REYNOLD’S APPARATUS

Aim

To study different types of flow and to determine the Reynold’s number.

Theory

In Reynold’s experiments, the ration of inertial to viscous forces was observed to be

dimensionless and related to viscosity, average pipeline velocity and geometrically similar

boundary conditions. For a homogeneous Newtonian fluid, this dimensionless ration is Re

expressed as

Re = ρDV/µ (dimensionless)

ρ = density of fluid (kg/m3)

V = Velocity of fluid (m/s)

D = Diameter of glass tube (m)

µ = Viscosity of fluid (NS/m2)

For,

NRe < 2100 – Laminar flow

NRe > 4000 – Turbulent flow

2100< NRe <4000 - Transition flow

Depending on the relative magnitudes of viscous and inertial forces, flow can occur in two

different manners. A stream line flow is defined as a line, which lies in the direction of flow at a

given instant. For lower Reynold’s number streamline flow or laminar flow occur. As Reynold’s

number increases, eddies are generated and flow becomes turbulent.

Procedure

Clean the apparatus and make all tanks free from dust. Close the drain valves provided. Close

flow control valve at the end of test section ie glass tube. Fill sump tank with clean water and

ensure no foreign particles are there. Prepare a dye solution (KMnO4) in clean water in a separate

vessel. Close the control valve for dye, given on the P.V. tubing. Put this section in dye vessel after

ensuring no foreign particles. Regulate minimum flow rate with the help of dye through capillary

so that a fine color thread is observed indicating laminar flow. Increase the flow through glass tube

and observe the color threads, if it is still straight the flow still remains to be in laminar flow and if

waviness starts, it is indication of non –laminar flow. Measure flow rate using measuring cylinder

and stop watch.

Table 1:

Sl. No.

Volume of water collected,Vo (ml)

Time taken, s

Discharge, Qm3/s

Velocity, m/s

Reynolds Number, NRe

Actual flow type

Observed type of flow

1

2

3

4

5

6

17

18

19

20

Given Data:

Diameter of pipe = 0.079m Area = 0.0049m2

MODEL CALCULATION:

Discharge = Velocity = NRe =

RESULT

The variation of Reynold’s number for laminar, transition and turbulent flow has been

studied using Reynolds apparatus.

REASONING

PITOT TUBE APPARATUS

Objective:

To measure the velocity of flow at a given point in a pipe.

Aim

(1) To find the co-efficient of pitot tube

(2) To find the point velocity at the centre of a tube for different flow rates.

(3) To plot velocity profile across the cross section of pipe.

Introduction

It is a device used for measuring the velocity of flow at any point in a pipe. It is based on

the principle that if the velocity of flow at a point becomes zero, there is increase in pressure due to

the conversion of kinetic energy into pressure energy. The pitot consist of a capillary tube bent at

right angle. The lower and which is bent through 900, is directed in the upstream direction the

liquid rises up in the tube due to conversion of kinetic energy into pressure energy. The velocity is

determined by measuring the rise of liquid in the tube.

Theory

When a pitot tube is used for measuring the velocity of flow in a pipe or other closed

conduct the Pitot tube may be inserted in the pipe as shown in fig. Since a pitot tube measures the

stagnation pressure head at its dipped end, the pressure head may be determined directly by

connecting a suitable differential manometer between the Pitot tube and pressure taping at the pipe

surface. Consider two point s (1) and (2) at the same level in such a way that point (2) is just at the

inlet of the h pitot tube and point(1) is far away from the tube. At point (1) the pressure is P, and

the velocity of the stream, is V1 . However at point (2) called stagnation point the fluid is brought

to rest and the energy has been converted to pressure energy. There fore the pressure at (2) is P2,

the velocity V2 is zero and since (1) and (2) are in the same horizontal plane so Z1 = Z2

Applying Bernoulli’s equation at points (1) and (2)

P1 + v12 = P2 + v2

2

W 2g W 2g

V12 = P2 - P1 ; V2 = 0

2g W W

V1 = 2g (P2 – P1)

W

V1 = √ (2gH)

DESCRIPTION

The apparatus consists of a pitot tube made of copper and fixed below a pointer gauge. The

pointer gauge is capable to measure the position of pitot tube in transparent test section. The pipe

has a flow control valve to regulate the flow. A manometer is provided to determine the velocity

head. A pump is provided to calculate the water. Discharge is measured with the help of measuring

tank and stop watch.

