UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
Course No: CE 222
Course Title: Hydraulics Lab
Experiment No
1
2
3
4
5
6
7
8
9
10
11
Experiment Name
Determination of Center of Pressure
Bernoulli’s Theorem
Flow through Venturimeter
Flow through an Orifice
Coefficient of Velocity by the Coordinate Method
Flow through an External Cylindrical Mouthpiece
Flow over a V-notch
Flow over a Sharp- Crested Weir
Flow over a Broad-Crested Weir
Flow beneath a Sluice Gate
Flow through a Parshall Flume
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222: Hydraulics Sessional
Experiment No. 1
CENTER OF PRESSURE
Introduction
The center of pressure is a point on the immersed surface at which the resultant of liquid
pressure force acts. In the case of horizontal area the pressure is uniform and the resultant
pressure force passes through the centroid of the area, but for an inclined surface this point
lies towards the deeper end for the surface, as the intensity of pressure increases with depth.
The objective of this experiment is to locate the centre of pressure of an immersed
rectangular surface and to compare this position with that predicted by theory.
Description of the Apparatus
The apparatus is comprised basically of a rectangular transparent water tank, which supports
a torroidal quadrant of rectangular section complete with an adjustable counter-balance and a
water level measuring device. The clear perspex (acrylic resin) rectangular water tank has a
drain tap at one end and a knurled leveling screw at each corner of the base. Centrally
disposed at the top edge of the two long sides, are mounted on the brass knife-edge supports.
Immersed within the tank and pivoted at its geometric centre of curvature on the knife-edge
supports, is an accurate torroidal quadrant (ring segment). This is clamped and dowelled to an
aluminium counter-balance arm which has a cast-iron main weight with a knurled head brass
weight for fine adjustment at one end and a laboratory type weight pan at the other end. Two
spirit levels are mounted on the upper surface of the arm.
The water level is accurately indicated by a point gauge, which is at one end of the tank.
Theory
The magnitude of the total hydrostatic force F will be given by_
F = ρgyA
Where,
ρ = density of fluid
g = acceleration due to gravity
y = depth to centroid of immersed surface
A = area of immersed surface
This force will act through the centre of pressure (C.P) at a distance yp (measured vertically)
from point O, where O is the intersection of the plane of the water surface and the plane of
the rectangular surface.
Theoretical Determination of yp:
Theory shows that
ICG
yp = y +
Ay
Where,
y
ICG
=
distance from O to the centroid (CG) of the immersed surface
=
2nd moment of area of the immersed surface about the
horizontal
axis through CG.
Experimental Determination of yp:
For equilibrium of the experimental apparatus, mements about the pivot P give
where
F.y
=
=
W.z
Mgz
y
M
Z
=
=
=
distance from pivot to centre of pressure
mass added to hanger
distance from pivot to hanger
Therefore
MgZ
y=
F
But
and
y
y
=
=
yp + r – y1
yp + r + y1
[ Fully Submerged ]
[ Partially Submerged ]
yp
yp
=
=
y – (r – y1)
y – (r + y1)
[ Fully Submerged ]
[ Partially Submerged ]
r
y1
=
=
distance from pivot to top of rectangular surface
depth of water surface from top of rectangular surface
Therefore
and
where,
Counter Balance
Z
p
r
y
R
y1
TORROID
Water Level
y
W=Mg
y
p
2 L
LL
ρgy2
CENTRE OF PRESSURE
Fig. 01 Partially submerged condition
Counter Balance
Z
P
r
y
R
WATER LEVEL
ρg(y2-L)
y1
O
W=Mg
yp
y2 L
TORROID
ρgy2
CENTRE OF PRESSURE
Fig. 02 Fully submerged condition
PROCEDURE
The apparatus was placed in a splash tray and correctly levelled.
The length ‘L’ and width ‘b’ of the rectangular surface, the distance r from the pivot to the
top of the surface and the distance from the hanger to the pivot were recorded.
The rectangular surface was positioned with the face vertical (θ = 0) and clamped.
The position of the movable jockey weight was adjusted to give equilibrium, i.e. when the
balance pin was removed there was no movement of the apparatus. The balance pin was
replaced.
Water was added to the storage chamber. This created an out of balance clockwise moment in
the apparatus. A mass M was added to the hanger such that the system was brought almost to
equilibrium, the clockwise moment still marginally greater. Water was slowly removed from
the storage chamber via the drain hole until equilibrium was attained. At this condition the
drain hole was closed and the balance pin again removed to check equilibrium.
The balance pin was replaced and the values of y1, y2 and M were recorded.
The above procedure was repeated for various combinations of depth.
OBJECTIVE
To plot the Mass on the pan (M) against y2 in plain graph paper.
ASSIGNMENT
i.
ii.
Discuss
What are the practical applications of the centre of pressure?
DISCUSSION
Comments on the results, sources of error, nature of the curves etc.
Experiment No. 1
CENTRE OF PRESSURE
Experiment data Sheet
Inner radius of curvature, r
Outer radius of curvature, R
Width of plane surface, b
Height of plane surface, L
Distance from pivot to hanger, Z
No.
of
Obs
01
y1
y2
y
A
(cm)
(cm)
(cm)
2
(cm )
=
=
=
=
=
10 cm
20 cm
7.5 cm
10 cm
27.5 cm
F
ICG
yp
theo.
M
(gm)
y
(cm)
yp
exp. (cm)
Submerged
Condition
Partially/Fully
Partially
02
Partially
03
Partially
04
Fully
05
Fully
06
Fully
Group No.
: ____________
Date
: ____________
Name
: ____________
Roll No.
: ____________
___________________
Signature of the Teacher
Comment
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222: Hydraulics Sessional
Experiment No. 2
BERNOULLI’S THEOREM
INTRODUCTION
Energy is the ability to do work. It manifests in various forms and can change from one form to
another. The various forms of energy present in fluid flow are elevation, kinetic, pressure and
internal energies. Daniel Bernoulli in the year 1938 stated that in a steady flow system of
frictionless (or non-viscous) incompressible fluid, the sum of pressure, elevation and velocity heads
remains constant at every section, provided no energy is added to or taken out by an external source.
