DARSHAN INSTITUTE OF ENGINEERING AND TECHNOLOGY Manual... · To validate Bernoulli’s Theorem as...

DARSHAN INSTITUTE OF ENGINEERING AND

TECHNOLOGY

FLUID MECHANICS (2141906)

INDEX

Sr. No.

Experiment Start Date End Date Sign Grade

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 determine Fluid friction factor for the

given pipes.

10 To determine loss coefficients for

different pipe fittings.

11 To study pressure and pressure

measurement devices.

12 To obtain surface profile of free and

forced vortex flow.

13

To study Laminar and Turbulent Flow

and It’s visualization on Reynolds’s

Apparatus.

14 To determine Hydraulic Co-efficients

using Orifice and Mouthpiece.

Bernoulli’s Theorem

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Fluid Mechanics (2141906)

Department of Mechanical Engineering

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

EXPERIMENT NO. 1

1.1 Objective:

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

1.2 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

1.2.1 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

meter above the horizontal datum (arbitrary chosen), the potential energy of liquid particle

will be gZ per kg of liquid. Potential head of the liquid, at that point, will be Z meters of the

liquid.

1.2.2 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 m/sec, then the kinetic energy of the particle

will be V2 2⁄ per kg of the liquid. Velocity head of the liquid, at that velocity, will be

V2 2g⁄ meter of liquid.

1.2.3 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/𝜌

per kg of liquid, where 𝜌 is the density of the liquid. Pressure head of the liquid under that


____________________________________________________________________________________________________




pressure will be 𝑝/𝑤 or 𝑝/𝜌𝑔 meter of the liquid. Where 𝑤 is the specific weight of the

liquid.

1.2.4 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

𝜌𝑔+

𝑉2

2𝑔+ 𝑍, meter of liquid

1.3 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

𝜌𝑔+

𝑉2

2𝑔+ 𝑍 = Constant

1.4 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.

1.5 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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1.6 Observation & Calculation Table

Piezometer Tube

Number 1 2 3 4 5 6 7

Diameter of Cross-

Section (m) 0.0348 0.03043 0.02605 0.025 0.02605 0.03043 0.0348

Area of Cross-Section,

A,( m2) 9.511E-4 7.27E-4 5.33E-4 4.91E-4 5.33E-4 7.27E-4 9.511E-4

Piezometer Tube

Distance, (m) 0 0.025 0.050 0.0725 0.095 0.120 0.145

Potential Head, Z 0 0 0 0 0 0 0

Ru

n N

o. 1

𝐿=

10

𝑙𝑖𝑡

,𝑡=

____

____

____

Sec

𝑄1 =𝐿

𝑡, 𝑚3/𝑠

V = Q1 A⁄ , 𝑚/𝑠

𝑝 𝜌𝑔⁄ , 𝑚

𝑉2 2𝑔⁄ , 𝑚

𝐸 =𝑝

𝜌𝑔+

𝑉2

2𝑔+ 𝑍

Ru

n N

o. 2

𝐿=

10

𝑙𝑖𝑡

,𝑡=

____

____

____

Sec

𝑄2 =𝐿

𝑡, 𝑚3/𝑠

V = Q2 A⁄ , 𝑚/𝑠


𝑉2 2𝑔⁄ , 𝑚

𝐸 =𝑝

𝜌𝑔+

𝑉2

2𝑔+ 𝑍

Ru

n N

o. 3

𝐿=

10

𝑙𝑖𝑡

,𝑡=

____

____

____

Sec

𝑄3 =𝐿

𝑡, 𝑚3/𝑠

V = Q3 A⁄ , 𝑚/𝑠


𝑉2 2𝑔⁄ , 𝑚

𝐸 =𝑝

𝜌𝑔+

𝑉2

2𝑔+ 𝑍


____________________________________________________________________________________________________




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.

1.7 Conclusion

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Pitot Tube

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Darshan Institute of Engineering & Technology, Rajkot.

2-1

EXPERIMENT NO. 2

2.1 Objective

To study and measure velocity of flow using Pitot tube

2.2 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 or Total pressure = Static pressure + Dynamic pressure

Figure 2.1 Pitot tube

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

2.5 Observation Table

Diameter of flow pipe, D = 0.03 m

Run No.