UTILITIES REQUIRED

(1) Water supply

(2) Drain

(3) Electricity 0.5 KW, 220 VAC, Single phase

(4) Floor area 1.5 0.75 m

EXPERIMENTAL PROCEDURE

Clean the apparatus and make tank free from dust.

Close the drain valves provided

Fill sump tank ¾ th with clean water and ensure that no foreign particles are there.

Close all flow control valves given on water line and open by-pass valve.

Close all pressure taps of manometer connected to manometer.

Ensure that on/off switch given on the panel is at off position.

Now switch on the main power supply.

Switch on the pump.

Operate the flow control valve to regulate the flow of water through orifice.

Open pressure taps of manometer of related test section.

Now open the air release valve provided on the manometer, slowly to release the air from

the manometer.

When there is no air in the manometer, close the air release valve.

Adjust water flow to desired rate with the help of control valve.

Set the Pitot tube at the centre of test section.

Record the manometers reading and measure the discharge with the help of measuring tank

and stop watch.

Now move the Pitot tube up & down at the same flow rate and note the manometer

readings to find out the velocity at different points in pipe.

Calculate the coefficient of Pitot tube from actual and theoretical velocities and plot the

velocities at different points inside the pipe.

Repeat the same procedure for different flow rates of water, operating control valve and by-

pass valve.

CLOSING PROCEDURE

When experiment is over, first of all close all pressure taps of the manometer.

Switch off pump

Switch off power supply to panel

Drain water from all tanks with the help of given drain valves

FORMULA USED

a) Discharge

Q=A×R (m3/s)

t×100

b) Actual velocity

Va= Q/a (m/s)

c) Theoretical velocity

Vth = √(2gH), m/s

H =h/100(ρm/ρw -1) , m

d) Co efficient of pitot tube

Cv = Va/Vth

e) Velocity at any point

V=Cv * √(2gH), m/s

Nomenclature

A=Area of measuring tank, m2

a=Cross section area of test section, m2

Cv=coefficient of pitot tube

g=acceleration due to gravity, m/s2

h=manometer reading, cm

H=pressure head in meter of water, m

Q=Discharge, m3/s

R= Rise of water level in measuring tank,cm

ρm=Density of manometer fluid(CCl4)Rg/m3

ρw= Density of water, Rg/m3

t=time taken for R, sec

V=Velocity at any point, m/s

Va=Actual velocity of fluid, m/s

Vth=Theoretical velocity of fluid, m/s

Given Data:

Area of the discharge tank= 0.1m2

Area of the pipe = 0.0006157m2

ρ(water) = 1000 kg/m3

ρ(manometer liquid) = 1590 kg/m3

g = 9.81 m/s2

Tabular Column:

To calculate the coefficient of velocity of pitot tube

Sl h(cm) Manometer Reading (cm) t(s)

No:

R1 R2 R

1.2.3.4.5.

To calculate coefficient of velocity of Pitot tube

SlNo:

H(m) Q(m3/s) Va(m/s) Vth(m/s) CV

1.2.3.4.5.

To plot velocity profile

Sl No: Manometer readings for pitot tube readings above centre

at center Manometer readings for pitot tube readings below the center

Position 8 mm 6 mm 4 mm 2 mm 0 position -2 mm -4 mm -6 mm -8 mm

Head, H

Velocity, V

MODEL CALCULATION:

a) Discharge Q=

b) Actual velocity Va=

c) Theoretical velocity Vth = √(2gH)

H = h/100(ρm/ρw -1)

d) Co efficient of pitot tube Cv =

e) Velocity at any point V= Cv * √(2gH)

RESULT

1. The coefficient of pitot tube =

2. The point velocity at the centre of tube for different flow rates has been measured and the

velocity profile across the cross section has been plotted.

REASONING

VERIFICATION OF BERNOULLI’S THEOREM

Aim

To verify Bernoulli’s equation experimentally, to calculate the total energy at different

points and to plot the graph between total energy vs distance.

