc)
When, y = Yc dy/dx = ∞,
When, y = Yn , dy/dx = 0
Zone
(iii) dy/dx = +ve
When y=Yc, dy/dx = ∞,
Y= 0, dy/dx = 0
For steep slope channel (Yn<Yc)
Zone
(i) dy/dx = +ve
When, y=Yc, dy/dx = ∞,
Y= ∞,, dy/dx = So
21
Zone
(ii) dy/dx = -ve
When, y= Yn, dy/dx = 0
Y=Yc, dy/dx = ∞,
Zone
(iii) dy/dx = +ve
When, y = Yn, dy/dx =∞,
Y =0 dy/dx = 0
Similarly for Critical slope(Yn=Yc)
Zone
(i) y > Yn, dy/dx = +ve
When, y = Yc, dy/dx = So = Sc
Y = ∞, dy/dx= So =Sc
Zone
(ii) y < Yc = Yn, dy/dx = =ve
As y= Yc dy/dx = So= Sc
Y = ∞, dy/dx= So =Sc
(iii) Horizantal slope channel
(iv) Adverse slope profile can also be obtained in similar manner.
DYNAMIC EQUATION FOR GVF
Assumptions:Flow is steady ( Q is constant)
Pressure distribution is hydrostatic.
Loss of head due to friction is as per uniform condition i.e. Mannings and Chezy’s equation can be
used to calculate the slope energy line in GVF as well
Bed slope is small
Channel is prismatic
Velocity distribution does not changes (α = 1)
Roughness coefficient n is constant and it does not depend on the flow depth.
Total head H= z+y+v2/2g
Differentiating with respect to x
dH/dx =dz/dx +dy/dx +d (v2/2g)/dx
-Sf = -So +dy/dx +d/dx(v2/2g)
multiply the velocity term by dy / dy
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dy/dx+ d/dx(v2/2g)dy/dy = So – Sf
dy / dx = (So – Sf) ÷ (1+ d/dy[v2/2g])……………….(1)
equation 1 is dynamic equation of GVF which gives variation of depth y w.r.t.distance along the
bottom of the channel x.
If dy/dx = 0 (uniform Slope)
If dy/dx = +ve (y increases with x , back water curve)
If dy/dx = -ve (y decreases with x, drawdown curve)
Alternative form of equation (i)
V = Q/A
d/dy (v2/2g) = d/dy (q2 / {A2 x 2g)
dy / dx = (So – Sf) ÷ (1- Q2T/gA3)………………………(ii)
Fr2 = Q2 T /gA3
Dy / dx = (So – Sf ) ÷ (1- Fr2 )
Sf / So = (Ko / K)2
Q=√(S)
Dy/dx = So (1- (Kn/K) 2 )÷ ( 1- (Zc/Z) 2 )
The final genral form of GVF equation is as follows:Dy / dx = So (1- (Yn/Y)n ÷ (1 – (Yc / Y ))
CLASSIFICATION OF CHANNEL SLOPES:i) Mild slope  Yn > Yc
ii) Step slope--- Yn < Yc
iii) Critical Slope -- Yn = Yc
iv) Horizontal slope -- So = 0
v) Adverse Slope --- So = -ve
Some of the possible water surface profiles are shown in the sketch
i) Mild slope followed by a steep slope
ii) Steep slope followed by a mild slope
iii) Horizontal slope channel followed by steep slope
iv) Steep followed by horizontal ending in free fall
RESULT:-Gradually varied flow (GVF) profiles have been studied.
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EXPERIMENT NO.10
NAME OF THE EXPERIMENT: Study of Hydraulic jump in a rectangular channel
APPARATUS:
1. A glass Walled rectangular channel of sufficient length equipped with head and tail gates.
2. A pointer gauge which can be moved along the length of the channel on top rails provided on
the side walls.
3. A regulated water supply with a discharge measurement unit in the supply line.
FIGURE
THEORY
In an open channel when rapidly flowing stream abruptly changes to slowly flowing stream, a
distinct rise or jump in the elevation of liquid surface takes place, this phenomenon is know as
distinct rise or jump in the elevation of liquid surface takes place this phenomenon is know as
hydraulic jump. The hydraulic jump converts kinetic energy of stream rapidly flowing into potential
energy. Due to this there is a loss of kinetic energy. At the place where hydraulic jump occurs rollers
of turbulent water form, which cause dissipation of energy. A hydraulic jump occurs in practice at
the toe of spillways or below a sluice gate where the velocity is very high.

y1 1 
  1  8( Fr1 ) 2  1 
y2 2 

Where, Fr1 =
V1
gy1
 Froude’s number corresponding to the pre-jump depth.
The other elements of the jump
Height of jump,
H j = y2 – y1
Length of jump,
L j  5Hj
Loss of energy head occurring in the jump, EL=
( y 2  y1 ) 3
4 y1 y 2
PROCEDURE :
1. Take point gauge reading corresponding to the bed level of the channel (y0).
2. Open the supply valves fully and allow the water to flow in the channel. Allow the flow to
stabize, and measure the discharge Q actual with the help of orifice meter.
3. Adjust the depth of flow with the help of head gate such that it is less than the critical depth i.e.
Fr1>1
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4. Adjust the height of tailgate to set up a hydraulic jump approximately midway along the channel.
5. Let the jump stabilize and take the pointer readings corresponding to the water surface just
upstream (y1’) and downstream (y2)of the jump
6. Measure the length of the jump Lj
7. Repeat steps 3 to6 for different values of Fr1 always keeping it greater than one adjusting the
opening of the head gate.
OBSERVATIONS
Pointer gauge
readings
Discharge
S.No
( / S )
y1
3
Q
(cm)
y2
Initial
Sequent
Height of
Length
depth
depth
jump
of jump
y1(cm)
y2(cm)
Hj =( y1- y2)
Lj (cm)
(y2/y1)
(y2/y1)
act
th.
(cm)
CALCULATION:
1. Initial depth , y1 = y1 ‘-y0 ,and Final Depth y2 ‘-y0
y
2.  2
 y


Using y1 and y2 calculated aborut.
 actual
3. Fr1 
Q
B
gy 
3
4. Hj = y1- y2
5. E L 
( y1 - y 2 ) 3
4y1 y 2
6. Plot the following curves

y2/y1 vs Fr1

L/y2 vs Fr1

EL vs Fr1
RESULT:PRECAUTIONS:1. Pointer gauge readings must be taken only after the jump stabilizes.
2. Pointer gauge readings upstream and downstream of the jump should be taken at the section
where the water surface is tranquil.
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