Fluid_Mechanics_Lab_Manual_Acc_TU_Syllab (1).pdf

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Fluid Mechanics Lab Manual (Acc. TU Syllabus)
for Civil Engineering Students
Method · January 2016
DOI: 10.13140/RG.2.2.13865.39524
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Saraswati Thapa
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Kathmandu Engineering Collage
(Affiliated to Tribhuvan University)
Department of Civil Engineering
Kalimati, Kathmandu,Nepal
Lab on Fluid Mechanics
CIVIL - II/I
Prepared By:
Senior Lr./Er. Saraswati Thapa
Lr. /Er. Tirtha Raj Karki
January 27, 2016

Prepared by: Er. /Sl. Saraswati Thapa and Er./ Lr. Tirtha Raj Karki Lecturer, Dept. of Civil Engineering, KEC, Kalimati Page 1
Contents
EXPERIMENT NO: 1 HYDROSTATIC FORCE ON A SUBMERGED SURFACE ..............................2
EXPERIMENT NO: 2 DETERMINATION OF META-CENTRIC HEIGHT OF FLOATING BODY ...7
EXPERIMENT NO: 3 VERIFICATION OF BERNOULLI'S THEOREM............................................12
EXPERIMENT NO: 4 IMPACT OF JET..............................................................................................16
EXPERIMENT NO: 6 FLOW OVER BROAD-CRESTED WEIR.......................................................20

EXPERIMENT NO: 1
HYDROSTATIC FORCE ON A SUBMERGED SURFACE
OBJECTIVE:
The purpose of this experiment is to experimentally locate the center of pressure of a vertical submerged
surface. The experimental measurement is compared with a theoretical prediction.
APPARATUS REQUIRED:
Figure 1 is a sketch of the device used to measure the center of pressure on a submerged vertical surface.
It consists of an annular sector of solid material attached to a balance beam. When the device is properly
balanced the face of the sector that is not attached to the beam is directly below (coplanar) with the pivot
axis. The solid sector and the balance beam are supported above a tank of water.
Figure1: Apparatus for measuring the center of pressure
y
yR
D
CG
CP
Balancing Beam
Balance adjustment

THEORY:
Hydrostatic Pressure on Partially submerged body (P) = ƿgh, where, h = y/β and hydrostatic force acting
on the vertical face of the annular sector is
F = P x A = ƿgh x yb
Center of pressure, yR of the hydrostatic force is
Figure: 2 Diagram of partially submerged vertical face Figure: 3 Diagram of fully submerged
vertical face of annular sector
Figure 3 shows the submerged surface viewed from the left side of the tank in Figure 1. The
depth of the centroid below the surface of the water is h. Center of pressure, yR, is
yR h…………(i)
= ………… (ii)
From equation (i) and (ii)
yR = + h
yR = + h
where, Ixc is the moment of inertia of the surface about the x-axis, and A is the surface area.
The location of the center of pressure can be measured using the apparatus sketched in Figure 1. The
counterweight is adjusted so that the beam is horizontal when there is no water in the tank and no weight
in the pan. When the tank is filled with water the unbalanced hydrostatic force causes the beam to tilt.
Adding weight W to the pan at a distance L from the pivot O exerts a moment WL that counterbalances
the resultant moment due to the hydrostatic forces on the quarter-annulus-shaped body ABPQ. When the
water level is as shown in the figure, there are hydrostatic forces on surfaces AB, BS and AT. Since BS
and AT are concentric cylindrical surfaces with the common axis passing through O, the hydrostatic
forces on BS and AT do not exert any moment about O. As a result WL is equal to the moment due to the
hydrostatic force F acting on the vertical plane surface AB. In this experiment the force F is not measured.
Instead the theoretical value F = ghA is assumed, where h is the depth of the centroid of the surface of
water. The moment due to F is measured and the theoretical value of F is used to compute the location of
the center of pressure.
Balancing the moments about O gives