This statement of Daniel Bernoulli, known as the Bernoulli’s Energy Equation, can be applied in
practice for the construction of flow measuring devices such as Venturimeter, Flow nozzle,
Orificemeter and Pitot tube. Furthetmore, it can be applied to the problems of flow under a sluice
gate, free liquid jet, radial flow and free vortex motion.
DESCRIPTION OF THE APPARATUS
The unit is constructed as a single Perspex fabrication. It consists of two cylindrical reservoirs interconnected by a Perspex Venturi of rectangular cross-section. The Venturi is provided with a number
of Perspex piezometer tubes to indicate the static pressure at each cross-section. An engraved plastic
backboard is fitted which is calibrated in British and Metric units. This board can be reversed and
mounted on either side of the unit so that various laboratory configurations can be accommodated.
The inlet vessel is provided with a dye injection system. Water is fed to the upstream tank through a
radial diffuser from the laboratory main supply. For satisfactory results the mains water pressure
must be nearly constant. After flowing through the Venturi, water is discharged through a flow
regulating device. The rate of floe through the unit may be determined either volumetrically or
gravimetrically. The equipment for this purpose is excluded from the manufacturer’s supply.
The apparatus has been made so that the direction of flow through the Venturi can be reversed for
demonstration purposes. To do this the positions of the dye injector and discharge fitting have to be
interchanged.
PROCEDURE
The apparatus should be accurately leveled by means of screws provided at the base. Connect the
water supply to the radial diffuser in the upstream tank. Adjust the level of the discharge pipe by
means of the stand and clamp provided to a convenient position. Allow water to flow through the
apparatus until all air has been expelled and steady flow conditions are achieved. This can be
accomplished by varying the rate of inflow into the apparatus and adjusting the level of the
discharge tube. Readings may then be taken from the piezometer tubes and the flow through the
apparatus measured. A series of readings can be taken for various through flows.
WORKING FORMULA
Assuming frictionless flow, Bernoulli’s Theorem states that, for a horizontal conduit
P1
γ
+
V12 P 2 V22
=
+
γ
2g
2g
where, P1,P2
γ
V1, V2
g
=
=
=
=
(1)
pressure of flowing fluid at sections 1 and 2
unit weight of fluid
mean velocity of flow at sections 1 and 2
acceleration due to gravity.
The equipment can be used to demonstrate the validity of this theory after an appropriate allowance
has been made for friction losses.
OBJECTIVE
i.
To plot the static head, velocity head and total head against the length of the passage in
one plain graph paper.
ii.
To plot the total head loss, hL against the inlet kinematics head, V2/2g, for different
inflow conditions in plain graph paper.
ASSIGNMENT
i.
What are the assumptions underlying the Bernoulli’s energy equation?
ii.
Do you need any modification (s) of Eqn(1) when (a) the frictional head loss is to be
considered, and (b) the conduit is not horizontal?
DISCUSSION
Comment on the results, sources of error, etc.
Experiment No. 2
BERNOULLI’S THEOREM
Experimental Data Sheet
Cross-sectional area of the measuring tank = 45 x 30 = 1350 cm2
Initial point gage reading
= _________________ cm
Final point gage reading
= _________________ cm
Collection time
= _________________ seconds
Piezometer
tube no.
A (cm2)
1
2
3
4
5
6
7
8
9
6.45
5.48
3.55
2.39
2.39
3.48
4.65
5.81
6.45
V=Q/A (cm/s)
V2/(2g) (cm)
P/γ (cm)
H=P/γ+V2/(2g)
(cm)
Gr. No.
V /2g (cm)
1
2
3
4
5
6
2
1
hL (cm)
Group No.
: ____________
Date
: ____________
Name
: ____________
Roll No.
: ____________
Signature of the Teacher
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222: Hydraulics Sessional
Experiment No. 3
FLOW TROUGH VENTURIMETER
THEORY
Fig. 1: Flow through a Venturimeter
Consider the Venturimeter shown in the above figure. Applying the Bernoulli’s equation between
Point 1 at the inlet and Point 2 at the throat, we obtain
P1
γ
+
V12 P2 V22
= +
2g γ
2g
(1)
where P1 and V1 are the pressure and velocity at Point 1, P2 and V2 are the corresponding quantities
at Point 2, γ is the specific weight of the fluid and g is the acceleration due to gravity. From
continuity equation, we have
(2)
A1V1 = A2V2
Where A1 and A2 are the cross-sectional areas of the inlet and throat, respectively. Since
π
π
A1= D12 ; A2 = D22
4
4
from Equns. (1) and (2), we have
V1 =
( P1 − P2 )
2g
D
( 1 )4 − 1 γ
D2
= K1H 1 / 2
(3)
where,
K1=
2g
and, H =
( P1 − P2
)
D1 4
γ
( ) −1
D2
The head H is indicated by the piezometer tubes connected to the inlet and throat.
The theoretical discharge, Qt is given by
Qt =A1V1
=KH 1 / 2
(4)
where,
K = K1A1
(5)
Now, if Cd is the coefficient of discharge (also known as the meter coefficient) and Qa is the actual
discharge, then
Cd =
Qa
Qt
(6)
OBJECTIVE
i.
ii.
iii.
iv.
v.
To find Cd for the Venturimeter
To plot Qa against H in plain graph paper
To plot Qa against H in log-log paper and to find (a) the exponent of H, and (b) Cd
To calibrate the Venturimeter
To plot Cd against corresponding Reynolds number (Re) at throat.
ASSIGNMENT
i.
Why is the diverging angle smaller than the converging angle for a Venturimeter?
ii.
What are the uses of a Venturimeter?
iii.
On what factors does the meter co-efficient depend?
iv.
