FLUID MECHANICS - darshan.ac.in€¦Lab Manual 3rd Sem Civil ... Experiment Start Date End Date Sign Remark 1. To validate Bernoulli’s Theorem as applied to ... Pitot tube. 3

Department of Mechanical Engineering

Darshan Institute of Engineering & Technology, Rajkot

FLUID MECHANICS Lab Manual

3rd Sem Civil Engineering

Darshan Institute of Engineering & Technology

Certificate

This is to certify that Mr./Ms.____________________________________

Enrollment No. ________________Branch_____________________________

Semester 3rd has satisfactory completed the course in the subject Fluid

Mechanics in this institute.

Date of Submission: - ___ / ___ / ______

____________ _________________

Staff in Charge Head of Department

DARSHAN INSTITUTE OF ENGINEERING AND

TECHNOLOGY, RAJKOT

FLUID MECHANICS

Sr.

No. Experiment Start Date End Date Sign Remark

1. To validate Bernoulli’s Theorem as applied to

the flow of water in a tapering circular duct.

2. To study and measure velocity of flow using

Pitot tube.

3. To calibrate the given Rectangular, Triangular

and Trapezoidal Notches.

4. To determine the Metacentric height of a given

floating body.

5. To calibrate and study Venturimeter.

6. To calibrate and study Orifice meter.

7. To calibrate and study Nozzle meter.

8 To calibrate and study Rota meter.

9 To study pressure and pressure measurement

devices.

10 To study Laminar and Turbulent Flow and It’s

visualization on Reynolds’s Apparatus.

Bernoulli’s Theorem

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Fluid Mechanics


Darshan Institute of Engineering & Technology, Rajkot. 1-1

Date: ___ /___ /______

EXPERIMENT NO. 1

Objective

To validate Bernoulli’s Theorem as applied to the flow of water in a tapering circular duct.

Introduction

Bernoulli's principle is named after the Dutch-Swiss mathematician Daniel Bernoulli who

published his principle in his book Hydrodynamica in 1738.

Bernoulli’s principle in its simplest form states that "the pressure of a fluid [liquid or gas]

decreases as the speed of the fluid increases." The principle behind Bernoulli’s theorem is the

law of conservation of energy. It states that energy can be neither created nor destroyed, but

merely changed from one form to another.

The energy, in general, may be defined as the capacity to do work. Though the energy exists

in many forms, yet the following are important from the subject point of view:

1. Potential Energy

2. Kinetic Energy and

3. Pressure Energy

Potential energy of a Liquid in Motion

It is the energy possessed by a liquid particle, by virtue of its position. If a liquid particle is Z

meters above the horizontal datum (arbitrary chosen), the potential energy of the particle will

be Z meter-kilogram (briefly written as mkg) per kg of liquid. Potential head of the liquid, at

that point, will be Z meters of the liquid.

Kinetic Energy of a liquid Particle in Motion

It is the energy, possessed by a liquid particle, by virtue of its motion or velocity. If a liquid

particle is flowing with a mean velocity of v meter per second, then the kinetic energy of the

particle will be v2/2g meter of the liquid. Velocity head of the liquid, at that velocity, will be

v2/2g meter of liquid.

Pressure Energy of a liquid Particle in Motion

It is the energy, possessed by a liquid particle, by virtue of its existing pressure. If a liquid

particle is under a pressure of p kg/m2, then the pressure energy of the particle will be p/w


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Fluid Mechanics



mkg per kg of liquid, where w is the specific weight of the liquid. Pressure head of the liquid

under that pressure will be p/w meter of the liquid.

Total Energy of a liquid Particle in Motion

The total energy of a liquid particle, in motion, is the sum of its potential energy, kinetic

energy and pressure energy. Mathematically,

Total Energy, E = P

w+

v2

2g+ Z in

m kg

kg of liquid

Bernoulli’s Equation

It states, “For a perfect incompressible liquid, flowing in a continuous stream, the total

energy of a particle remains the same; while the particle moves from one point to another.”

This statement is based on the assumption that there are no losses due to friction in pipe.

Mathematically,

Total Energy, E = P

w+

v2

2g+ Z = Constant

Apparatus Description

The apparatus is made from transparent acrylic and has both the convergent and divergent

sections. Water is supplied from the constant head tank attached to the test section. Constant

level is maintained in the supply tank. Piezometric tubes are attached at different distance on

the test section. Water discharges to the discharge tank attached at the far end of the test

section and from there it goes to the measuring tank through valve. The entire setup is

mounted on a stand.

Experimental Procedure

1. Note down the area of cross-section of the conduit at sections where piezometers have

been fixed.