WL = F (H + yR), where H = (D – y)
Substituting F =ρghA, where A = bd and solving for yR yields
yR = - H
PRACTICAL RELEVANCE:
We can clear about the hydrostatic force acting on the water retaining structure, like: dam, gate,
submerged structure etc.
PROCEDURE:
1. Arrangement of the apparatus is placed on the level surface or table.
2. Measure the dimension of the vertical face (Breadth, b and Depth, d) of annular sector. Similarly
measured vertical height of that object from pivot level to the bottom edge (D) and also measure the
moment arm (L) from pivot to the loaded point.
3. With the apparatus empty, the plane face was made vertical and a preliminary balance was made by
using the empty mass banger and the adjustable screw at the end. In the balanced condition, the
beam has placed in the horizontal position.
4. Now, water is poured into the tank due to the rise of water level which acts hydrostatic force on the
vertical face of the object and the beam was tilted.
5. At this stage, masses were added in the mass arm until balance was restored y and m were
measured.
6. Additional masses were put on the mass arm and water was carefully added or removed to restore
balance.
7. This procedure was repeated for 10 more readings.
OBSERVATION AND CALCULATION:
Moment arm, L =
Breadth of plane face, b =
Depth of plane face, d =
Vertical height of annular sector from pivot to the bottom edge of the vertical plane, D =
Distance between bottom edge of plane below water surface, y
No. of observations Depth of water (y) cm Mass (m) grams
1
2
3
4
5
6
7
8
9
10
11

12
13
14
15
16
17
18
19
20
S.N
Mass
(m)
kg
Depth of
Immersion
(y) from
Waterline
m
Depth
of
water
level to
the
CG(h)
m
Hydro
static
pressu
re(P)
Pa
Hydro
static
Force
(F)
N
C of
P(Z)
From
Water
line
(m)
Th.
Distance
form pivot
to water
surface (H)
m
Moment
(M),
Nm
C of
P(Z)
From
Water
line
(m)
Exp.
Error
% of
C of
P(Z),
Th.&
Exp.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Prepared by: Er./Lr. Saraswati Thapa and Er./ Lr. Tirtha Raj Karki Lecturer, Dept. of Civil Engineering, KEC, Kalimati Page 6
 Hydrostatic Pressure on Partially submerged body (P) = ƿgh, since, h = y/β
 Hydrostatic Pressure on Fully submerged body (P) = ƿgh, since, h = (y - d/2)
 Hydrostatic Force or Pressure force on partially submerged body (F) = ƿgy2
b/2
 Hydrostatic Force or Pressure force on Submerged body (F) = ƿgh*bd
 Centre of pressure in partially submerged body (Z) = , theoretically.
 Centre of pressure in submerged body (Z) = + h, theoretically.
Where, y- Depth of free level water to the bottom edge of vertical plane
h- Depth of free level water to the CG of vertical plane (For Fully Submerged)
h = (y - d/2)
 Distance from the pivot to the free water level, (H) = D-y
 Moment due to load added to balance the beam with respect to pivot (hinge), (M) = WL= (mg) L
 Centre of pressure from water level (Z) = - H, experimentally
RESULT:
CONCLUSION AND DISCUSSION:

EXPERIMENT NO: 2
DETERMINATION OF META-CENTRIC HEIGHT OF FLOATING BODY
OBJECTIVE:
To experimentally determine the metacentric heights of Floating body with different conditions of
loadings and compare them with the values computed by theoretical (Analytical methods) formulas.
APPARATUS REQUIRED:
The experimental setup consists of a water tank for floating the experimental boat. The boat is provided
with a weight on a central mast. The position of C.G. can be located by means of a knife edge assembly.
The size of boat can be measured by a ruler.
Figure:Boat Figure:Water Tank with Boat
Figure: Boat L-Section (Dimension in cm)

THEORY:
The determination of metacentric height is important while investigating the stability of the floating
bodies such as ships, during the design phase by theoretical computations and after the ship have been
built by inclining experiments.
(a). Analytical method
An object with water line AC, B as the Centre of
Buoyancy(CB) and G as the Centre of Gravity in
original position. When the vessel is tilted
through a small angle θ, the CB changes from B
to B’, the position of water line changes to ED
and two wedges AOE and COD are formed. M
is the metacenter, W is the weight of object and
FB is the buoyant force.
Where, I- Moment of inertia of plan of object
=
L-Length of boat
B-Width of boat
V- Immersed volume of object OR
Displaced volume of water
Where, w1- weight of boat
w- Weight of applied load
Then, GM = BM – BG
– BG
Where, GM- Metacentric height
M
(b).Experimental method
The metacentric height GM
of a floating object is
determined by equating the
moment due to the shifting of
a small lateral weight and the
moment created due to the
shifting of the position of the
combined center of gravity of
the pontoon and the lateral
weight.
M X
P
a) Equilibrium condition b) Tilted condition
GM = ……………………. (i)
Where, GM = Metacentric Height
w = lateral weight
θ
G
G � G’
θ
FB =W
G
B B’
O
C
D
A
E