Theory

This is the energy equation and based on the law of conservation of energy. This equation

states that at two sections of flow field the total energy remains the same; provided that there is no

loss or gain energy between the two sections. This equation is valid only for steady flow. This eqn.

expressed as:

E = P1/ g + V12/2g + Z1 = P2/ρg + V2

2/2g + Z2

If Z1 = Z2,

E =P1/ρg + V12/2g = P2/ ρg + V2

2/2g

PROCEDURE

a) Ensure that all on / off switches given on the panel are at of position.

b) Close all the drain valves provided.

c) Fill sump tank 3/4 th with clean water and ensure that no foreign particles are there.

d) Close flow control valve given at the end of test section.

e) Open by-pass valve given on the water supply line.

f) Now switch on the main power supply.

g) Switch on the pump.

h) Partially close by-pass valve to allow water to fill the over head tank.

i) Wait until over flow occurs from over head tank.

j) Regulate the flow of water through the test section with the help of test section.

k) Ensure that over flow still occurs; if not partially close the by-pass valve to do so.

l) Measure pressure head by piezometer tubes.

m) Measure flow rate of water using measuring tank and stop watch.

n) Repeat (j) to (m) for different flow rate of water.

CLOSING PROCEDURE

a) When experiment is over, switch of pump.

b) Switch of power supply to panel.

c) Drain water from all tanks with the help of given drain valves.

FORMULAE USED

Total energy, E =P/ρg +V2/2g +Z (m)

Velocity of fluid, V = Q/a m/s

Discharge

Q = A×R (m3/s)

t ×100

Kinetic energy = V2/2g

OBSERVATION

Tube No:

Cross section area, a(m2) Distance from referred point, S(m)

1.2.3.4.5.6.7.

4.91 x 10-4

3.14 x 10-4

1.77 x 10-4

0.785 x 10-4

1.77 x 10-4

3.14 x 10-4

4.91 x 10-4

0.040.07850.0920.11050.13580.15620.1915

SlNo:

Manometer Readings (cm)

T(s) Height at piezometric tube no: h(cm)

R1 R2 R 1 2 3 4 5 6 712345

Tube No:

Q(m3/s) Velocity(m/s)

Z(m) Pressure energy, P/

Kinetic energy,

Total Energy

ρg=h (m) V2/2g (m) (m)1234567

MODEL CALCULATION

Discharge Q=

Velocity V1 = Q/ a1

Pressure Energy =

Kinetic Energy =

Total Energy E =

NOMENCLATURE

ρ = Density of fluid, kg/m

A = Area of measuring tank, m2

a = Cross section area at test point, m

E = Total energy,

g = Acceleration due to gravity, m/s

h = Pressure head, mm of water

P = Pressure of fluid

Q = Discharge through the test section, m3/s

R = Rise of water level in measuring tank, cm

R1 = Final height of water in measuring after time t1, cm

R2 = Initial height of water in measuring tank, cm

T = Time taken in seconds

V = Velocity of fluid (m/s)

Z = Potential energy per unit weight or potential head

RESULT

a) The Bernoulli’s theorem was experimentally verified

b) The graph between pressure energy, kinetic energy and total energy Vs distance was

plotted.

REASONING

DISCHARGE COEFFICIENT OF VENTURIMETER AND ORIFICEMETER

AIM

To demonstrate the use of venturimeter and orifice meter as flow meters and to determine

the coefficient of discharge Cd for venturimeter and orifice meter.

THEORY

Venturimeter

A venturimeter consists of

1) An inlet section followed by a convergent cone.

2) A cylindrical throat

3) A gradually divergent cone

The inlet section of venturimeter is of same diameter as that of the pipe, followed

by a convergent cone. The convergent cone is a short pipe which tapers from original size

of the pipe to that of the throat of the venturimeter. The throat of the venturimeter is a short

parallel side tube having its cross-sectional area smaller than that of the pipe. The divergent

cone of the venturimeter is a gradually diverging pipe with its cross sectional area

increasing from that of the throat to original size of the pipe. At inlet section and throat of

the pipe, pressure taps are provided.

Orificemeter

An orificemeter consists of a flat circular plate with a circular hole called orifice with pipe

axis.

SPECIFICATION

Venturimeter: Material clear Acrylic compatible to 1n pipe

Orificemeter: Material clear Acrylic compatible to 1n pipe

Water- circulation: FHP PUMP

Flow measurement: Using measuring tank with piezometer, capacity 25 Ltrs.

Sump tank: Compatible capacity, material SS

Control panel comprises of: Standard make on /off switch, mains indicator etc.

Tanks made of stainless steal.

PROCEDURE

Clean the apparatus and make all tanks free from dust. Close the drain valves provided. Fill

sump tank ¾ with clean water and ensure no foreign particles are present. Open the by-pass valve.