What is cavitation? Discuss its effect on flow through a Venturimeter. How can you
avoid cavitation in a Venturimeter?
DISCUSSION
Comment on the results, sources of error, etc.
Experiment No. 3
FLOW THROUGH A VENTURIMETER
Experimental Data and Calculation Sheet:
Cross-sectional area of the measuring tank, A= 45 x 45 = 2025 cm2
Pipe diameter,
D1 = 3.175 cm
Area of the pipe,
A1=
Area of the throat,
A2=
Throat diameter,
D2 = 1.58 cm
0
Temperature of water t = 20 c
Kinematic viscosity of water
=
Initial point gage reading = ____________cm
Final point gage reading
=
No.
of
Obs.
Volume
of water
V(cm3)
Collection
time T
(seconds)
Actual
Discharge
Qa
(cm3/s)
Piezometer reading
Left
h1
Right
h2
K1
Diff
H
K
Theoretical
discharge
Qt (cm3/s)
1
2
3
4
5
6
Group No.
: ____________
Date
: ____________
Name
: ____________
Roll No.
: ____________
___________________
Signature of the Teacher
__________cm2
__________ cm2
1 x 10-6 m2/s
__________cm
Cd=
Qa
Qt
V 2=
Qa
A2
Reynolds number
Re
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222, Hydraulics Sessional
Experiment No. 4
FLOW TROUGH AN ORIFICE
THEORY:
Fig. 1 Flow Through an Orifice
An orifice is an opening with a closed perimeter in the wall of a tank or in a plate normal to the
axis of the pipe through fluid can flow.
Consider a small orifice having a cross-sectional area A and discharging water under a constant
head H as shown in the above figure. Then the theoretical discharge, Qt is given by
Qt = A 2 gH
(1)
Where, g is the acceleration due to gravity. Let Qa be the actual discharge. Then the coefficient
of discharge, Cd, is given by
Q
Cd = a
(2)
Qt
Coefficient of velocity, Cv is defined as the actual velocity at vena contracta to the theoretical
velocity. Thus,
Cv =
Va
=
Vt
Va
2 gH
(3)
Coefficient of contraction, Cc is defined as the area of jet at vena contracta to the area of orifice.
Thus,
A
Cc = a
(4)
A
It follows from (1), (2), (3) and (4) that
Cd = CcxCv
(5)
Note: Reference Value of Cd (0.59 – 0.68)
OBJECTIVE
i.
ii.
iii.
iv.
To find the value of Cd for the orifice.
To plot a graph for Qa vs. Qt in plain graph paper.
To plot a graph for Qa vs. H in plain graph paper.
To plot Qa vs. H in log-log paper and to find the value of (a) the exponent of H and
(b) Cd.
ASSIGNMENT
i.
ii.
iii.
iv.
v.
What is an orifice? Why is it used?
What are the coefficient of velocity, coefficient of contraction and coefficient of
discharge for an orifice? On what factors do these coefficients depend? What are the
average values of these coefficients for a sharp-crested orifice?
What is the effect of rounding the edge of an orifice?
What is a submerged orifice? What are the average values of the coefficient of
velocity, coefficient of contraction and coefficient of discharge for a submerged
orifice?
Why is the actual discharge through an orifice less than the theoretical discharge?
DISCUSSION
Comment on the results obtained, sources of error, etc.
Experiment No. 4
FLOW THROUGH AN ORIFICE
Observation and Calculation Sheet
Cross-Sectional area of the measuring tank = 2025 cm2
Diameter of the orifice, D = 1.3 cm
Area of the orifice = 1.33 cm2
Head correction, h′ = 23 cm
No.
of
Obs
Observed head
h (cm)
Initial
Final Mean
Point gage reading (cm)
Initial
Collection
time
T (seconds)
Vol. Of
water
V (cm3)
Actual head
H=h- h′
=cm
Final Diff.
Group No.
: ____________
Date
: ____________
Name
: ____________
Roll No.
: ____________
___________________
Signature of the Teacher
Actual
discharge
Qa
(cm3/s)
Theo.
Discharge
Qt
(cm3/s)
Coeff. of
discharge
Cd
Mean
Cd
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222, Hydraulics Sessional
Experiment No. 5
COEFFICIENT OF VELOCITY BY THE COORDINAE METHOD
THEORY
Fig. 1 Coefficient of Velocity by the Coordinate Method
Let H be the total head causing flow and section-c-c conditions the vena contracta as shown in
the figure. The jet of water has a horizontal velocity but is acted upon by gravity with a
downward acceleration of g. Let us consider a particle of water in the jet at P and let the time
taken for this particle to move from 0 to P be t.
Let x and y be the horizontal and vertical co-ordinates of P from 0, respectively. Then,
x = Va t
and
1
y = 2 gt2
(1)
(2)
Equating the values of t2 from these two equations, one obtains
x2 2y
=
g
Va2
Va =
gx 2
2y
(3)
But, the theoretical velocity, Vt = 2 gH
Hence, the coefficient of velocity, Cv is given by
Va
x2
=
4 yH
Vt
And the head loss is given by
HL =(1-Cv2)H
Cv =
(4)
(5)
Reference Value: 0.95 – 0.99
OBJECTIVE
i.
ii.
iii.
iv.
To find Cv for the orifice.
To find the head loss, HL.
To plot Va vs. Vt in plain graph paper and find Cv.
To plot Va vs. H in log-log paper and to find (a) Cv and (b) the exponent of H.
ASSIGNMENT
i.
ii.
iii.
iv.
Define vena contracta. Why does it form?
Explain the inversion of jet with the help of sketches.
How can you determine the coefficient of contraction Cc for an orifice?
Will the value of Cv be different for sharp-edged and rounded orifices? Why?
DISCUSSION
Comment on the results obtained, sources of error, etc.