X = lateral displacement
W = combined weight of pontoon plus lateral weight
 = angle of tilt for displacement x
L= length of boat
B= Width of boat
This experiment clears that the metacentre of floating body always lies above the centre of gravity to
regain in the original position. And the inclination of floating body in water surface should be limited
angle for its stability.
PROCEDURE:
1. Record the exact dimensions (width, length, and height) of the boat with the help of ruler.
2. Fill the tank 2/3 with clean water and ensure that no foreign particles are there.
3. Weight the boat model to find w1 .
4. Float the ship model in water and ensure that it is stable equilibrium.
5. Apply the known weight (w) at the centre of model.
6. Give the model a small angular displacement in clockwise or anti-clockwise direction by moving
the applied weight small distance away from centre either right or left side.
7. Measure the distance moved by the weight applied with the help of scale.
8. Repeat the experiment for different weights.
OBSERVATIONS & CALCULATIOS:
OBSERVATIONS:
Weight of boat, w1 = ……….. gm
S. No. Lateral weight, w(gm)
Left or Right
X(cm) 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

CALCULATION:
Weight of boat (w1) =
Moment of Inertia of plan of object, (I) =
Distance between centre of Gravity and Buoyancy of boat (BG) =
Density of water (ρwater) =
Specific weight of water ( water) =
Combined Weight, (W) = (w1 + w) =
Experimental Method Analytical Method
S.
No.
Lateral
weight,
w(kg)
Combined
Weight,
W(kg)
Distance X
(cm)
Average
Tilt()
degree
Meta-centric
Height
(GM),(cm)
Immersed
Volume
(V),(cm3
)
Meta-
centric
Height
(GM),(cm)
1
2
3
4
5
6
7
8
9
10
and
so
on

RESULT:

EXPERIMENT NO: 3
VERIFICATION OF BERNOULLI'S THEOREM
OBJECTIVE:
To verify the Bernoulli’s theorem.
APPARATUS REQUIRED:
A supply tank of water, a set of different diameters pipe fitted with manometer tube at two points,
discharge measuring tank, scale, and stop watch.
THEORY:
Bernoulli’s theorem states that when there is a continues connection between the particle of
flowing mass liquid, the total energy of any sector of flow will remain same provided there is no
reduction or addition at any point.
Formula Used:-
H1 = Z1 + p1/ɤ + V1
2/2g
H2 = Z2 + p2/ɤ + V2
2/2g
Where, H1= H2 = total energy head
Z1 + p1/ɤ + V1
2/2g = Z2 + p2/ɤ + V2
2/2g + HL
Where, HL= Total Head Loss (=hf)
hf=frictional head loss neglecting minor losses
For Given Instrument set up
Z1=Z2
V1
2
/2g = V2
2
/2g, (If flow through constant diameter pipe)
p1/ɤ -p2/ɤ = HL
PROCEDURE:
1. Open the inlet valve slowly and allow the water to flow from the supply tank.
2. Now adjust the flow to get a constant head in the supply tank to make flow in and out flow equal.
3. Note down the quantity of water collected in the measuring tank for a given interval of time.
4. Compute the area of cross-section connected to the manometer.
5. Change the inlet and outlet supply and note the reading.
6. Take at least three readings as described in the above steps.