Close all pressure taps of manometers connected to venturimeter and orificemeter. Switch on the

pump. Operate flow control valve to regulate the flow. Now release the air valve provided on

DPTO to release air from the manometer and then close it. Measure the discharge using stop watch

and measuring tank. Repeat steps for different flow rates. After experiment is over for one rest

section. Repeat the same for the next section.

FORMULAE USED

Actual discharge Qa = A X R m3/s

t X 100

Theoretical discharge

Qt = a1 a2 √(2gH) m3/s

√(a12 – a2

2)

Coefficient of discharge, Cd = Qa/Qt

Loss of head, H = h/1000 m of water

Given Data:

Area of the discharge tank ‘A’ = 0.1m2

Diameter of the pipe section ‘d1’ = 0.028mDiameter at the orifice section ‘d2’ = 0.014mDiameter at the throat section ‘d2’ = 0.014m

OBSERVATION

Venturimeter

Sl No:

h(m) Manometer Reading T(s)R1(cm) R2(cm) R(cm)

1234567

Orificemeter

Sl No: h(m) R(cm) R(cm) T(s)R1(cm) R2(cm)

1234567

CALCULATION

Venturimeter

Sl No: H(m) Qa(m3/s) Qt(m3/s) Cd

Orificemeter

Sl No: H(m) Qa(m3/s) Qt(m3/s) Cd

MODEL CALCULATION

RESULT

1) The coefficient of discharge

Cd = (venturimeter)

Cd = (orificemeter)

2) Graph between Qt Vs Qa and H Vs Qa has been plotted.

REASONING

FLOW THROUGH ORIFICE AND MOUTH PIECE

AIM

1) To study the flow through orifice and mouth piece.

2) To determine the coefficient of discharge.

3) To determine the coefficient of velocity.

THEORY

Orifice

When a liquid flows from a vessel or a tank through an orifice it changes its direction. Due

to the change of direction the jet is acted up by lateral or side force which gradually reduces its

area up to certain section. This area does not reduce further beyond. With it causes and stream line,

first become parallel known as Vena contracta.

Mouth piece

A short piece of length about three times of its diameter connected to the face of the orifice

is known as a mouth piece; in what follows it will be proved that under a given head the rate of

discharge through a mouth piece will be more than that through the orifice of the same diameter

the reason being that while entering in to the mouth piece the liquid yet a vena contracta. Due to

the increase in the velocity of liquid, pressure decreases. The pressure at vena contracta is less

than at the atmosphere. This may be verified by applying Bernoulli’s Theorem at the outlet and at

the vena contracta.

Coefficient of viscosity

It is defined as the ratio between the actual velocity of jet of liquid at vena contracta and

the theoretical velocity of the jet. It is denoted by Cv and Cv is given by

Cv= Actual velocity of jet at vena contracta

Theoretical velocity

Cv= Va/√ (2gH)

Coefficient of discharge

It is defined as the ratio of the actual discharge from an orifice to the theoretical discharge.

It is denoted by Cd. If Qa is the actual discharge and Qt is the theoretical discharge then,

Cd = Qa/Qt .

EXPERIMENTAL PROCEDURE

a) Clean the apparatus and make all tanks free from dust.

b) Close the drain valves provided.

c) Fill the sump tank ¾ with clean water and ensure that no foreign particles are there.

d) Close all flow control valves given on the water line.

e) Open the by-pass valve.

f) Fix desired test piece at testing section.

g) Ensure that all ON/OFF switches given on the panel are at OFF position.

h) Now switch on the main power supply.

i) Switch on the pump.

j) Open the flow control valve to regulate the flow of water on the measurement tank.

k) Adjust the read of water in the tank with the help of given flexible varying head system in

the centre of the tank.

l) Now the pointer gauge at vena contracta observes water coming out from the tank.

m) Record the pointer gauge reading.

n) Measure the flow of water discharged through desired test section using stop-watch and

measuring tank.

o) Repeat the experiment for different water reads.

p) When the experiment is over for one desired test piece first open the by-pass valve fully.

q) Then close the flow control valve

r) Drain the variable head tank in sumo tank by means of given drain valve.

s) Change second test piece.

Closing procedure

a) Switch off the pump

b) Switch off power supply to panel

c) Drain water from all tanks with the help of given drain valves.