Experiment No. 5
COEFFICIENT OF VELOCITY BY THE COORDINATE METHOD
Observation and Calculation Sheet
Diameter of the orifice, D = 1.3 cm
Head correction,
No.
of
Obs
Observe d
head
h (cm)
h′ = 23 cm
Actual
head H
(cm)
Actual
Theoretical Hor.
Vertical
velocity y Coordinate Coordinate velocity
y
Vt (cm/s)
X (cm)
Y (cm)
Va
(cm/s)
Coeff.
Of
velocity
y
Head
Loss
HL
Cv
Group No.
: ____________
Date
Mean Cv =
: ____________
Name
: ____________
Roll No.
: ____________
___________________
Signature of the Teacher
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CEE 222, Hydraulics Sessional
Experiment No. 6
FLOW THROUGH AN EXTERNAL CYLINDRICAL MOUTHPIECE
THEORY
If a small tube is attached to an orifice, it is called mouthpiece. The standard length of a
mouthpiece is 3d, where d is the diameter of the orifice. If the length is less than 3d, jet after
passing the vena contracta does not occupy the tube fully and thus acts as orifice. If the length is
greater than 3d, it acts as pipe.
The effect of adding a mouthpiece to an orifice is to increase the discharge. The pressure at vena
contracta is less than atmospheric, so a mouthpiece decreases the pressure vena contracta and
increases the effective head causing the flow, hence, discharged is increased.
Fig. Flow Through an External Cylindrical Mouthpiece
Consider an external cylindrical mouthpiece of area A discharging water under a constant head
H as shown in the figure. Applying Bernoullis equation at point 1 and 3.
V2
H=
2g
or, V = 2 gH
Then the theoretical discharge, Qt, is given by
Qt = A 2 gH
Where A is the area of the mouthpiece.
Let Qa be the actual discharge. Then the coefficient of discharge, Cd, is given by
Q
Cd = a
Qt
(1)
(2)
(3)
(4)
APPARATUS
i.
ii.
iii.
iv.
v.
Constant head water tank
Mouth piece
Discharge measuring tank
Stop watch
Point gauge
PROCEDURE
Measure the diameter of the mouthpiece. Attach the mouthpiece to the orifice of the constant
head water tank. Supply water to the tank. When the head at the tank (measured by a
manometer attached to the tank) is steady, record the reading of the manometer. Measure the
flow rate. Repeat the procedure for a different combinations of discharge.
OBJECTIVE
i.
ii.
To find Cd for the mouthpiece.
To plot Qa vs. H in log-log paper, and to find (a) Cd and (b) the exponent of H.
ASIGNMENT
i.
ii.
iii.
iv.
v.
Explain why the discharge through an orifice is increased by fitting a standard short
tube to it.
What will happen to the coefficient of discharge if the tube is shorter than the length
or the head causing the flow is relatively high?
What is the effect of rounding the entrance of the mouthpiece?
Why the coefficient of contraction for an internal mouthpiece is less than that of an
orifice?
What is a submerged tube? Does the coefficient of the tube change due to
submergence?
DISCUSSION
Comment on the results obtained, sources of error, etc.
Experiment 6
FLOW THROUGH AN EXTERNAL CYLINDRICAL MOUTHPIECE
Calculation Sheet
Diameter of the mouthpiece, D = __________________
Area of the mouthpiece, A = ________________
Cross-sectional area of the measuring tank = _________________
Head correction, h′ = _________________
Initial point gauge reading = __________________
Final point gauge reading = __________________
Difference in gauge reading = ________________
Observed head, h = ________________
No. of
Obs.
Actual
head
H=h-h′
Level/Term
Student No.
Group No.
Volume
of water
V
: _____________
: _____________
: _____________
Collection Actual
Time
discharge
T
Qa
Theoretical Co-eff. of
Discharge discharge
Qt
Cd
Mean
Cd
Dept. : _____________
Section : _____________
Date : ______________
Signature of the Teacher
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222. Hydraulics Sessional
Experiment No. 7
FLOW OVER A V-NOTCH
THEORY
The measure of flow rate in flumes or channels is of obvious importance to the practicing
engineer in the fields of irrigation, water conservation and flood alleviation.
Hydraulic structures used for flow measurement can be listed as follows:
1. Sharp-crested thin plate weirs;
2. Solid long base weirs;
3. Throated flumes;
Sharp crested weirs are overflow structures whose length of crest in the direction of flow is
equal to or less than 2 mm. The use of sharp crested weirs is generally limited to laboratories,
small channels, and streams which do not carry debris and sediment.
The most common types of sharp-crested weir are the rectangular weir and the V-notch weir.
The upstream face must be installed vertically and the edge of the weir plate must be accurately
shaped. The V-notch weir is preferred when small discharges are involved, because the
triangular cross-section of the flow ‘nappe’ leads to a relatively greater variation in head. The
wetted perimeter is dependent on head and co-efficient of discharge remains fairly constant.
Fig. Flow Over a V- Notch
Consider the V-notch shown in the figure. Let H be the height of water surface and θ be the
angle of notch. Then, width of the notch at the water surface
θ
L = 2H tan
(1)
2
Consider a horizontal strip of the notch of thickness dh under a head h. Then,
Width of the strip, W = 2(H-h)tan
θ
2
Hence, the theoretical discharge through the strip
dQt = area of the strip x velocity = 2(H-h) tan
θ
2
dh 2 gh
(2)
(3)
Integrating between the limits 0 and H and simplifying, the total theoretical discharge over the
notch is given by
θ
8
2 g tan H sup 5 / 2
15
2
(4)
= KH5/2
Qt =
(5)
where,
θ
8
2 g tan
15
2
Let Qa be the actual discharge. Then the coefficient of discharge, Cd, is given by
K=
Cd =
Q
actual − disch arg e
= a
theoretical − disch arg e Qt
Qa = K CdH5/2
(6)
(7)
(8)
The co-efficient of discharge depends on relative head (H/P), relative height (P/B) and angle of
the notch ( θ ).