It helps to illustrate the importance and usefulness of Bernoulli’s equation for real fluids including energy
losses. The validity of total of energy losses proposed and the expanded Bernoulli’s equation.
Discharge calculation
Width of tank, B=
Length of Tank, L=
Area of Tank, A =B*L=………… (cm2
)
For First Pipe of Diameter, D1=
Initial
Heighth,H1(cm)
Final
Height,H2(cm)
Time Interval
(T)sec
Height
Difference
H=H2-H1(cm)
Volume=
A*H (cm3
)
Discharge
Q=
V/T(cm3
/sec)
Manometer Reading (p1/ɤ -p2/ɤ)
Pipe Diameter ,D1= (p1/ɤ -p2/ɤ)= HL Remarks
Q1=
Q2=
Q3=
Q4=
Q5=
For Second Pipe of Diameter, D2=
Initial
Heighth,H1(cm)
Final
Height,H2(cm)
Time Interval
(T)sec
Height
Difference
H=H2-H1(cm)
Volume=
A*H (cm3
)
Discharge
Q=
V/T(cm3
/sec)
Pipe Diameter ,D2= (p1/ɤ -p2/ɤ)= HL Remarks
Q1=
Q2=

Q3=
Q4=
Q5=
For Third Pipe of Diameter, D3=
Initial
Heighth,H1(cm)
Final
Height,H2(cm)
Time Interval
(T)sec
Height
Difference
H=H2-H1(cm)
Volume=
A*H (cm3
)
Discharge
Q=
V/T(cm3
/sec)
Pipe Diameter ,D3 = (p1/ɤ -p2/ɤ)= HL Remarks
Q1=
Q2=
Q3=
Q4=
Q5=

RESULT:

EXPERIMENT NO: 4
IMPACT OF JET
OBJECTIVE:
To determine the coefficient of impact for vanes (flat and curved) and compare with theoretical value.
APPARATUS REQUIRED:
Collecting tank, transparent cylinder, nozzle of diameter 10 mm and vane of different shape (flat and
curved)
THEORY:
Momentum equation is based on Newton’s second law of motion which states that the algebraic sum of
external forces applied to control volume of fluid in any direction is equal to the rate of change of
momentum in that direction. The external forces include the component of the weight of the fluid & of
the forces exerted externally upon the boundary surface of the control volume.
If a vertical water jet moving with velocity is made to strike a target, which is free to move in the
vertical direction then a force will be exerted on the target by the and impact of jet, according to
momentum equation this force (which is also equal to the force required to bring back the target in its
original position) must be equal to the rate of change of momentum of the jet flow in that direction.
Figure1: Impact of jet on curve plate axis vertical
Balancing Weight
1. Nozzle
2. Direction of Velocity before impact
3. Direction of Velocity after impact
4. CV- curve vane

Figure 2: Illustrative figure of impact of jet apparatus
Formula Used:-
F'=ρ Q V (1-cos )
F'=ρ QV (1-cos ) , as v=Q/a
Where F' =force (calculated)
ρ = density of water
=angle of difference vane
V =velocity of jet angle
Q =discharge
A =area of nozzle (πd2/4)
(i) For flat vane =90o
F' = ρ QV= ρ Q2/a
(ii) For hemispherical vane =180o
F' = βρ QV= 2 ρ Q2/a
F = Force (due to putting of weight)
For % error = (F- F')/ F'x10

PROCEDURE:
1. Note down the relevant dimension or area of collecting tank, dia of nozzle, and density of water.
2. Install any type of vane i.e. flat or curved.
3. Install any size of nozzle i.e. 10mm or 12mm dia.
4. Note down the position of upper disk, when jet is not running.
5 Note down the reading of height of water in the collecting tank.
6. As the jet strike the vane, position of upper disk is changed, note the reading in the
scale to which vane is raised.
7. Put the weight of various values one by one to bring the vane to its initial position.
8. At this position finds out the discharge also.
9. The procedure is repeated for each value of flow rate by reducing the water supply.
10. This procedure can be repeated for different type of vanes and nozzle.
It helps to illustrate the momentum principle used to convert the rate of change of momentum into force.
And also help to understand the concept of electricity energy is generation through hydropower.
Dia of nozzle = 10mm
Mass density of water ρ = 1000kg/mβ
Area of collecting tank =
Area of nozzle =
Horizontal flat vane
When jet is not running, position of upper disk is at =
S.N.
Discharge measurement Balancing Theoretical Force
F'=
ρ Q2
/a (dyne)
Error in %
= (F-F')/F'
Initial
(cm)
Final
(cm)
Time
(sec)
Discharge
(cm3/sec) Q
Mass,
W (gm)
Force
F (dyne)
1.
2.
3.
4.
5.
Curved hemispherical vane
When jet is not running, position of upper disk is at =
S.N.
Discharge measurement Balancing Theoretical Force
F'= βρQ2
/a (dyne)
Error in %
= (F-F')/F'
Initial
(cm)
Final
(cm)
Time
(sec)
Discharge
(cm3/sec) Q
Mass W
(gm)
Force
F (dyne)
1.
2.
3.
4.
5.