FORMULAE USED

a) Coefficient of velocity

Cv = V/√2gh = x/√4yh

b) Actual discharge Qa= A*R/(t*100) m3/s

c) Theoretical discharge, Qt=a*√(2gH)

d) Coefficient of discharge, Cd = Qa/Qt

Orifice

Sl No:

Height of water in tank, H(cm)

x(cm) Y(cm) Time taken, t(s)

Piezometric reading R(cm)

R1 R2

Mouth piece

Sl No: Height of water in

tank, H(cm)

x(cm) Y(cm) Time taken, t(s)

Piezometric reading R(cm)

R1 R2

CALCULATION

Orifice

Sl No:

H(m) Qa(m3/s) Qt(m3/s) Cd Cv V=Q/a(m/s)

Mouth piece

S H(m) Qa(m3/s) Qt(m3/s) Cd Cv V=Q/a

l No:

(m/s)

Given Data:

Area of the discharge tank ‘A’ = 0.1m2

Area at the orifice and mouthpiece opening ‘a’ = 7.853 x 10-5 m2

MODEL CALCULATION

Actual discharge =

Theoretical discharge =

Coefficient of discharge =

Coefficient of velocity =

Velocity =

RESULT

a) The flow characteristics have been studied and the coefficient of discharge and

coefficient of velocity for mouth piece and orifice have been found out.

b) The coefficient of discharge for

orifice , Cd=

Mouthpiece, Cd =

The coefficient of velocity for

Orifice, Cv =

Mouthpiece Cv=

REASONING

DISCHARGE OVER THE NOTCHES

AIM

To study the discharge over different types of notches.

To determine the coefficient of discharge through different types of notches.

a) Rectangular notch

b) V-notch-450

c) V-notch-600

THEORY

Coefficient of discharge

The ratio of actual discharge over a notch to the theoretical discharge is known as the

coefficient of discharge. Mathematically, the coefficient of discharge is

Cd=Actual discharge/Theoretical discharge

Discharge over a trapezoidal notch

Qa = Cd * [2/3*L*√ (2g) H3/2+8/15* /2 *√ (2g) *(H) 5/2]

Discharge over a triangular notch

Qa=Cd [8/15* /2 √ (2g) * (H)5/2]

Discharge over a rectangular notch

Qa=Cd [2/3 * L*√ (2g) *H3/2]

EXPERIMENTAL PROCEDURE

Starting procedure

a) Clean the apparatus and make free from dust

b) Close the drain valves provided

c) Close the flow control valve provided first water line

d) Open by-pass valve

e) Fix desired notch on the flow channel

f) Fill sump tank ¾ with clean water and ensure that no foreign particles are there.

g) Ensure that ON/OFF switches given on the panel ate at OFF position.

h) Now switch on the main power supply

i) Switch on the pump

j) Record crest height for notch

k) Regulate flow of water through channel with the help of pointer gauge

l) Record the height of water level in the channel with the help of provided drain valves.

CLOSING PROCEDURE

a) When experiment is over, switch off the pump.

b) Switch off power supply to panel.

c) Drain water from all three tanks with the help of provided drain valves.

FORMULAE USED

a) Actual discharge

Qa = A X R/(t x 100)

b) Head over crest

H = h-hc/100

c) Theoretical discharge over triangular notch

Qt = [8/15* /2 √ (2g) * (H)5/2]

d) Theoretical discharge over rectangular notch

Qt = 2/3 * L*√ (2g) *H3/2]

e) Coefficient of discharge

Cd = Qa/Qt

For rectangular Notch, L =6.5 cm

Observation: V- Notch, ho=5.4 cm

Sl No: h(cm) t(s) R1(CM) R2(cm) R(cm)

Trapezoidal notch, ho = 5.4 cm

Sl No: h(cm) t(s) R1(CM) R2(cm) R(cm)