From hydraulic point of view a weir may be fully contracted at low heads while at increasing
head it becomes partially contracted. The flow regime in a weir is said to be partially contracted
when the contractions along the sides of the V-notch are not fully developed due to proximity of
the walls and / or bed of approach channel. Where as a weir which has an approach channel and
whose bed and sides of the notch are sufficient remote from the edges of the V-notch to allow
for a sufficiently great approach velocity component parallel to the weir face so that the
contraction is fully contracted weir. In case of a fully contracted weir Cd is fairly constant for a
particular angle of notch.
APPRATUS
1.
2.
3.
4.
5.
A constant steady water supply with a means of varying the flow rate.
An approach channel
A V-notch weir plate
A flow rate measuring facility
A point gauge for measuring H.
PROCEDURE
Position the weir plate at the end of the approach channel, in a vertical plane, with the sharp
edge on the upstream side. Admit water to channel until the water discharges over the weir plate.
Close the flow control valve and allow water to stop flowing over weir. Set the point gauge to
datum reading. Position the gauge abut half way between the notch plate and stilling baffle.
Admit water to the channel and adjust flow control valve to obtain heads, H, increasing in steps
of 1 cm. For each flow rate, stabilize conditions, measure and record H. Take readings of
volume and time using the volumetric tank to determine the flow rate.
OBJECTIVE
i.
ii.
iii.
To find for the V-notch
To plot Qt vs. Qa in a plain graph paper.
To plot Qa vs. H in a log-log paper and to find (a) the exponent of H and (b) Cd.
ASSIGNMENT
i.
ii.
iii.
iv.
v.
Why does the V-notch give more accurate flow measurement than any other weirs
and orifices when the flow is slightly fluctuating?
On which factor does the value of Cd depend?
What is the average value of Cd for a 90o V-notch? Does it depend on floe condition
(partially or fully contracted)?
Why should the tail water level remain below the vertex of the notch? What
minimum ventilation below the flow over the notch at downstream side should be
maintained?
Why the water head measurement is made at some distance upstream from the notch?
What is this minimum distance in case of a V-notch?
DISCUSSION
Comment on the results obtained, sources of error, etc.
Experiment No. 7
FLOW OVER A V-NOTCH
Observation and Calculation Sheet
Angle of the notch, θ = __________________
K = ________________
Cross-sectional area of the measuring tank = ______________
Initial point gauge reading = _____________
Final point gauge reading = _____________
Difference in reading = ________________
Datum water level reading = _____________
Water level above vertex = ______________
Final water level reading =_______________
No. of
Obs.
Level/Term
Student No.
Group No.
Vol. Of
water
V
Collection
time
T
: ___________
: ___________
: ____________
Actual
discharge
Qa
Effective
head H
Theoretical
discharge
Qt
Co-eff. of
discharge
Cd
Dept. : ____________
Section: ____________
Date : ____________
Signature of the Teacher
Mean
Cd
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222 Hydraulics Sessional
Experiment No. 8
FLOW OVER A SHARP-CRESTED WEIR
THEORY
The relationship between discharge and head over the weir can be developed by making the
flowing assumptions as to the flow behaviour:
1. Upstream of the weir, the flow is uniform and the pressure varies with depth
according to the hydrostatic equation P = pgh.
2. The free surface remains horizontal as far as the plane of the weir, and all
particles passing over the weir move horizontally. (In fact, the free surface drops
as it approaches the weir).
3. The pressure through out the sheet of liquid or nappe, which passes over the crest
of the weir, is atmospheric.
4. The effects of viscosity and surface tension are negligible.
5. The upstream approach velocity head is neglected.
Fig. Flow Over a Sharp-Crested Weir
Now consider the Sharp-crested weir in the figure. Let H be the working head and B is the
length of the weir.
Let us consider a small horizontal string of thickness dh under a head h. The strip can be
considered as an orifice.
Therefore, the theoretical discharge through the strip
dQt = area of the strip x velocity
(1)
= (Bdh) 2 gh
(2)
Integrating between the limits 0 and H, the total theoretical discharge over the weir is given by
2
Qt =
(3)
2 g BH 3 / 2
3
Let Qa be the actual discharge. Then the co-efficient of discharge, Cd is given by
Qa
Qt
Therefore,
Cd =
(4)
2
Qa = C d 2 g BH 3 / 2
3
= KCdH3/2
(5)
(6)
where,
K=
2
2g B
3
(7)
A suppressed rectangular weir is one which extends across the full width of the approach
channel. It the length of the weir crest (B) is less than the width of the channel, the end
contraction occurs. In that case, B is equation (5) should be replaced by effective length (B′)
which is given by
B′ = B-0.1 nH
Where n is the number of end contraction.
It is important to notice that the nappe should be ventilated or fully aerated otherwise the
pressure below the nappe will not be atmospheric.
APPARATUS:
1.
2.
3.
4.
5.
A constant steady water supply with a means of varying the flow rate.
An approach channel
A rectangular weir plate
A flow rate measuring facility
A point gauge for measuring H.
PROCEDURE:
Measure the height and length of the weir. Position the weir plate at end side of the approach
channel, in a vertical plane, with sharp edge on the upstream side. Allow water to the channel so
that water flows over the weir. Measure the head H and rate of discharge at a steady condition.
Vary the discharge and record a series of readings of Q and H.
OBJECTIVE
i.
Observation of the nappe for ventilated and non-ventilated conditions.
ii.
To find Qd for the weir
iii.
To plot Qa vs. H in a plain graph paper
iv.
To plot Qa vs. H in a log-log graph paper and to find (1) the exponent of H and (2)
Cd .
ASSIGNMENT
i.
Derive Equation (5). What are the assumptions made in deriving this equation? What
is the extent of their validity?
ii.
Why the pressure distribution over the weir-crest is less than hydrostatic?
iii.
What is the effect of rounding the weir edge?
iv.
Why it is necessary to ventilate the space below the nappe?
v.
Discuss the effects of lateral contraction, in case of contracted weir, on the flow over
the weir.