RESULT:

EXPERIMENT NO: 6
FLOW OVER BROAD-CRESTED WEIR
OBJECTIVE:
To determine the coefficient of discharge of broad- crested weir
APPARATUS REQUIRED:
Arrangement for finding the coefficient of discharge inclusive of supply tank, collecting tank, pointer
gauge, scale & different type of notches
THEORY:
A broad-crested weir is a weir with a crest, which is sufficiently wide to prevent the jet from
springing clear at the upstream corner. There are many different profiles in use; in the present case
we consider a simple rectangular block with a rounded upstream corner, placed in a horizontal
channel with unrestricted flow downstream. The acceleration of the water as it flows on to the weir
crest causes a reduction in surface level. Along the crest, the fall in level continues (to an extent
determined by the weir height and breadth in relation to the water depth in the channel) until it drops
over the downstream corner. There is a region of re circulating flow behind the drop, as indicated in
Figure (a), before the flow settles down to more or less uniform conditions some distance
downstream of the weir.
Flow over the broad-crested weir is shown in Figure (a). For the purpose of a simple analysis, the
conditions illustrated in Figure (b) are assumed. The motion is taken to have uniform velocity Vi
in the approaching stream, and to flow at uniform depth y and uniform velocity V along the crest.
(a) General characteristics of flow
(b) Idealized conditions assumed in analysis

(c) Flow over the broad-crested weir
Let H = height of water above crest, L = Length of crest, h =height of water at the middle of weir which is
constant, v = velocity of flow over weir
Applying Bernoulli’s equation to the still water surface on the upstream side and running water at the end
of the weir
Z1 = Z2, V1 = 0, , V2 = v Substituting these values
then √
Discharge over weir = Cd x Area of flow x velocity
√ √
Finding maximum discharge
Q will be maximum if is maximum
It gives
Substituting the value of h,
Formula Used: For Broad crested weir
Where,
Q = Discharge
H =Height above crest level
L = Width of weir
v
h
H

The weir can be used for flow measurement using a single measurement of upstream water height the
from the weir crest level (H).
PROCEDURE:
1. Set the channel slope to horizontal.
2. Measure and record the height of the weir using calipers.
3. Set the broad-crested weir carefully in position such that center of the weir will be at a station
approximately 2 m from upstream of the channel.
4. Before starting the experiment observe the general characteristics of the water surface profile,
which may be produced in the flume by steadily changing the discharge using the control valve.
5. Measure and record the discharge by using gravimetric tank.
6. Measure and record the upstream depth yc at 20 cm from the middle of the broad crested weir.
7. Measure and record the critical depth yc at the center of the broad crested weir.
8. Change the discharge and repeat the steps 5-7 for seven more times for different discharges.
OBSERVATIONS AND CALCULATION:
For Discharge computation
Breath of tank, B t = 0. 6 m
Length of tank, L t = 0.6 m
Area of tank A = L t*B t= 0.36 m2
Height of water above the broad crested weir is, H
Width of Rectangular weir, L = 0.33m
Weir height, d = 0.115 m
S.N.
For Discharge Computation
Q=V/t
(m3/se
c)
Static
head
above
weir ,h
Total
Head
above
crest
level, H
(2/3)H
Initial
height of
tank, a
(cm)
Final
height of
tank, b
(cm)
Differenc
e In
height=b-
a (cm)
Volume
V= A*(b-
a) *10-4
m3
Time of
flow, t
Cd = H/d h/d
1.
2.
3.
4.
5.

RESULT:
Plot the graph
a) H and h vs Q,
b) H/d and h/d vs Cd
(Discussion: How the discharge coefficient changes with increasing upstream depth and flow discharge.
Based on head to weir depth ratio vs. discharge coefficient plot how does the importance of the velocity
head on discharge coefficient calculation changes as the ratio of head to weir height h/d increases.
The value of the coefficient of discharge, Cd, which relates discharge Q to static head, h has been found
to exceed unity.)
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