Total Pressure

Head

Pt, (m)

Static Pressure

Head

Ps, (m)

Dynamic Pressure

Head

(Pt − Ps), (m)

Time for L=5 lit,

t, (sec)

1

2

3

4

5

2.6 Calculations

1. Actual Discharge,

Qact = L

t=

0.005

𝑡= _________________ 𝑚3/𝑠𝑒𝑐

2. Actual Velocity,

Vact =Qact

A= _________________ 𝑚

𝑠𝑒𝑐⁄

Pitot Tube

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2-3

3. Theoretical Velocity

Vth = √2g (Pt − Ps) = _________________ 𝑚𝑠𝑒𝑐⁄

4. Co-efficient of Pitot Tube

Cv =Vact

Vth= _________________

2.7 Result Table

Run

No.

Theoretical Velocity,

Vth, (m/sec)

Actual Discharge,

Qact, (m3/sec)

Actual Velocity,

Vact, (m/sec)

Co-efficient of

Velocity, Cv

1

2

3

4

5

2.8 Conclusion

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Notches

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3-1

EXPERIMENT NO. 3

3.1 Objective

To calibrate the given Rectangular, Triangular and Trapezoidal Notches

3.2 Introduction

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

Notches and Weirs are used to measure the rate of flow of liquid (discharge) indirectly from

measurements of the flow depth.

Notch is a device used for measuring the rate of flow of liquid through a small channel or a

tank. It is an opening in the side of a measuring tank or reservoir extending above the free

surface. Weir is a concrete or masonry structure, placed in open channel over which the flow

occurs like a river. A notch is small in size whereas weir is a notch on a large scale.

A weir/notch 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/notch can be of different shapes - rectangular, triangular, trapezoidal etc. A

triangular weir is particularly suited for measurement of small discharges.

Equation of discharge for notch and weir will remain same.

3.2.1 Rectangular Notch

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

√

H = Head of water over the crest

L = Length of notch or weir

Figure 3.1 Rectangular notch

Notches

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3-2

3.2.2 Triangular Notch (V-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,

√

Figure 3.2 Triangular notch

3.2.3 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:

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

L = Bottom of notch width

H = Head above bottom of opening in meter

Figure 3.3 Trapezoidal notch

Notches

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3-3


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)

(1) Rectangular not (2) V- notch (3) Trapezoidal notch

Figure 3.4 Different types of notches used in apparatus


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.

Notches

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3-4

3.5 Observations

3.5.1 Notch Type: Rectangular

Sr.

No.

Still level reading,

s, (m)

Water height on upstream side,

h, (m)

Discharge time for 10 liters,

t, (sec)

1

2

3

3.5.2 Notch Type: Triangular

Sr.

No.


s, (m)


h, (m)


t, (sec)

1

2

3

3.5.3 Notch Type: Trapezoidal

Sr.

No.


s, (m)


h, (m)


t, (sec)

1

2

3

3.6 Calculations

3.6.1 Rectangular Notch

1. Head over the notch, ( )

2. Actual Discharge ,

3. Crest length of notch = 0.05 m

4.

√

5.

Notches

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3-5

3.6.2 Triangular notch




4.

√

5.

3.6.3 Trapezoidal Notch (or Cipolletti Weir)




4.

5.

3.7 Result Tables

3.7.1 Notch Type: Rectangular

Sr.

No.

Theoretical discharge,

Qth,. (m3/sec)

Actual discharge,

Qact,. (m3/sec)

Cd

1

2

3

3.7.2 Notch Type: Triangular

Sr.

No.


Qth,. (m3/sec)

Actual discharge,

Qact, (m3/sec)

Cd

1

2

3

Notches

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3-6

Notch Type: Trapezoidal

Sr.

No.


Qth,. (m3/sec)

Actual discharge,

Qact,. (m3/sec)

Cd

1

2

3

3.8 Conclusion

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Metacentre

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4-1

EXPERIMENT NO. 4

4.1 Objective

To determine the Metacentric height of a given floating body.

4.2 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.

4.3 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.

Figure 4.1 Metacentric height

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 𝑡𝑎𝑛 𝜃)

Where, W = weight of the floating body, (N)

m = movable weight, (N)

X = distance through which the movable load is shifted, (m)

= 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

4.6 Observation & Result Table

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

Given Movable Weights = 50 gm = 0.490 N

Metacentre

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4-3

Sr.

No.

Movable

Weight,

m, (N)

Distance of

Weight from

Center, X (m)

Angle of

Tilt, Tan

Metacentric

Height,

GM, (m)

1

2

3

4

5

4.7 Calculations

Metacentric height 𝐺𝑀 = (𝑚 𝑥 𝑋)

(𝑊 𝑥 𝑡𝑎𝑛𝜃)

Metacentric height, 𝐺𝑀 = _______________, 𝑚

4.8 Conclusion

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Venturimeter




5-1

EXPERIMENT NO. 5

5.1 Objective

To calibrate and study Venturimeter

5.2 Introduction

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

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

Orifice meter, 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.