2. Open the supply valve and adjust the flow in the conduit so that the water level in the

inlet tank remains at a constant level (i.e., the flow becomes steady)

3. Measure the height of water level (above an arbitrarily selected suitable horizontal

plane) in different piezometer tubes.

4. Measure the discharge by calculating time taken for L liters flow.

5. Repeat steps (2) to (4) for other discharges.


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Observation Table

Piezometer tube number 1 2 3 4 5

Area of cross-section, A

Distance of piezometer from

tank

Run No.1

Discharge

Q1 = L/ t

V=Q/A

V2/2g

(p/ρg) + z

E

Run No.1

Discharge

Q2 = L/ t

V=Q/A

V2/2g

(p/ρg) + z

E

Run No.1

Discharge

Q3 = L/ t

V=Q/A

V2/2g

(p/ρg) + z

E

Plot the following on an ordinary graph paper for all the runs taken.

1. {(p

ρg) + 𝑧} V/s distance (x) of piezometer tubes from some reference point.

Draw a smooth curve passing through the plotted points. This is known as the

hydraulic gradient line.

2. E = {(p

ρg) + z +

V2

2g} V/s distance (x) of piezometer tubes on the graph {(p/ρg) +

z} v/s distance. Draw a smooth curve passing through the plotted points. This is the

total energy line.

Conclusion

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….


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Fluid Mechanics



NOTES:

Pitot Tube

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Fluid Mechanics


Darshan Institute of Engineering & Technology, Rajkot.

2-1

Date: ___ /___ /______

EXPERIMENT NO. 2

Objective

To study and measure velocity of flow using Pitot tube

Introduction

A Pitot tube is a pressure measurement instrument used to measure fluid flow velocity. The

pitot tube was invented by the French engineer Henri Pitot in the early 1700s and was

modified to its modern form in the mid 1800s by French scientist Henry Darcy. It is widely

used to determine the airspeed of an aircraft and to measure air and gas velocities in industrial

applications.

The basic pitot tube consists of a tube pointing directly into the fluid flow. As this tube

contains fluid, a pressure can be measured; the moving fluid is brought to rest (stagnates) as

there is no outlet to allow flow to continue. This pressure is the stagnation pressure of the

fluid, also known as the total pressure or (particularly in aviation) the pitot pressure.

The measured stagnation pressure cannot of itself be used to determine the fluid velocity

(airspeed in aviation). However, Bernoulli's equation states:

Stagnation pressure = static pressure + dynamic pressure

Mathematically this can also be written:

Pt = PS + (V2

2g)

Solving that for velocity we get:

𝑉 = √2𝑔 (𝑃𝑡 − 𝑃𝑠)

Where, V is fluid velocity

Pt is stagnation or total pressure

Ps is static pressure;

Pitot Tube

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2-2

The dynamic pressure, then, is the difference between the stagnation pressure and the static

pressure.


The setup consist of simple clear Perspex channel with two tube each to measure static and

stagnation pressure of the fluid in the channel. Channel is supplied water with the help of

tank and the flow is controlled by a gate valve.

Scale is imprinted next to the tube to measure the pressure heads.


1. Switch on the pump and feel the tank that supplies water to the pitot apparatus.

2. Now slowly open the pitot outlet valve so that channel is filled completely with water

3. Observe and note down the pressure heads reading in m of water

4. Calculate time for discharge for known quantity of water

5. Calculate and compare theoretical and actual velocities

Observations Table

Area of flow Channel = 0.03 m

Sr. No. Pt (m) Ps (m) (Pt-Ps) (m) Vpitot m/s Time s Q m3/s Vmeasured m/s

1

2

3

4

5

Calculations

Area of flow Channel = 0.03 m2

𝑉 = √2𝑔 (𝑃𝑡 − 𝑃𝑠)

Conclusion

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….

Notches

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3-1

Date: ___ /___ /______

EXPERIMENT NO. 3

Objective

To calibrate the given Rectangular, Triangular and Trapezoidal Notches

Introduction

Measurement of flow in open channel is essential for better management of supplies of water.

Hydraulic structures such as weirs are emplaced in the channel. They are used to determine

the discharge indirectly from measurements of the flow depth.

A notch is an opening in the side of a measuring tank or reservoir extending above the free

surface. A weir is a notch on a large scale, used, for the measurement of discharge in free

surface flows like a river. A weir is an orifice placed at the water surface so that the head on

its upper edge is zero. Hence, the upper edge can be eliminated, leaving only the lower edge

named as weir crest. A weir can be of different shapes - rectangular, triangular, trapezoidal

etc. A triangular weir is particularly suited for measurement of small discharges.