V-Notch

Sl No: H(m) Qa(m3/s) Qt(m3/s) Cd ln Qt ln H

Trapezoidal Notch

Sl No: H(m) Qa(m3/s) Qt(m3/s) Cd ln Qt ln H

MODEL CALCULATION

RESULTS

1) The coefficient of discharge has been found and is

Cd for V notch (angle ө = ) =

Cd for Rectangular notch =

From the graph of ln v/s lnH was plotted in which, slope ‘n’ and intercept ‘k’ are found and

equation for discharge for V notch and trapezoid notch are as follows

1) V notch = Q = kHn =

2) Rectangular notch Q = kHn =

REASONING

LOSSES DUE TO PIPE FRICTION

1. OBJECTIVES

To study the losses due to friction in pipe lines 2. AIM

To determine the friction factor for Darcy-Weisbach equation 3. INTRODUCTION

When a fluid is flowing through a pipe , the fluid experiences due to which some of the energy of fluid is lost. This loss of energy in the pipelines comes under major energy losses and minor energy losses. In long pipelines the friction losses are much larger than the minor losses and hence, the latter are often neglected. The losses due to friction in pipelines are known as major energy losses. The friction in pipeline due to a viscous drag between the stream bands of fluid. The stream bands of adjacent to the solid surface are always at rest relative to the wetted surface. The viscous drag is due to the molecular attractions between the molecular of the fluid.

4. THEORY It is found that the total friction resistance to fluid flow depends on the following:

a) the area of the wetted surfaceb) The density of the fluid

C) The surface roughness d) it is independent of the fluid pressure e) It increase with the square of the velocity

The loss of head in pipe due to friction is calculated from Darcy-Weisbach equation which has been given by: .hf = 4f LV2/2gd

.hf =Loss of head due to friction .f = Co-efficient of friction L = Distance between pressure point V=Mean velocity of fluid .d= diameter of pipe .g= Acceleration due to gravity

5. DESCRIPTION The apparatus consist of two pipes of different diameter for which common inlet connection is provided with control valve to regulate the flow ,near the down stream end of the pipe .pressure taping are taken at suitable distance apart between which a manometer is provided to study the pressure loss due to the friction . Discharge is measured with the help of measuring tank and stop watch.

6. UTILITIES REQUIRED (a) Power supply: single phase ,220volts,50Hz, 5amp with earth (b) Water supply (c) Drain (d) Space required: 1.6m x0.6m

7. EXPERIMENTAL PROCEDURE Starting procedure

(a) clean the apparatus and make all tanks free from dust(b) Close the drain valve provided(c) Fill sump tank ¾ with clean water and ensure that no foreign particles are there (d) Close all flow control valves given on the water line and open by- pass valv e(e) Close all pressure taps of manometer connected to pipes (f) Ensure that On/Off switch given on the panel is at off condition (g) Now switch on the main power supply (h) Switch on the pump(i) Operate the flow control valve to regulate the flow of water in the desired test section (j) Open the pressure taps of manometer of related test section ,very slowly to avoid the blow

of water on manometer fluid (k) Now open the air release valve provided on the manometer ,slowly to release the air in

manometer .(l) When there is no air in the manometer ,close the air release valve(m) Adjust water flow rate in desired section with the help of control valve (n) Record the manometer reading (o) Measure the flow of water ,discharged through desired test section,using stop watch and

measuring tank (p) Repeat same procedure for different flow rates of water ,operating control valve and by

pass valve (q) When experiment is over for one desired test section ,open the by pass valve fully. then

close the flow control valve of running test section and open the control valve of secondly desired test section .

(r) Repeat the same procedure for selected test section and so on.

8. SPECIFICATION: Pipes (2 nos) : Material GI of ½’’ &3/4’’ diameter Pipe test section: length 1.5m for3/4’’ pipe 1m for ½’’ pipe Water circulation: FHP Pump Flow measurement: Using measuring tank with piezometer, capacity 25 ltrs Sump tank : Capacity 50ltrs Stop watch : electronic Control panel comprises of: Standard make on /off switch, main indicator, etc Tanks made of stainless steel The whole set up is well designed and arranged in a good quality painted structure

9. FORMULAE (a) Head losses , H =h/1000, m of water (b) Co- efficient of Friction: .f = hf 2gd / 4LV2

(c) Discharge Q= AxR / (t x 100) m3/s (d) Velocity of fluid V =Q/A m/s

OBSERVATIONS AND CALCULATIONS DATA: A = 0.1m2

.g = 9.81m/s2

.ρm = 13600kg/m3

. ρw = 1000 kg/m3

.d = 0.022m (for pipe 3/4’’) = 0.016m (for pipe 1/2’’) .a = 3.800 x 10-4m2(for pipe 3/4’’)

= 2.0106 x 10-4m2(for pipe 1/2’’)= 1.5m (for pipe 3/4’’)= 1m (for pipe 1/2’’)

OBSERVATION TABLE: S.No h(mm of water) R (cm) t(sec)