Figure 5.1 Venturimeter


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.

Venturimeter




5-2


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.

5.5 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

Manometric Reading Manometer Difference

(m of Hg)

𝒙 =𝒉𝟐 − 𝒉𝟏

𝟏𝟎𝟎

Time for 10 lit, t,

(sec) 𝒉𝟏 (𝒄𝒎 𝒐𝒇 𝑯𝒈) 𝒉𝟐 (𝒄𝒎 𝒐𝒇 𝑯𝒈)

1

2

3

4

5

Venturimeter




5-3

5.6 Calculations


𝑄𝑎𝑐𝑡 =𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟 𝑖𝑛 𝑚3

𝑇𝑖𝑚𝑒 𝑖𝑛 𝑆𝑒𝑐=

0.01

𝑡= ______________, 𝑚3 𝑠𝑒𝑐⁄

2. Difference in Pressure Head,

ℎ = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1] = ______________, 𝑚 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

3. Theoretical Discharge,

𝑄𝑡ℎ =𝑎1𝑎2√2𝑔ℎ

√𝑎12 − 𝑎2

2= ______________, 𝑚3 𝑠𝑒𝑐⁄

4. Co-efficient of Discharge,

𝐶𝑑 = 𝑄𝑎𝑐𝑡

𝑄𝑡ℎ= _______________

5.7 Result Table

Sr.

No.

Theoretical Discharge,

Qth, (m3/s)

Actual Discharge,

Qact, (m3/s) Cd

1.

2.

3.

4.

5.

5.8 Conclusion

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Orifice Meter

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6-1

EXPERIMENT NO. 6

6.1 Objective

To calibrate and study Orifice meter

6.2 Introduction

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. The

opening is normally at the centre of the plate as shown in Fig.6.1.

Major advantages of orifice meter are that it is low cost device, simple in construction & easy

to install in pipe lines.

The major disadvantage of using orifice plate is the permanent pressure drop that is normally

experienced in the orifice plate as shown in Fig. 6.1. The pressure drops significantly after the

orifice and can be recovered only partially. The magnitude of the permanent pressure drop is

around 40%, which is sometimes objectionable. It requires more pressure to pump the liquid.

This problem can be overcome by improving the design of the restrictions. Venturimeter and

flow nozzle are two such devices.

Figure 6.1 Simple orifice meter & permanent pressure drop

Orifice Meter

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6-2


Orifice 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.6.1. Pressure head



pipeline.





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.








Orifice Meter

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6-3

6.5 Observations

For Orifice meter: Diameter of pipe inlet d1= 26 mm; Area 𝑎1 = 5.31 x 10-4 m2

Diameter of orifice do = 16 mm; Area 𝑎𝑜 = 2.01 x 10-4 m2

Sr.

No


(m of Hg)

𝒙 =𝒉𝟐 − 𝒉𝟏

𝟏𝟎𝟎

Time for 10 lit, t,


1

2

3

4

5

6.6 Calculations




0.01

𝑡= ______________, 𝑚3 𝑠𝑒𝑐⁄


ℎ = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1] = ______________, 𝑚 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟


𝑄𝑡ℎ =𝑎𝑜𝑎1√2𝑔ℎ

√𝑎12 − 𝑎𝑜

2= ______________, 𝑚3 𝑠𝑒𝑐⁄

Where,

𝑎𝑜 = Area of cross section of the orifice

𝑎1 = Area of cross section of the pipe

ℎ = Difference in the Piezometric heads at manometer tappings

4. Co-efficient of Discharge


𝑄𝑡ℎ= _______________

Orifice Meter

____________________________________________________________________________________________________




6-4

6.7 Result Table

Sr.

No


Qth, (m3/s)

Actual Discharge,

Qact, (m3/s) Cd

1

2

3

4

5

6.8 Conclusion

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

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

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

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

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

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

Nozzle Meter

____________________________________________________________________________________________________




7-1

EXPERIMENT NO. 7

7.1 Objective

To calibrate and study Nozzle Meter

7.2 Introduction

The Flow nozzle or Nozzle meter is a compromise between Venturimeter and orifice meter as

shown in Fig. 7.1 The streamlined entrance of the nozzle causes a straight jet without

contraction, so its effective discharge coefficient is nearly the same as the venturi meter. 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.

Figure 7.1 Simple nozzle meter


Nozzle 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.7.1. Pressure head



pipeline.

Nozzle Meter

____________________________________________________________________________________________________




7-2

7.4 Technical Specifications of Nozzle meter

Size = 26 mm

Nozzle Size = 16 mm





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.