DISCUSSION
Comment on the results obtained, sources or error, etc.
Experiment No. 8
FLOW OVER A SHARP-CRESTED WEIR
Experimental Data Sheet
Width of the weir, B
Height of the weir, P
Elevation of bed level
Final water level
Difference in water level, H
No. of
Obs.
Vol. of Water
V
Level/Term
Student No.
Group No.
= _____________________
= _____________________
= _____________________
= _____________________
= _____________________
Time
T
: ____________
: ____________
: ____________
Signature of the Teacher
Actual
discharge
Qa
Ventilated Condition
Head
H
Dept. : ____________
Name : ____________
Date : ____________
Theoretical
discharge Qt
Co-eff. of
discharge
Cd
Mean
Cd
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222, Hydraulics Sessional
Experiment No. 9
FLOW BENEATH A SLUICE GATE
SLUICE GATE
Fig. Flow beneath a sluice gate
THEORY
The Bernoulli energy equation may be applied in those cases where there is a negligible loss of
total head from one section to another, or where the magnitude of the head loss is already
known. Flow under a sluice gate is an example of converging flow where the correct form of the
equation for discharge may be obtained by equating at Sections 1 and 2 as shown in the figure
4.1. As the energy loss between the section is negligible,
H1 = H2
(1)
V2
V12
= y2 + 2
2g
2g
(2)
And therefore,
y1 +
Expressing the velocities in terms of Q, the above equation becomes
Q2
Q2
y1 +
=
+
y
2
2 gb 2 y12
2 gb 2 y 22
where b is the width of the sluice gate.
(3)
Simplifying and re-arranging the terms, one obtains
Q = by1
2 gy 2
( y1 / y 2 + 1)
(4)
Q = by 2
2 gy1
( y 2 / y1 + 1)
(5)
Or alternatively,
The small reduction in flow velocity due to viscous resistance between Sections 1 and 2 may be
allowed for by a coefficient Cv. Then
Q = C v by 2
2 gy1
( y 2 / y1 + 1)
(6)
The coefficient of velocity, Cv varies in the range 0.95<Cv<1.0, depending on the geometry of
the flow pattern (expressed by the ratio yg/y1) and friction.
The downstream depth y2 may be expressed as a function of the gate opening, yg, i.e.
Y2 = Ccyg
(7)
Where, Cc is the coefficient of contraction whose commonly accepted value of 0.61 is nearly
independent of the ratio yg/y1. The maximum contraction of the jet occurs approximately at a
distance equal to the gate opening. Thus equation (6) becomes
Q = C c C v by g
2 gy1
(C c y g / y1 + 1)
(8)
The above equation can also be written as
Q = C d by g 2gy1
(9)
Where Cd is the coefficient of discharge and is a function of Cv, Cc, b, yg and y1. Therefore,
Cd =
Cc Cv
C c y g / y1 + 1
(10)
Equation (9) may also be written as
Qa = CdQt
(11)
Qt = by g 2gy1
(12)
So that
Where Qt and Qa are the theoretical and actual discharges, respectively.
The momentum equation may be applied to the fluid within any control volume where the
external forces are known or can be estimated to a sufficient degree of accuracy. The horizontal
components of these forces acting on the fluid within the control volume shown in fig. 4.1 are
the resultants of the hydrostatic pressure distributions at Sections 1 and 2, the viscous shear
force on the bed and the thrust of the gate. It should be noted that the equation permits the
resultant gate thrust (Fg) to be determined even though the pressure distribution along its surface
is not hydrostatic. Over a short length of smooth bed the contribution of the shear force may be
neglected. The resultant force applied to the fluid within the control volume in the downstream
direction is given by
Fx = [(1 / 2) ρgy12 − (1 / 2) ρgy 22 − Fg ]b
(13)
The effect of this force is to accelerate the fluid within the control volume in the downstream
direction. Hence,
Fx = ρQaV2 − ρQaV1
(14)
Substituting for Fx and gathering terms, one obtains
Fg =
ρQ 2
y
1
ρgy 22 [( y1 / y 2 ) 2 − 1] − 2 a [1 − 2 ]
2
b y2
y1
(15)
Simplifying and eliminating Qa, We get
Fg =
( y − y2 )3
1
ρg 1
2
y1 + y 2
(16)
The pressure distribution on the gate cannot be hydrostatic, as the pressure must be atmospheric
at both the upstream water level and at the point where the jet springs clear of the gate.
Note that the thrust on the gate, FH, for a hydrostatic pressure distribution is given by
1
FH =Error! Bookmark not defined. ρg(y1-yg) 2
2
(17)
OBJECTIVE
1.
2.
3.
4.
5.
To determine the discharge beneath the sluice gate.
To determine Cv, Cc and Cd.
To plot Cc and Cd Vs yg/y1 in plain graph paper.
To plot y1 Vs Qa for different yg in plain graph paper.
To plot Fg/FH Vs yg/y1 in plain graph paper.
TYPICAL QUALITATIVE SHAPES OF GRAPHS
Graph 2: y1 Vs Qa for different yg (Plain graph paper)
Graph 3: Fg/FH Vs yg/y1 (Plain graph paper)
ASSIGNMENTS
i.
ii.
iii.
iv.
Explain why the pressure distribution along the surface of the gate is not hydrostatic.
What happens when the gate opening is greater than the critical depth?
Verify equations (9) and (16).
When does the submergence occur and what is its effect on flow beneath a sluice
gate?
DISCUSSION
Comment on the results obtain, sources of error, etc.
Experiment No. 9
FLOW BENEATH A SLUICE GATE
Experimental Data Sheet
No. of
Obs.