CALCULATION TABLE:S.No hf ( m ) Q (m3/s) V (m/s) f

NOMENCLATURE A =Area of measuring tank, m2

a =Cross sectional area of pipe, m2

d = Inside diameter of pipe, m f =Coefficient of friction g = Acceleration due to gravity, m/s2

h = Manometer reading, cm hf =Head loss in m of water L =Distance between pressure tapings, m Q= Discharge, m3/s R= Rise of water level in measuring tank (cm) t = Time taken for R (sec) V= Velocity of fluid ,m/s ρm= Density of manometer fluid (Hg) kg/m3

ρw= Density of water,kg/m3

MODEL CALCULATION

RESULT

REASONING

LOSSES DUE TO PIPE FITTINGS

1. OBJECTIVESTo study the losses due to friction in pipe lines

2. AIMTo determine the friction factor for Darcy – Weisbatch equation

3. INTRODUCTION

When a fluid flowing through a pipe, the fluid experiences some resistance due to which some of the energy of fluid is lost. This loss of energy in the pipelines comes under major energy losses and minor energy losses . in long pipe lines the friction losses are much larger than the minor losses and hence , the latter are ofen neglected. The losses due to friction in pipeline known as major energy losses. The friction in the pipeline due to a viscous drag between the stream bands of fluid. The stream bands of adjacent to the solid surface. The viscous drag is due to the molecular attractions between the molecular of the fluid.

4. THEORYIt is found that the total friction resistance to fluid flow depends on the following:

a) the area of the wetted surfaceb) the density of the fluidc) the surface roughnessd) it is independent to the fluid pressuree) it increase with the square of the velocity

the loss of head in pipe due to friction is calculated from Darcy-Weisbatch equation . which has been given by :

hf = 4f LV2 / 2 g d

hf = loss of head due to the friction

f = co-efficient of friction

L = distance between pressure point

V = mean velocity of fluid

d = diameter of pipe

g = acceleration due to gravity

5. DESCRIPTION

The apparatus consist of two pipes of different diameter for which common inlet connection is provided with control valve to regulate the flow, near the down stream end of the pipe. Pressure tapings are taken at suitable distance apart between which a manometer is provided to study the pressure loss due to the friction. Discharge is measured with the help of measuring tank and stop watch.

6. UTILITIES REQUIREDa) power supply: single phase, 220 volts, 50 Hz , 5 Amp with earthb) water supply c) Draind) Space required : 1.6 m x 0.6 M

7. EXPEREMENTAL PROCEDURE Starting procedure

a) clean the apparatus and make all tanks free from dustb) close the drain valves providedc) fill sump tank ¾ with clean water and ensure that no foreign particles are thered) close all flow control valves given on the water line and open By-pass valve.e) Close all pressure taps of manometer connected to pipesf) Ensure that On/Off switch given on the panel is at OFF positiong) Now switch on the mail power supplyh) Switch on the pumpi) Operate the flow control valve to regulate the flow of water in the desired test sectionj) Open the pressure taps of manometer of related test section, very slowly to avoid the blow

of water on manometer fluidk) Now open the air release valve provided on the manometer, slowly to release the air in

manometerl) When there is no air in the manometer , close the air release valvesm) Adjust water flow rate in desired section with the help of control valven) Record the manometer readingso) Measure the flow of water, discharged through desired test section, using stop watch p) Watch and measuring tankq) Repeat same procedure for different flow rates of water, operating control valve and By-

pass valve.

r) When experiment is over for one desired test section, open the By-pass valve fully. Then close the flow control valve of running test section and open the control valve of secondly desired test section

s) Repeat the same procedure for selected test section and so on.

Closing procedure

a) when experiment is over , close all manometer pressure taps firstb) switch off pumpc) Switch off power supply to panel

8..SPECIFICATION

Sudden enlargement : from 15mm to25mm

Sudden contraction : From 25mm to 15mm

Bend : ½’’

Elbow : ½’’

Ball valve : ½’’

Gate valve : ½’’

Water circulation : FHP Pump

Flow measurement : Using measuring tank with piezometer,

Capacity25 ltrs

Sump tank : Capacity 50 ltrs

Stop watch : Electronic

Control panel : Standard make on /off switch ,mains indicator

,etc

The whole set up is well designed and arranged in a good quality painted structure

9.FORMULAE

(a) Discharge :