7.6 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


(m of Hg)

𝒙 =𝒉𝟐 − 𝒉𝟏

𝟏𝟎𝟎

Time for 10 lit, t,


1

2

3

4

5

Nozzle Meter

____________________________________________________________________________________________________




7-3

7.7 Calculations




0.01

𝑡= ______________, 𝑚3 𝑠𝑒𝑐⁄


ℎ = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1] = ______________, 𝑚 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟


𝑄𝑡ℎ =𝑎1𝑎2√2𝑔ℎ

√𝑎12 − 𝑎2

2= ______________, 𝑚3 𝑠𝑒𝑐⁄

4. Co-efficient of Discharge,


𝑄𝑡ℎ= _______________

7.8 Result Table

Sr.

No.

Theoretical Discharge,

Qth, (m3/s)

Actual Discharge,

Qact, (m3/s) Cd

1.

2.

3.

4.

5.

7.9 Conclusion

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

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

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

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

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

Rota meter

____________________________________________________________________________________________________




8-1

EXPERIMENT NO. 8

8.1 Objective

To calibrate and study Rotameter

8.2 Introduction

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.

Figure 8.1 Rotameter


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

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

pipeline.

8.4 Technical Specifications of Rotameter

Size = 1- 1000 LPH

Type = Thread Ends

S= Flow Force

A = Buoyancy

G= Gravity

Force

Rota meter

____________________________________________________________________________________________________




8-2





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


8.6 Observation & Calculation Table

Sr.

No

Time for 10 lit.,

t, (sec)

Rota meter Scale,

(LPH)

Actual discharge,

𝑸𝒂𝒄𝒕, (LPH)

1

2

3

4

5

8.7 Calculations

1. Actual discharge,



0.01

𝑡= _________________, 𝑚3 𝑠𝑒𝑐⁄

Discharge in LPH = 𝑄𝑎𝑐𝑡 × 3600 × 1000 = _________________, 𝐿𝑃𝐻

8.8 Conclusion

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

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

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

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

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

Pipe Friction Losses

____________________________________________________________________________________________________




9-1

EXPERIMENT NO. 9

9.1 Objective

To determine fluid friction factor for the given pipes.

9.2 Introduction

The flow of liquid through a pipe is resisted by viscous shear stresses within the liquid and

the turbulence that occurs along the internal walls of the pipe, created by the roughness of the

pipe material. This resistance is usually known as pipe friction and is measured is meters

head of the fluid, thus the term head loss is also used to express the resistance to flow.

Many factors affect the head loss in pipes, the viscosity of the fluid being handled, the size of

the pipes, the roughness of the internal surface of the pipes, the changes in elevations within

the system and the length of travel of the fluid.

The resistance through various valves and fittings will also contribute to the overall head loss.

In a well-designed system the resistance through valves and fittings will be of minor

significance to the overall head loss and thus are called Minor losses in fluid flow.

Figure 9.1 head loss due to friction

9.3 The Darcy-Weisbach equation

Weisbach first proposed the equation we now know as the Darcy-Weisbach formula or

Darcy-Weisbach equation.

ℎ𝑓 = 4𝑓𝐿𝑉2

2𝑔𝐷

Where, hf = Head loss in meter


____________________________________________________________________________________________________




9-2

f = Darcy friction factor

L = length of pipe work, (m)

V = Velocity of fluid, (m/sec)

D = inner diameter of pipe, (m)

g = Acceleration due to gravity, (m/sec2)

The Darcy Friction factor used with Weisbach equation has now become the standard head

loss equation for calculating head loss in pipes where the flow is turbulent.


The experimental set up consists of a large number of pipes of different diameters. The pipes

have tapping at certain distance so that a head loss can be measure with the help of a U –

Tube manometer. The flow of water through a pipeline is regulated by operating a control

valve which is provided in main supply line. Actual discharge through pipeline is calculated

by collecting the water in measuring tank and by noting the time for collection.

9.5 Technical Specification

Pipe: MOC = Polyurethane (P.U.)

Test length, L = 1000 mm

Pipe Dia. Pipe 1: Internal Diameter, D1: 16 mm

Pipe 2: Internal Diameter, D2: 21 mm

Pipe 3: Internal Diameter, D3: 26.5 mm





3. To find friction factor of pipe 1 open control valve of the same and close other to

valves

4. Open the vent cocks provided for the particular pipe 1 of the manometer.


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

water.