Rectangular Notch

The discharge over an unsubmerged rectangular sharp-crested notch is defined as:

Q = 2

3 Cd. L. √2g H

32

\

Rectangular notch

Triangular Notch

The rate of flow over a triangular weir mainly depends on the head H, relative to the crest of

the notch; measured upstream at a distance about 3 to 4 times H from the crest. For triangular

notch with apex angle , the rate of flow Q is obtained from the equation,

Q = 8

15 Cd √2g tan

θ

2 H

52

Notches

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3-2

Here, Cd is termed the coefficient of discharge of triangular notch

Triangular Notch

Trapezoidal Notch

Also known as Cipolletti weirs are trapezoidal with 1:4 slopes to compensate for end

contraction losses. The equation generally accepted for computing the discharge through an

unsubmerged sharp-crested Cipolletti weir with complete contraction is:

Q = 1.84. Cd. L. H32

Where, Q = Discharge over notch (m3/sec)

L = Bottom of notch width

H = Head above bottom of opening in meter

Trapezoidal notch


The pump sucks the water from the sump tank, and discharges it to a small flow channel. The

notch is fitted at the end of channel. All the notches and weirs are interchangeable. The water

flowing over the notch falls in the collector. Water coming from the collector is directed to

the measuring tank for the measurement of flow.

The following notches are provided with the apparatus:

1. Rectangular notch (Crest length L = 0.050m)

2. Triangular notch (Notch Angle – 600)

3. Trapezoidal notch (Crest length L = 0.075m; Slope = 4V:1H)

Notches

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3-3

(1) (2) (3)

Experimental Procedure:

1. Fit the required notch in the flow channel.

2. Fill up the water in the sump tank.

3. Open the water supply gate valve to the channel and fill up the water in the channel

up to sill level.

4. Take down the initial reading of the crest level (sill level)

5. Now start the pump and open the gate valve slowly so that water starts flowing over

the notch

6. Let the water level become stable and note down the height of water surface at the

upstream side by the sliding depth gauge.

7. Close the drain valve of measuring tank, and measure the discharge.

8. Take the reading for different flow rates.

9. Repeat the same procedure for other notch also.

Observations:

Notch Type: Triangular

Sr.

No.

Still level reading ‘s’

in meters

Water height on upstream side ‘h’

in meters

Discharge time for L liters ‘t’

in second

1

2

3

4

5

6

Notches

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3-4

Notch Type: Rectangular

Sr.

No.


in meters


in meters


in second

1

2

3

4

5

6

Notch Type: Trapezoidal

Sr.

No.


in meters


in meters


in second

1

2

3

4

5

6

Calculations:

Rectangular Notch

1. Head over the notch, H = (h − s) in meter

2. Actual Discharge , Qact = L

t in m3/sec

3. Crest length of notch = 0.05 m

4. Theoretical discharg, Qth = 2

3 L. √2g H

3

2 in m3/sec

5. Coefficient of discharge Cd = Qact

Qth

Triangular notch


Notches

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3-5

2. Actual Discharge , 𝑄𝑎𝑐𝑡 = 0.01

𝑡 𝑖𝑛 𝑚3/𝑠𝑒𝑐


4. Theoretical discharg, Qth = 8

15 √2g tan

60

2 H

5

2 in m3/sec


Qth

Trapezoidal Notch (or Cipolletti Weir)


2. Actual Discharge , 𝑄𝑎𝑐𝑡 = 0.01

𝑡 𝑖𝑛 𝑚3/𝑠𝑒𝑐


4. Theoretical discharg, Qth = 1.84. L. H3

2 in m3/sec


Qth

Calculation:

Notches

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3-6

Conclusion:

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….

Metacentre

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Fluid Mechanics



4-1

Date: ___ /___ /______

EXPERIMENT NO. 4

Objective

To determine the Metacentric height of a given floating body.

Introduction

Buoyancy

When a body is completely submerged in a fluid, or it is floating or partially submerged, the

resultant fluid force acting on the body is called the buoyant force. It is also known as the net

upward vertical force acting on the body. A net upward vertical force results because pressure

increases with depth and the pressure forces acting from below are larger than the pressure

forces acting above.

The Center of buoyancy is the center of gravity of the displaced water. It lies at the geometric

center of volume of the displaced water.

Metacentre

For the investigation of stability of floating body, it is necessary to determine the position of

its metacentre with respect to its centre of gravity. Consider a floating ship model, the weight

of the ship acts through its centre of gravity and is balanced by an equal and opposite buoyant

force acting upwards through the centre of buoyancy i.e. the centre of gravity of liquid

displaced by the floating body.