1
yg
y1
y2
Volm of
water
2
3
4
5
6
7
8
Level/Term: _______________
Roll No. : _______________
Group No. : _______________
Signature of the Teacher
Dept : ______________
Section: ______________
Date : ______________
Time
Qt
Qa
Cv
Cc
Cd
Yg/y1
Fg/FH
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CE 222, Hydraulics Sessional
Experiment No. 10
FLOW OVER BROAD CRESTED WEIR
LABORATORY SET-UP
Fig. 1.1 Flow over a broad-crested weir
Fig. 1.2 Flow diagram
DESCRIPTION
A board-crested weir is on overflow structure with a truly level & horizontal crest above which
the deviation from a hydrostatic pressure distribution because of centripetal acceleration may be
neglected. In other words, the streamlines are practically straight & parallel. To obtain this
situation the length of the weir crest in the direction of flow (L) should be related to the total
energy head over the weir crest as 0.07
≤H 1/L≤0.50. H1/L≥0.07 because otherwise the energy
losses above the weir crest cannot be neglected & the undulations may occur on the crest;
H1/L≤0.50, so that only slight curvature of stream occurs above the crest & a hydrostatic
pressure distribution may be assumed.
The upstream corner of the weir is rounded in such a manner that flow separation does not
occur. Te minimum radius of the upstream rounded nose r is 0.11 H1 max, although for the
economic design of field structures a value of r = 0.2 H1max is recommended. The length of the
horizontal weir crest should not be less than 1.45 H1. To obtain a favorable (high) discharge coefficient (Cd) the crest length (L) should be close to the permissible minimum (L≥1.75H 1).
The weir structure should be rigid & water tight & be at right angles to the direction of flow.
THEORY
Fig. 1.3 Flow over a broad-crested weir.
If the structure is so designed that there is no significant energy losses in the zone of acceleration
upstream of the control section, according to Bernoulli’s equation.
H 1 = h1 + α
v12
v2
= H = y +α
2g
2g
⇒ H1 = y +
v2
[Assuming α = 1 for all sections]
2g
v = 2 g ( H 1 − y)
Discharge, Q = A * 2 g ( H 1 − y )
Provided that critical flow occurs at the control section (y = yc), then
Q = Ac [2 g ( H 1 − y c )]0.5
For rectangular broad crested weir, Ac = Byc and yc can be computed from specific energy
equation
H = y+
v2
Q2
Q2
= y+
=
+
y
2g
2 gA 2
2 gB 2 y 2
dH
Q2
v2 2
= 1−
=
−
1
.
dy
2g y
gB 2 y 3
For critical section H=constant.
∴
dH
=0
dy
y
v2 2
v2
∴1 −
= c
. =0⇒
2 g yc
2g
2
∴ H = yc +
yc
2
∴ yc =
2
2
H = H1
3
3
∴ Q = By c [2 g ( H 1 − y c )]0.5
2
2
= B H 1 [2 g ( H 1 − H 1 )]0.5
3
3
2 2
= ( ) 0.5 Bg 0.5 H 11.5
3 3
2
Q = ( )1.5 Bg 0.5 H 11.5
3
(1)
This formula is based on idealized assumptions such as:
i.
ii.
iii.
absence of centripetal forces in the upstream & downstream cross-sections bounding
the considered zone of acceleration.
Absence of viscous effects & increased turbulence.
Uniform velocity distribution so that also the velocity distribution co-efficient can be
omitted.
In reality these effects do occur & they must therefore be accounted for by the introduction of a
discharge co-efficient Cd. The Cd value depends on the shape & type of the measuring structure.
2
(2)
Q = C d ( )1.5 Bg 0.5 H 11.5
3
Naturally in a field installation it is not possible to measure the energy head H1 directly & it is
therefore common practice to relate the discharge to the upstream water level h1 over the crest in
the following way.
2
Q = C d C v ( )1.5 Bg 0.5 h11.5
3
(3)
Where Cv is a correction co-efficient for neglecting the velocity head in the approach channel,
αv 2 / 2 g.
Generally, the approach velocity co-efficient,
Where, H 1 = h1 +
Cv = [
H1 u
]
h1
(4)
v12
Q2
= h1 +
2g
2 gB 2 y12
Where u equals the power of h1 in the head discharge equation, being u=1.50 for a rectangular
control section.
Thus Cv is greater than unity & is related to the shape of the approach channel section & to the
power of h1 in the head discharge equation.
Generally affect of Cv is considered in Cd and head discharge equation becomes.
2
Q = C d ( )1.5 Bg 0.5 h11.5
3
(5)
LIMITS OF APPLICATION:
i.
ii.
iii.
iv.
The practical lower limit of h1 is related to the magnitude of the influence of fluid
properties, to the boundary roughness, and to the accuracy with which h1 can be
determined. The recommended lower limit is 0.06 m or 0.05 L, whichever is greater.
The limitations on H1/P arise from difficulties experienced when the Froude number
Fr1=v1/(gA1/B)0.5 in the approach channel exceeds 0.45.
The limitations on H1/L arise from the necessity of ensuring a sensible hydrostatic
pressure distribution at the critical section of the crest and of preventing the
formation of undulations above the weir crest. Values of the ratio H1/L should
therefore range between 0.08 and 0.7.
The breadth (B) of the weir crest should not be less L/5.
OBJECTIVE
i.
ii.
iii.
To find Cd for the weir.
To plot Qa vs. h in plain graph paper.
To plot Qa vs. h in log-log paper & hence find
- exponent of h &
- Cd
iv.
v.
vi.
vii.
To plot h/L vs. Cd on plain graph paper.
To calibrate the weir.
Observe the conditions when h/L <0.07 & h/L >0.50 and explain the situations.
To plot h vs. Cd on plain graph paper.
ASSIGNMENT
i.
ii.
iii.
iv.
What is the difference between the working principles of a sharp-crested weir? When
does a weir become in effect a sharp-crested weir or a broad-crested weir?
Will the discharge per unit width be same for the same depth of flow over sharpcrested and broad-crested weirs? Why?
Upon which parameter does the value of Cd depend?
Derive equation (1) and state the conditions under which this equation is valid.
DISCUSSION
Comment on the results obtained, sources of error etc.