7. Close the drain valve of the collection tank and collect known quantity of water


____________________________________________________________________________________________________




9-3

8. Note down the time required for the same.



10. Similarly for pipe 2 and 3. Repeat the same procedure indicated in step 4-9


9.7 Observations Table

Length of test section L = 1000 mm = 1 m

Pipe 1 Internal Diameter of Pipe, D1 = 16 mm

Cross Sectional Area of Pipe, A1 = 200.96 mm2 = 2.0 x 10-4 m2

Sr.

No


(m of Hg)

𝑥 =ℎ2 − ℎ1

100

time for 10 lit, t,

(sec) ℎ1 (𝑐𝑚 𝑜𝑓 𝐻𝑔) ℎ2 (𝑐𝑚 𝑜𝑓 𝐻𝑔)

1

2

Pipe 2 Internal Diameter of Pipe, D2 = 21 mm


Sr.

No


(m of Hg)

𝑥 =ℎ2 − ℎ1

100

time for 10 lit, t,


1

2

Pipe 3 Internal Diameter of Pipe, D3 = 26.5 mm


Sr.

No


(m of Hg)

𝑥 =ℎ2 − ℎ1

100

time for 10 lit, t,


1

2


____________________________________________________________________________________________________




9-4

9.8 Calculations

1. Actual Discharge



0.01

𝑡

2. Mean velocity

𝑉𝑎𝑐𝑡 = 𝑄𝑎𝑐𝑡

𝐴


ℎ𝑓 = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1]

4. Friction factor

𝑓 =2𝑔𝐷ℎ𝑓

4𝐿𝑉2

9.9 Result Table

Sr. No. Actual Discharge

𝑄𝑎𝑐𝑡, 𝑚3/𝑠𝑒𝑐

Actual Velocity

𝑉𝑎𝑐𝑡, 𝑚/𝑠𝑒𝑐

Diff. in Pressure Head,

ℎ𝑓 , 𝑚 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟

Friction Factor,

f

1 Pipe 1

2

3 Pipe 2

4

5 Pipe 3

6

9.10 Conclusion

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

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

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

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

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

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

Minor Losses

____________________________________________________________________________________________________




10-1

EXPERIMENT NO. 10

10.1 Objective

To determine loss coefficients for different pipe fittings.

10.2 Introduction

While installing a pipeline for conveying a fluid, it is generally not possible to install a long

pipeline of same size all over a straight for various reasons, like space restrictions, aesthetics,

location of outlet etc. Hence, the pipe size varies and it also changes its direction. Also,

various fittings are required to be used. All these variations of sizes and the fittings cause the

loss of fluid head.

Losses due to change in cross-section, bends, elbows, valves and fittings of all types fall into

the category of minor losses in pipelines. In long pipeline, the friction losses are much larger

than these minor losses and hence, the latter are often neglected. But, in shorter pipelines,

their consideration is necessary for the correct estimate of losses.

The minor loses are, generally expressed as

HL = KL (V2

2g)

Where, HL is the minor loss (i.e. head loss)

KL, the loss coefficient, V is the velocity of flow in the pipe


The experimental set-up consists of a pipe of diameter about 24.3 mm fitted with

1. A right angle bend

2. An elbow

3. A Gate Valve

4. A sudden expansion (larger pipe having diameter of about 24.3 mm) and

5. A sudden contraction (from about 24.3 mm to about 13.8 mm)

Sufficient length of the pipeline is provided between various pipe fittings. The pressure taps

on either side of these fittings are suitably provided and the same may be connected to a multi

tube manometer bank. Supply to the line is made through a storage tank and discharge is

regulated by means of outlet valve provided near the outlet end.

Minor Loss

____________________________________________________________________________________________________




10-2


1. Fill up sufficient clean water in the sump tank

2. Fill up mercury in the manometer

3. Connect the electric supply. See that the flow control valve and bypass valve are fully

open and all the manometer cocks are closed. Keep the water collecting funnel in the

sump tank side

4. Start the pump and adjust the flow rate. Now slowly open the manometer tapping

connection of small bend. Open both the cocks simultaneously

5. Open air vent cocks. Remove air bubbles and slowly & simultaneously close the

cocks. Note down the manometer reading and flow rate.

6. Close the cocks and similarly, note down the readings for other fittings. Repeat the

procedure for different flow rates.

10.5 Observations

1. Type of fitting – Elbow

Diameter of the elbow, d = 33.4 mm = 0.0334 m

Mean Area of elbow, A =π

4d2 = 8.76 x 10−4 m2

Sr. No.