A small angular displacement shifts the centre of buoyancy and the intersection of the line of

action of the buoyant force passing through the new centre of buoyancy and the extended line

would give the metacentre.

The distance between centre of gravity (G) and metacentre (M) is known as Metacentric

height (GM).

Metacentre

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4-2

There are three conditions of equilibrium of a floating body

1. Stable Equilibrium - Metacentre lies above the centre of gravity

2. Unstable Equilibrium- Metacentre lies below the centre of gravity

3. Neutral Equilibrium - Metacentre coincides with centre of gravity

The Metacentric height (GM) is given by

GM = (m x X)

(W x tanθ)

Where, W = weight of the floating body

m = movable weight

X = distance through which the movable load is shifted

= Angle of Heel


The apparatus consist of a SS tank and is provided with a drain cock. The floating body is

made from Clear Transparent Acrylic. It is provided with movable weights, protractor to

measure the angle of Heel and pointer. Weights are also provided to increase the weight of

floating body by known amount.


1. Fill the SS tank to about 2/3 levels

2. Place the floating body in the tank.

3. Apply momentum to the floating body by moving one of the adjustable weights (m)

through a known distance.

4. Note down the angle of heel corresponding to this shifts of weight with the help of

protractor and pointer.

5. Take about 4-5 such readings by changing the position of the adjustable weight and

find out centre of gravity in each case

Observation Table:

Weight of the ship model = 1.5 X 9.81 = 14.715 N

Given Movable Weights = 100 gm; 50 gm

= 0.981 N; 0.490 N

Metacentre

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4-3

Sr.

No.

Movable Weight

(m) N

Distance moved

(X) M

Angle of

Tilt Tan

Metacentric Height

GM M

1

2

3

4

5

Calculations

Metacentric height GM = (m x X)

(W x tanθ)

Conclusion

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….

Metacentre

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4-4

NOTES:

Venturi Meter

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5-1

Date: ___ /___ /______

EXPERIMENT NO. 5

Objective

To calibrate and study Venturimeter

Introduction

The most important class of flow meter is that in which the flow is either accelerated or

retarded at the measuring sections by reducing the flow area, and the change in the kinetic

energy is measuring sections by reducing the flow area and the change in the kinetic energy is

measured by recording the pressure difference produced. This class includes Venturimeter

Venturi Meter

Venturimeter is used for the measurement of discharge in a pipeline. Since head loss caused

due to installation of venturi meter in a pipeline is less than that caused due to installation of

orficemeter, the former is usually preferred particularly for higher flow rates. A venturimeter

consists of a converging tube which is followed by a diverging tube. The junction of the two

is termed as 'throat' which is the section of minimum cross-section.

Venturi Meter


Venturimeter is mounted along a pipeline with sufficient distance to stabilize flow between

two meters. The pressure taps are provided at sections as given in the fig. Pressure head

difference between sections can be read on manometer having mercury as the manometer

fluid. A valve, fitted at the end of the pipeline, is used for regulating the discharge in the

pipeline.

Venturi Meter

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Fluid Mechanics



5-2

Technical Specifications

Venturimeter Size = 26 mm

Throat Size = 16 mm

Dia Ratio = 0.6


1. Fill the storage tank/sump with the water.

2. Switch on the pump and keep the control valve fully open and close the bypass valve

to have maximum flow rate through the meter.

3. Open control valve of the venturimeter.

4. Open the vent cocks provided at the top of the manometer to drive out the air from the

manometer limbs and close both of them as soon as water start coming out.

5. Note down the difference of level of mercury in the manometer limbs.

6. Keep the drain valve of the collection tank closed till its time to start collecting the

water.

7. Close the drain valve of the collection tank and note down the initial level of the water

in the collection tank.

8. Collect known quantity of water in the collection tank and note down the time

required for the same.

9. Change the flow rate of water through the meter with the help of control valve and

repeat the above procedure.

10. Take about 2-3 readings for different flow rates.

Observations

For Venturimeter, Diameter at inlet D1 = 26 mm; Area A1 = 5.31 x 10-4 m2

Diameter at throat D2 = 16 mm; Area A2 = 2.01 x 10-4 m2

Sr. No Manometer Difference In mm of Hg Flow rate (time for 10 lit) t in sec

1

2

3

4

5

Venturi Meter

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Fluid Mechanics



5-3

Calculations

Actual Discharge,

Qact =0.01

time required to collect 10 ltrs of water in m3/sec

As per theory,

∴ Qact =Cd. a2√2g(h1 − h2)

√1 − (a2

a1)

2

Before Substituting Values of Qact and (h1 – h2) into the above equation, it will simpler to

establish the value of

= a2√2g

√1 − (a2

a1)

2= =

2.0096 x 10−4√2x9.81

√1 − 0.3782= 9.65 x 10−4

∴ Qact = Cd x 9.65x 10−4x √(h1 − h2)

∴ Cd = 1036.26 x Qact

√(h1 − h2)

Put the values of Q and (h1 - h2) from observations

Cd = …………..