Experiment No. 10
FLOW OVER BROAD CRESTED WEIR
Experimental Data Sheet
Length of weir,
L =________________
Width of the weir,
B = _______________
Height of the weir,
P = ________________
No. of
obs.
Volume
of water
V (m3)
Time
T
(Sec)
Depth
H
(m)
Actual
discharge
Qa=V/t
(m3/Sec)
Level/Term
: ____________
Department
: ____________
Roll No.
: ____________
Section
: ____________
Group No.
: ____________
Date
: ____________
(Signature of the Teacher)
Theoretical
discharge
Qt=(2/3)1.5
g0.5Bh11.5
(m3/Sec)
Coefficient
of
discharge
Cd=Qa/Qt
h1/L
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
CEE 222, Hydraulics Sessional
Experiment No. 11
FLOW THROUGH A PARSHALL FLUME
PARSHALL FLUME
Parshall flumes are calibrated devices for the measurement of water through open channel in
which canal water flows over a broad flat converging section through a narrow downward
sloping throat section and then diverges on an upward sloping floor.
Fig. Plan and elevation of a parshall flume.
Parshall flume dimensions (mm)
3″
6″
W
76.2
152.4
A
467
621
a
311
414
B
457
610
C
178
394
D
259
397
E
457
610
L
152
305
G
305
610
K
25
76
1′
304.8
914
845
914
610
914
76
609.6
914
1206
914
610
914
76
4′
1219.
2
2438.
4
6096
1524
1937
914
610
914
76
2743
3397
914
610
914
76
7315
9144
15240
-
134
3
149
5
179
4
239
1
762
0
823
0
610
2′
137
2
152
4
182
9
243
8
-
1727
2
1852
9
213
4
213
4
182
9
182
9
365
8
609
6
30
5
30
5
8′
20
′
50
′
101
6
121
9
162
6
284
5
589
3
M
30
5
38
1
38
1
45
7
45
7
-
N
57
11
4
22
9
22
9
22
9
22
9
68
6
68
6
P
902
149
2
185
4
271
1
417
2
-
R
40
6
50
8
50
8
61
0
61
0
-
-
-
X
25
51
Y
38
76
51
76
51
76
51
76
51
76
30
5
30
5
22
9
22
9
THEORY
The discharge theory a parshall flume is given by
Qt = kHan
Where k = a dimensional factor which is a function of throat width (W)
n = exponent which varies between 1.522 and 1.607
Ha = upstream depth measured at the location shown in fig
Qt = theoretical discharge
Table: Values of k, n and head range for different w
W
3″
6″
1′
2′
4′
8′
20′
50′
k
0.1771
0.3812
0.6909
1.428
2.953
6.112
14.45
35.41
n
1.55
1.58
1.522
1.55
1.578
1.607
1.6
1.6
Head range (m)
03-0.33
0.03-0.45
0.03-0.76
0.046-0.76
0.06-0.76
0.076-0.76
0.09-1.83
0.09-1.83
For free flow condition of a parshall flume of 3″ throat width as calibrated empirically (from
Table)
K = 0.1771, n = 1.55
∴ Depth discharge relationship
Qt = 0.1771 Ha1.55
Where Ha in m
Qt in m3/s
The relationship between the theoretical and the actual discharges is given by
Qa = CdQt
(2)
Where, Qa = actual discharge
Cd = co-efficient of discharge.
The percentage of submergence for the Parshall flume is given by 100 Hb/Ha, where Hb is the
downstream depth from the invert datum.
When the percentage of submergence exceeds 0.6 for 3″, 6″, 9″ flumes the flume discharge is
reduced. The discharge of Parshall flume then equals
Where, Qs
Qt
QE
= corrected discharge due to submergence
= theoretical free flow discharge
= correction of discharge as found from the attached figure.
LIMITS OF APPLICATION
a) It should be constructed exactly to the dimensions listed in Table
b) It should be carefully leveled in both longitudinal and transverse
directions.
c) The practical range of heads Ha for each type as listed in Table 3.2 is
recommended as a limit on ha
d) The submergence ratio hb/ha should not exceed 0.90.
OBJECTIVE
i.
ii.
iii.
iv.
To observe the free flow discharge and the effect of submergence.
To determine the value of co-efficient of discharge Cd.
To plot Qa vs. Qt in plain graph paper.
To plot Qa vs. Ha for free flow condition in a log-log paper and to find (a) Cd and (b)
the exponent of Ha.
TYPICAL QUALITATIVE SHAPES OF GRAPHS
Graph 1: Qa vs Qt (Plain graph paper)
Graph 2: Qa vs Ha for free flow condition (log-log paper)
ASSIGNMENT
i.
ii.
iii.
iv.
Draw the qualitative flow profiles showing free flow condition and submerged
condition for the flow through Parshall flume.
Do you find any reason for the sidewall convergence and sudden dip in the bed of the
Parshall flume?
Does the pressure of sediment in the stream affect the performance of the Parshall
flume? Discuss.
State the difference between the working principle and the performance of a weir and
a flume.
DISCUSSION
Comment on the results obtained, sources of error, etc.
Experiment No. 11
FLOW THROUGH A PARSHALL FLUME
Experiment Data Sheet
Throat width, w = _________________
No Volume Time Actual
Free flow
of of
discharge
Ha Theoretical
obs water
Qa
discharge
Qt
Submerged flow
Cd =
Qa/
Qt
Ha
Hb
Submerg Correctio
ence in % n of
100Hb/Ha discharge
QE (Fig.)
1
2
3
4
5
6
7
8
Level/Term
: ______________
Dept. : ____________
Roll No.
: ______________
Section: ____________
Group No.
: ______________
Date
: ____________
Signature of the Teacher
Corrected
discharge
Qs=Qt-Qa
UNIVERSITY OF ASIA PACIFIC
Department of Civil Engineering
Course No: CE 222
Course Title: Hydraulics Lab
MANUAL
Last Update: 17.04.2006