Manometer Reading Manometer difference

(𝑚 𝑜𝑓 𝐻𝑔)

𝑥 =ℎ2 − ℎ1

100

Time for 10 lit,

t (sec) ℎ1 (𝑐𝑚 𝑜𝑓 𝐻𝑔) ℎ2 (𝑐𝑚 𝑜𝑓 𝐻𝑔)

1

2

3

2. Type of fitting – Bend

Diameter of the bend, d = 33.4 mm = 0.0334 m

For bend, mean area A =π

4d2 = 8.76 x 10−4 m2

Sr. No.



𝑥 =ℎ2 − ℎ1

100

Time for 10 lit,


1

2

3

Minor Losses

____________________________________________________________________________________________________




10-3

3. Type of fitting – Valve

Diameter of the valve opening, d = 33.4 mm = 0.0334 m

For gate valve mean area, A =π

4d2 = 8.76 x 10−4 m2

Sr. No.



𝑥 =ℎ2 − ℎ1

100

Time for 10 lit,


1

2

3

4. Type of fitting – Sudden Contraction

Inlet diameter = 24.3 mm = 0.0243 m; Therefore Ai = 4.64 X 10-4 m2

Outlet diameter = 13.8 mm = 0.0138 m; Therefore Ao = 1.50 x 10-4 m2

Sr. No.



𝑥 =ℎ2 − ℎ1

100

Time for 10 lit,


1

2

3

5. Type of fitting – Sudden Expansion

Inlet diameter = 24.3 mm = 0.0243 m; Therefore Ai = 4.64 X 10-4 m2

Outlet diameter = 13.8 mm = 0.0138 m; Therefore Ao = 1.50 x 10-4 m2

Sr. No.



𝑥 =ℎ2 − ℎ1

100

Time for 10 lit,


1

2

3

Minor Loss

____________________________________________________________________________________________________




10-4

10.6 Calculations

1. Elbow

Actual discharge,

Q =L

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

Mean velocity of flow,

V = Q

A m/s

Difference (loss) in pressure head,

HL = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1]

The loss coefficient of the elbow,

HL = KL (V2

2g) meter of water

2. Pipe Bend

Actual discharge,

Q =L



V = Q

A m/s

Difference in pressure head,

HL = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1]

Loss coefficient of the bend,

HL = KL (V2

2g) meter of water

3. Valve

Actual discharge,

Q =L



V = Q

A m/s


Minor Losses

____________________________________________________________________________________________________




10-5

𝐻𝐿 = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1]

The loss coefficient of the valve,

HL = KL (V2

2g) meter of water

4. Sudden Contraction

Actual discharge,

Q =L


Velocity of fluid at inlet,

Vi = Q

Aim s⁄

Velocity of fluid at outlet,

Vo = Q

Aom s⁄

Loss of head due to increase in velocity,

hv = vi

2

2g−

vo2

2g


HL = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1]

Loss of head due to sudden contraction,

HLC = HL − hv

The loss coefficient of sudden contraction,

HLc = KL (Vo

2

2g)

5. Sudden Expansion

Actual discharge,

Q =L


Velocity of fluid at inlet,

Vi = Q

Aim s⁄

Velocity of fluid at outlet,

Minor Loss

____________________________________________________________________________________________________




10-6

Vo = Q

Aom s⁄

Loss of head due to decrease in velocity,

hv = vi

2

2g−

vo2

2g


HL = 𝑥 [𝑆ℎ

𝑆𝑜− 1] = 𝑥 [

13.6

1− 1]

Loss of head due to sudden expansion

HLe = hv − HL

The loss coefficient of sudden expansion,

𝐻Le = KL

(Vi − Vo)2

2g

10.7 Result Table

Sr

No.

Bend Elbow Valve Sudden

Contraction

Sudden

Expansion

HL KL HL KL HL KL HLc KL HLe KL

1

2

3

10.8 Conclusion

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

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

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

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

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

Pressure Measurement

____________________________________________________________________________________________________




11-1

EXPERIMENT NO. 11

11.1 Objective

To study pressure and pressure measurement devices.

11.2 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.


____________________________________________________________________________________________________




11-2

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.

11.3 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


____________________________________________________________________________________________________




11-3

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


____________________________________________________________________________________________________




11-4

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


____________________________________________________________________________________________________




11-5

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

11.6 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

11.7 Calculations


____________________________________________________________________________________________________




11-6

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 g h (in N/m2)

Where g =9.81 m/s2; h in mm

11.8 Conclusion

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

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

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

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

…………………………………………………………………………………………………

Free and Forced Vortex Flow

____________________________________________________________________________________________________




EXPERIMENT NO. 12

12.1 Objective

To obtain surface profile of free and forced vortex flow.

12.2 Introduction

A vortex is a spinning, often turbulent, flow of fluid. Any spiral motion with closed

streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a

vortex.