Venturi Meter

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5-4

Conclusion

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….

Orifice Meter

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Fluid Mechanics



6-1

Date: ___ /___ /______

EXPERIMENT NO. 6

Objective

To calibrate and study Orifice meter

Introduction




measured by recording the pressure difference produced. This class includes orifice meter.

Orifice Meter

A circular Opening in a plate which is fitted suitably in a pipeline is a simple device to

measure the discharge flowing in the pipeline. Such a device is known as orifice meter and is

as shown in the figure. the opening is normally at the centre of the plate as shown in figure.

Applying Bernoulli's equation between section 1 and 2 and using continuity equation, it can

be shown that,

∴ Qact =Cd. a2√2g(h1 − h2)

√1 − (a2

a1)

2

Where, A2 = Area of cross section of the orifice

(h1 – h2) = Difference in the piezometeric heads at section 1 and 2

Simple orifice meter


Orifice meter is mounted along a pipeline with sufficient distance to stabilize flow between




pipeline.

Orifice Meter

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Fluid Mechanics



6-2


Orifice meter: Size = 26 mm

Orifice Size = 16 mm

Dia Ratio = 0.6





3. Open control valve of the orifice meter.




6. Keep the drain valve of the collection tank closed till it’s time to start collecting the

water.








Observations

For Orifice meter: Diameter at inlet D1= 26 mm; Area A1 = 5.31 x 10-4 m2

Diameter at orifice D2 = 16 mm; Area A2 = 2.01 x 10-4 m2

Sr. No Manometer Difference In mm of Hg Flow rate (time for L liters) t in sec

1

2

3

4

5

Orifice Meter

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Fluid Mechanics



6-3

Calculations

Actual Discharge,

Qact =L

time required to collect L ltrs of water in m3/sec

As per theory,

∴ Qth =Cd. a2√2g(h1 − h2)

√1 − (a2

a1)

2



= a2√2g

√1 − (a2

a1)

2= =

2.0096 x 10−4√2x9.81

√1 − 0.3782= 9.65 x 10−4

∴ Qact = Cd x 9.65x 10−4x √(h1 − h2)

∴ Cd = 1036.26 x Qact

√(h1 − h2)


Cd = …………..

Orifice Meter

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6-4

Conclusion:

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….

Nozzle Meter

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Fluid Mechanics



7-1

Date: ___ /___ /______

EXPERIMENT NO. 7

Objective

To calibrate and study Nozzle meter

Introduction




measured by recording the pressure difference produced. This class includes Nozzle meter.

Nozzle Meter

The flow nozzle is a venturimeter that has been simplified and shortened by eliminating the

gradual downstream expansion. The streamlined entrance of the nozzle causes a straight jet

without contraction, so its effective discharge coefficient is nearly the same as the

venturimeter. Flow nozzles allow the jet to expand of its own accord.

The flow nozzle costs less than venturimeter. It has the disadvantage that the overall losses

are much higher because of the lack of guidance of the jet downstream from the nozzle

opening.

Simple nozzle meter


Nozzle meter is mounted along a pipeline with sufficient distance to stabilize flow between




pipeline.

Nozzle Meter

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Fluid Mechanics



7-2


Nozzle meter: Size = 26 mm

Nozzle Size = 16 mm

Dia Ratio = 0.6





3. Open control valve of the nozzle meter.




6. Keep the drain valve of the collection tank closed till it’s time to start collecting the

water.








Observations

For Nozzle meter: Diameter at inlet D1= 26 mm; Area A1 = 5.31 x 10-4 m2

Diameter at orifice D2 = 16 mm; Area A2 = 2.01 x 10-4 m2

Sr. No Manometer Difference In mm of Hg Flow rate (time for 10 lit) t in sec

1

2

3

4

5

Nozzle Meter

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Fluid Mechanics



7-3

Calculations

Actual Discharge,

Qact =0.01

time required to collect 10 ltrs of water in m3/sec

As per theory,

∴ Qth =Cd. a2√2g(h1 − h2)

√1 − (a2

a1)

2



= a2√2g

√1 − (a2

a1)

2= =

2.0096 x 10−4√2x9.81

√1 − 0.3782= 9.65 x 10−4

∴ Qact = Cd x 9.65x 10−4x √(h1 − h2)

∴ Cd = 1036.26 x Qact

√(h1 − h2)


Cd = …………..