When a liquid contained in a cylindrical vessel is given the rotation surface of water no

longer remains horizontal but it depresses at the centre and rises near the walls of the vessel.

A rotating mass of fluid is called vortex and motion of rotating mass of fluid is vortex

motion. Vortices are of two type viz., forced vortex and free vortex. When a cylinder is in

rotation then a vortex is called forced vortex. If water enters a stationary cylinder then a

vortex is called free vortex.

Forced vortex flow is an example of rotational flow and can be generated by rotating a

cylinder containing a fluid about its axis (e.g., in a kitchen mixing machine) or by rotating a

paddle in a large volume of fluid (e.g., the stirring of tea cup). Under Steady conditions, each

particle will move with the same angular velocity and there will not be any relative motion

between fluid particles. Streamlines for such a flow will be concentric circles and total energy

is constant along a streamline but varies from one streamline to another.

Figure 12.1 Forced vortex: total energy line and surface profile

Free and Forced vortex Flow

____________________________________________________________________________________________________



Darshan Institute of Engineering & Technology, Rajkot. 12- 2


The apparatus consists of a Perspex cylinder with drain at centre of bottom. The cylinder is

fixed over a rotating platform which can be rotated with the help of a D.C. motor at different

speeds. A tangential water supply rip is provided with flow control valve. The whole unit is

mounted over the main frame. Water is supplied by a pump. Exit orifice of different sizes are

provided which can be easily replaced.

Figure 12.2 Vortex measurement


A. Forced Vortex

1. Close the drain valve of the cylinder vessel. Fill up some water (Say 4-5 cms

height from the bottom) in vessel

2. Switch ON the supply and slowly increase motor speed. Do not start the

pump.

3. Keep motor speed constant and wait till the vortex formed in the cylinder

stabilizes. Once the vortex is stabilized note down the co-ordinates of the

vortex and complete the observation table

4. With the surface speed attachment of tachometer, measure outside surface

speed of vessel and note down in observation table (Tachometer is not

supplied with the unit).

Free and Forced Vortex Flow

____________________________________________________________________________________________________




B. Free Vortex

1. Open the bypass valve and start the pump

2. Slowly close the water bypass valve and drain valve of the cylinder. Water is

now getting admitted through the tangential entry pipe to the cylinder

3. Properly adjust the bottom drain valve of vessel so that a stable vortex is

formed

4. Note down co-ordinate of the vortex. Also measure time required for L lit

level rise in measuring tank and complete observation table.

12.5 Observation Table:

A. Forced Vortex

Sr. No. RPM of motor (N”) Radius (X coordinate) cms Height (z) (Y coordinate) cms

1

B. Free Vortex

Sr. No Radius

(X coordinate), cms

Height (z)

(Y coordinate), cms

Time for L=______ lit. level

rise, t (sec)

1

12.6 Calculations

A. Forced Vortex

Free and Forced vortex Flow

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Darshan Institute of Engineering & Technology, Rajkot. 12- 4

B. Free Vortex

Pipe diameter, d = 1.6 cm; A=2.01 x 10-4

m2

(Note- For forced vortex, linear velocity of the cylinder does not equal the actual water

velocity near I.D. of cylinder. Also for free vortex, as water does not enter exactly

tangentially & velocity changes after it enters the cylinder which is not known, it is very

difficult to calculate velocity of water exactly, the theoretical calculations deviate much from

the observations. It can be readily observed that water comes out from pipe with high

velocity, but velocity of water near the walls of cylinder appears to be very less)

12.7 Conclusion

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12.8 Precautions

1. While making the experiment forced vortex, see that water does not spill away from

the vessel. Do not increase the speed of rotation excessively.

2. Do not start pump for forced vortex experiment

Graph of Forced and Free Vortex:

Reynolds’s Apparatus

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13-1

EXPERIMENT NO. 13

13.1 Objective

To study Laminar and Turbulent flow and it’s visualization on Reynolds’s apparatus

13.2 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.

13.3 Types of flow

13.3.1 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

13.3.2 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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13-2

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

13.4 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


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 Equipment required are

1. Stop Watch

2. Measuring Flask

3. Color Dye

4. Water Supply


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13-3


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

13.7 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.13.1.

Figure 13.1 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.13.2 this is shown that flow is no longer laminar.

This is transition flow.

Figure 13.2 Transition flow

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

in water as shown in fig.13.3.

Figure 13.3 Turbulent flow


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13-4


Sr.

No.