Nozzle Meter

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Fluid Mechanics



7-4

Conclusion

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….

Rota meter

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Fluid Mechanics



8-1

Date: ___ /___ /______

EXPERIMENT NO. 8

Objective

To calibrate and study Rota meter

Introduction




measured by recording the pressure difference produced. This class includes rotameter.

Rotameter

The rotameter is an industrial flow meter used to measure the flow rate of liquids and gases.

The rotameter consists of a tube and float. The float response to flow rate changes is linear.

The rotameter is popular because it has a linear scale, a relatively long measurement range,

and low pressure drop. It is simple to install and maintain.

The rotameter's operation is based on the variable area principle: fluid flow raises a float in a

tapered tube, increasing the area for passage of the fluid. The greater the flow, the higher the

float is raised. The height of the float is directly proportional to the flow rate. With liquids,

the float is raised by a combination of the buoyancy of the liquid and the velocity head of the

fluid. With gases, buoyancy is negligible, and the float responds to the velocity head alone.

Rota meter


Rota meter is mounted along a pipeline with sufficient distance to stabilize flow between two

meters. The pressure taps are provided at sections as given in the fig. Pressure head

S= Flow Force

A = Buoyancy

G= Gravity

Force

Rota meter

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Fluid Mechanics



8-2



pipeline.


Rota meter: Size = 1- 1000 LPH

Type = Thread Ends





3. Verify the rotameter readings flow marking provided by manufacturer.


Observations

Sr. No Rota meter Scale (in LPH) Flow rate (time for 10 lit) t in sec

1

2

3

4

5

Calculations:

Actual discharge,

Qact =L

time required to collect L ltrs of water in m3/sec

Discharge in LPH = Qact x 60000

Rota meter

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8-3

Conclusion

………………………………………………………………………………………………….

…………………………………………………………………………………………………..

………………………………………………………………………………………………….

Rota meter

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Fluid Mechanics



8-4

NOTES:

Pressure Measurement

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Fluid Mechanics



9-1

Date: ___ /___ /______

EXPERIMENT NO. 9

Objective

To study pressure and pressure measurement devices.

Introduction

Fluid pressure can be defined as the measure of force per-unit-area exerted by a fluid, acting

perpendicularly to any surface it contacts The standard SI unit for pressure measurement is

the Pascal (Pa) which is equivalent to one Newton per square meter (N/m2) or the Kilopascal

(kPa) where 1 kPa = 1000 Pa.

Pressure can be expressed in many different units including in terms of a height of a column

of liquid. The Table below lists commonly used units of pressure measurement and the

conversion between the units.

Pressure measurements can be divided into three different categories: absolute pressure, gage

pressure and differential pressure.

Absolute pressure refers to the absolute value of the force per-unit-area exerted on a surface

by a fluid. Therefore the absolute pressure is the difference between the pressure at a given

point in a fluid and the absolute zero of pressure or a perfect vacuum.

Gauge pressure is the measurement of the difference between the absolute pressure and the

local atmospheric pressure. Local atmospheric pressure can vary depending on ambient

temperature, altitude and local weather conditions. A gage pressure by convention is always

positive. A negative’ gage pressure is defined as vacuum. Vacuum is the measurement of the

amount by which the local atmospheric pressure exceeds the absolute pressure. A perfect

vacuum is zero absolute pressure. Figure below shows the relationship between absolute,

gage pressures and vacuum.


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Relationship between various pressure measurement devices

Differential pressure is simply the measurement of one unknown pressure with reference to

another unknown pressure. The pressure measured is the difference between the two

unknown pressures. This type of pressure measurement is commonly used to measure the

pressure drop in a fluid system. Since a differential pressure is a measure of one pressure

referenced to another, it is not necessary to specify a pressure reference. For the English

system of units this could simply be psi and for the SI system it could be kPa.

In addition to the three types of pressure measurement, there are different types of fluid

systems and fluid pressures. There are two types of fluid systems; static systems and dynamic

systems. As the names imply, a static system is one in which the fluid is at rest and a dynamic

system is on in which the fluid is moving.

Pressure Measurement Devices

Manometer

A Manometer is a device to measure pressures. A common simple

manometer consists of a U shaped tube of glass filled with some liquid.

Typically the liquid is mercury because of its high density.

In the figure to the right we show such a U shaped tube filled with a liquid.

Note that both ends of the tube are open to the atmosphere. Thus both points

A and B are at atmospheric pressure. The two points also have the same

vertical height


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Now the top of the tube on the left has been closed. We imagine that there is a sample of gas

in the closed end of the tube. The right side of the tube remains open to the atmosphere. The

point A, then, is at atmospheric pressure.

The point C is at the pressure of the gas in the closed end of the tube. The point B has a

pressure greater than atmospheric pressure due to the weight of the column of liquid of height

h. The point C is at the same height as B, so it has the same pressure as B. And this is equal to

the pressure of the gas in the closed end of the tube. Thus, in this case the pressure of the gas

that is trapped in the closed end of the tube is greater than atmospheric pressure by the

amount of pressure exerted by the column of liquid of height h.

Some "rules" to remember about U-tube manometry

Manometer height difference does not depend on tube diameter.

Manometer height difference does not depend on tube length.

Manometer height difference does not depend on tube shape.

Shape of a container does not matter in hydrostatics. This implies that a U-tube manometer

does not have to be in a perfect U shape. There is a way to take advantage of this, namely one

can construct an inclined manometer, as shown here. Although the column height difference

between the two sides does not change, an inclined manometer has better resolution than does


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9-4

a standard vertical manometer because of the inclined right side. Specifically, for a given

ruler resolution, one "tick" mark on the ruler corresponds to a finer gradation of pressure for

the inclined case.

Burdon Pressure Gauge

A Bourdon gauge uses a coiled tube, which, as it expands due to pressure increase causes a

rotation of an arm connected to the tube. In 1849 the Bourdon tube pressure gauge was

patented in France by Eugene Bourdon.

Parts of Burdon tube

The pressure sensing element is a closed coiled tube connected to the chamber or pipe in

which pressure is to be sensed. As the gauge pressure increases the tube will tend to uncoil,

while a reduced gauge pressure will cause the tube to coil more tightly. This motion is

transferred through a linkage to a gear train connected to a pointer. The pointer is presented

in front of a card face is inscribed with the pressure indications associated with particular

pointer deflections.


The manometers and gauges unit is a framed structure with a backboard, holding a:

Vertical U-tube manometer

U-tube manometer with an inclined limb

Bourdon gauge for measuring vacuums

Bourdon gauge for measuring positive pressure, and


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Syringe assembly for pressurizing and reducing pressure in the measurement devices.

Each gauge and manometer has a delivery point to connect to the syringe using plastic

tubing (included). All connections are push-fit, and T-pieces are provided to enable

two instruments to be connected to one point.


1. Using the syring connects its plastic tubing to Pressure gauge. Push the syring arm to

generate pressure. Observe the deflection on the gauge

2. Now connect the syring tubing to vacuum gauge. Release the arm of syring to

generate vacuum and observe the change in deflection.

3. U tube Manometer can be connected to any of the flow meter devices. Switch the

pump and observe the change in mercury levels in the manometer. Calculate the

pressure difference.

4. Similarly connect the Inclined U tube manometer to any of the flow meter and

calculate pressure difference

Observations:

Density of liquid flowing in pipe =

Density of liquid flowing in pipe =

Sr. No. Type of Manometer Manometric Reading

Pressure/Pressure Difference h1 h2

1 U tube Manometer

2 Inclined Tube Manometer

3 Pressure Gauge

4 Vacuum Gauge

Calculations


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In the above figure, since the pressure at the height of the lower surface of the manometer

fluid is the same in both arms of the manometer, we can write the following equation:

P1 + ρ1gd1 = P2 + ρ2gd2 + ρf g h

Here, ρ1 = ρ2 = ρw = Density of water;

P1 - P2 = ρwgd2 + ρf g h – ρwgd1

Also d1- d2 = h

P1 - P2 = (ρf - ρw) g h

Here ρf = Density of Mercury;

Substituting Standard Values,

P1- P2 = 13580 – 1000 (kg/m3) x g (m/s2) x h/1000 (m) = 12.58 gh (in N/m2)

Where g = 9.81 m/s2; h in mm

Calculation:

Conclusion

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Reynolds’s Apparatus

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Date: ___ /___ /______

EXPERIMENT NO. 10

Objective

To study Laminar and Turbulent Flow and It’s visualization on Reynolds’s Apparatus

Introduction

The properties of density and specific gravity are measures of the “heaviness” of fluid. These

properties are however not sufficient to uniquely characterize how fluids behave since two

fluids (such as water and oil) can have approximately the same value of density but behaves

quite differently when flowing. There is apparently some additional property that is needed to

describe the “fluidity” of the fluid.

Viscosity is defined as the property of a fluid which offers resistance to the movement of one

layer of fluid over another adjacent layer of the fluid. It is an inherent property of each fluid.