Time for 500 ml

discharge, t, (sec)

Discharge

Q, (m3/s)

Velocity,

V, (m/s)

Reynolds

No. Re

Observe the flow

(Laminar, Transition,

Turbulent)

1

2

3

4

5

13.9 Conversion Factors

1 liter/sec = 0.001 m3/sec

0.5 liter/sec = 0.0005 m3/sec

13.10 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

𝑉 =𝑄

𝐴=

𝑄

0.000314

𝑅𝑒 =𝑉𝐷

=

𝑉𝐷

𝑣 (𝑏𝑒𝑐𝑎𝑢𝑠𝑒

)

Where, = Kinematic viscosity of water which, (m2/s)

V = Velocity of Water, (m/s)

D = Diameter of pipe is 0.030 m


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13-5

13.11 Conclusion

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13.12 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

Orifice and mouthpiece’s Apparatus

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14-1

EXPERIMENT NO. 14

14.1 Objective

To determine Hydraulic Co-efficients using Orifice and Mouthpiece

14.2 Introduction

An orifice is an opening in the wall of a tank or in a plate which may be fitted in a pipe such

that the plate is normal to the pipe axis. An orifice is used for the discharge measurement.

Usually an orifice has a sharp edge as shown in figure 14.1. A mouthpiece is a short pipe

whose length does not exceed two to three times its diameter. It may be of uniform section or

may have varying section.

Orifice and mouthpiece are used for discharge measurement. The jet approaching the orifice

continues to converge beyond the orifice till the streamlines are parallel. This section of the

jet is, then a section of minimum area and is known as vena contracta, as shown in figure

14.1

Figure 14.1 Sharp Edged Orifice

The ratio of the area of the jet at the vena contracta, to the area of orifice, is called the

Coefficient of contraction . Thus,

If there is no friction, the jet will attain some velocity, say √ , where h is the height

of water level in the tank above the centre of the orifice. However, owing to the friction, the


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14-2

jet attains a lower velocity . The ratio of (i.e., actual velocity) to is called the

coefficient of velocity, . Thus,

√

Similarly, the ratio of the actual discharge to the discharge to in absence of friction and

contraction is termed as the Coefficient of Discharge, . Thus,

Where √ Also, Thus,

( )( ) Or Or

So,

And, √

i.e.,

√

Above Equation is valid if the head h in the tank to which orifice has been fixed, remains

constant. The corresponding method of determining the Coefficient of Discharge is

therefore named as the constant head method.

If x and y (measured +ve downward) represent, respectively the horizontal and vertical

coordinates of the lowest point at any section on the trajectory of the jet (origin being taken

as the lowest point of the jet at vena contracta or at the orifice) then it can be shown that

√


The unit consists of a supply tank to which orifice or mouthpiece can be fitted. The tank is

provided with flow settling arrangement. A tracer pointer is provided at the discharge of

orifice to demonstrate and to determine X-Y co-ordinates of jet. Arrangement is provided to

vary and measure the head over orifice or mouthpiece. A fixture is provided for orifice or

mouthpiece fitting which can easily adopt both. Thus, we can determine , & of

orifice as well as of mouthpiece.


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14-3


1. Fill up the water in the sump tank.

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

the main tank.

3. Let the water level become stable till the level of overflow pipe.

4. Note the height H

5. Using the X-Y Probe measure the X and Y Coordinate at certain point on the flow jet

as shown in figure

6. Close the drain valve of measuring tank and measure the discharge.

7. Repeat the same procedure for Mouthpiece also.

Figure 14.2 Setup for Orifice Jet Measurement


14.5.1 For Orifices

Diameter of Orifice = 10 mm

Area of Orifice = _______ m2

Sr.

No.

Constant Head

H, m

X Co-ordinate,

m

Y Co-ordinate,

m

Discharge time for 5 litres,

‘t’, sec




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14-4

Sr.

No.

Constant Head

H, m

X Co-ordinate,

m

Y Co-ordinate,

m


‘t’, sec



Sr.

No.

Constant Head

H, m

X Co-ordinate,

m

Y Co-ordinate,

m


‘t’, sec

14.5.2 To Plot Graph


Constant Head H, m

X Co-ordinate, m

Y Co-ordinate, m

14.5.3 For Mouthpiece

Diameter of Mouthpiece = 12 mm

Area of Mouthpiece = ________m2

Sr. No. Constant Head

H, m

Discharge time for 5 litres

‘t’ sec

14.6 Calculations

14.6.1 For Orifice

1. Constant Head,



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14-5

3. Now, Theoretical Discharge

√


5. Co-efficient of Velocity

√

14.6.2 For Mouthpiece

1. Constant Head,


3. Now, Theoretical Discharge

√


14.7 Conclusion

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