Its effect is similar to the frictional resistance of one body sliding over other body. As

viscosity offers frictional resistance to the motion of the fluid consequently. In order to

maintain the flow, extra energy is to be supplied to overcome effect of viscosity. The

frictional energy generated comes out in form of heat and dissipated to the atmosphere

through boundary surfaces.

Types of flow

Laminar flow

Laminar flow is that type of flow in which the particle of the fluid moves along well defined

parts or streamlines. In laminar flow all streamlines are straight and parallel. In laminar flow

one layer of fluid is sliding over another layer, whenever the Reynolds number is less than

2000, the flow is said to be laminar. In laminar flow, energy loss is low and it is directly

proportional to the velocity of the fluid. The following reasons are for the laminar flow, fluid

has low velocity, fluid has high viscosity and diameter of pipe is large

Turbulent Flow:

The flow is said to be turbulent flow it he flow moves in a zigzag way. Due to movement of

the particles in a zigzag way the eddies formation take place which are responsible of high-

energy losses.


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In turbulent flow, energy loss is directly proportional to the square of velocity of fluid. If

Reynolds number is greater than 4000, then flow is said to be turbulent

Reynolds’s Number

Reynolds was first to determine the translation from laminar to turbulent depends not only on

the mean velocity but on the quality

Re =VD

Where, = Density of Fluid

D = Diameter of pipe

=Dynamic Viscosity

The term is dimensionless and it is called Reynolds Number (Re). It is the ration of the inertia

force to the viscous force

Re =Intertia Force

Viscous Force

Re =V2

(VD)

Re =VD

This indicates that it is non-dimensional number.


The apparatus consists of

1. A tank containing water at constant head

2. Die container

3. A glass tube

4. The water from the tank is allowed to flow through the glass tube. The velocity of

flow can be varied by regulating valve. A liquid die having same specific weight as

that of water has to be introduced to glass tube.

Additional materials or Equipments required are

1. Stop Watch

2. Measuring Flask

3. Color Dye

4. Water Supply


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1. Switch on the pump and fill the head tank. Manually also fill the dye tank with some

amount of bright dye liquid provided.

2. Open the control valve slowly at the bottom of the tube and release small flow of dye.

3. Observe the flow in the tube.

4. Note down the time for 1 liter of discharge with the help of stopwatch and measuring

flask.

5. Repeat the above process for various discharges

Observations

The following observations are made:

1. When the velocity of flow is low, the die filament in the glass tube is in the form of a

straight line of die filament is parallel to the glass tube which is the case of laminar

flow as shown in fig.

Laminar flow

2. With the increase of velocity of flow the die filament is no longer straight line but it

becomes wavy one as shown in fig. this is shown that flow is no longer laminar. This

is transition flow.

Transition flow

3. With further increase of velocity of the way die filament is broken and finally mixes

in water as shown in fig.

Turbulent flow


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Observation Table

Sr.

No.

Time for 500 ml

discharge in (Sec)

Discharge

Q (m3/s)

Velocity V

(m/s)

Reynolds

No. Re

Observe the flow

(Laminar,

Transition,

Turbulent)

1

2

3

4

5

Conversion Factors

1 liter/sec = 0.001 m3/sec

0.5 liter/sec = 0.0005 m3/sec

Calculations

Since D = 0.02 m

Area = A =π

4d2 =

π

4 x 0.022 = 0.000314 m2

Ambient Temperature is 300 C, = 0.801 x 10-6

Q =0.0005

time required to collect 0.5 ltrs of water in m3/sec

V =Q

A=

Q

0.000314 in m/sec

Re =VD

=

VD

v (because

)

Where, = Kinematic viscosity of water which in m2/s

V = Velocity of Water in m/s

D = Diameter of pipe is 0.030 m

Calculation:


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Conclusion

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Appendix

Dynamic and Kinematic Viscosity of Water in SI Units:-

Temperature t

(0C)

Dynamic Viscosity µ (N.s/m2) x

10-3

Kinematic Viscosity ν (m2/s) x

10-6

0 1.787 1.787

5 1.519 1.519

10 1.307 1.307

20 1.002 1.004

30 0.798 0.801

40 0.653 0.658

50 0.547 0.553

60 0.467 0.475

70 0.404 0.413

80 0.355 0.365

90 0.315 0.326

100 0.282 0.294

Documents

FLUID MECHANICS - darshan.ac.in€¦Lab Manual 3rd Sem Civil ... Experiment Start Date End Date Sign Remark 1. To validate Bernoulli’s Theorem as applied to ... Pitot tube. 3