Q = A x R / t x 100

(b) Velocity

V1 = Q/a1

V2 = Q/a2

(c) Loss Coefficient (for contraction ) KL = hL 2g / V1

2

(d)Loss coefficient (for expansion)

KL = hL 2g / (V2 - V1)2

(e) Loss of head

H = h/1000,m of water

(f)Loss coefficient for pipe fittings

KL = hL 2g / V12

10.OBSERVATIONS AND CALCULATIONS

DATA:

A = 0.1 m2

g = 9.81m/s2

d = 0.016m & 0.028m

a1=2.0106x10-4m2

a2=6.157x10-4m2

OBSERVATION TABLE:

S.No h(mm of water) R(cm) t(sec)

CALCULATION TABLE:

Sl No Q m3/s V1 m/s V2 m/s hL m KL

11. NOMENCLATURE:

A = Area of measuring tank,m2

a1 = Cross sectional area of small dia .pipe m2

a2 = Cross sectional area of large dia .pipe m2

d = Diameter of pipe g =Acceleration due to gravity, m/s2

h = Manometer reading, cm hL = head loss ,m of water KL = Loss coefficient Q = Discharge, m3/s R = Rise of water level in measuring tank, cm t = Time taken for R (sec) V1 = Velocity of fluid in pipe of small diameter, m/s V2 = Velocity of fluid in pipe of large diameter, m/s ρm = Density of manometer fluid (Hg) kg/m3

ρw = Density of water, kg/m3

MODEL CALCULATION

RESULT

REASONING

PRESSURE DROP THROUGH A PACKED BED

AIM

To study the pressure drop through a packed bed

To determine the pressure drop per unit length of bed

To plot modified Reynolds no. vs. modified friction factor on a log –log plot

INTRODUC TION

Packed bed provides a large surface area of contact between two fluids and is thus extensively used

in distillation, extraction, absorption etc.As the fluid passes through the bed, it does so through

the voids present in the bed. the void form continuous channels through out the bed. The flow

may be laminar through some channels

THEORY

Friction factor is given by Kozeny-Carman equation

. f = ∆P/ρl x ε3/(1- ε) x VP/ SPV2 = Function of (Re)m ……………….(i)

For spherical particles, VP /SP = DP and for non spherical particle

. f = ∆P/ ρ V2 x фs DP ε3 / l (1- ε)

Where DP is the equivalent diameter and фs is the sphericity of the particle defined as

фs = 6 VP / DPSP

VP is the volume of one particle and SP is surface area .Ergun has derived a packed bed for

spherical particles,

∆P ε3DP /ρ l (1- ε) V2 = f = 150(1- ε) μ /ρ V DP +1.75

Modified Reynold’s no (Re)m is defined as

VP ρ V / SP μ (1- ε) =(Re)m = DP фs ρ V / μ(1- ε)

DESCRIPTION

The apparatus consist of a glass column packed with rasching glass packing and the water

flow through rotameter, fitted in pipe line .The pump takes the water and passes to the column

and discharge is controlled by using the ball valveand gate valve. pressure tapping are taken out

from inlet.discharge is measured with the help of rotameter.

EXPERIMENTAL PROCEDURE

Allow the water to flow down from the bottom to top in the packed bed

Regulate flow of water by means of valves

Record the flowrates of water from rotameter

Note the pressure drop across the bed using manometer

Repeate the same procedure at different flow rates of water.

FORMULAE

1. Surface area SP = π LP (do+di)+2 π/4(do2+di2)

2. Volume VP = π/4(do2+di2) LP

3. Sphericity of particle фs = 6 VP / DPSP

4. Discharge of water Q =FW x 10-3 /3600

5. Velocity of water v = Q/A

6. Modified (Re)m = DP фs ρ V / μ(1- ε)

7. Ergun’s friction factor fr = 150/ Re

fr =150/ (Re)m +1.75 ((Re)m> 1000)

8. experimental friction factor f p = ∆P фs DP ε3 / ρ V2l (1- ε)

9. pressure drop per unit length of bed ∆P /l = h x (0.8853) (N/m2)

DATA

D = 0.05m A= 1.964 x 10-3 m2

SP=4.95 x10-4 m3 do = 0.009m g = 9.81m/s2 di = 0.006m ρ= 1000kg/ m3 LP=0.009m DP= 0.00847m L = 0.36m

ε =0.66 фs=0.455 μ = 8.29 x 10-4 Ns/ m2

OBSERVATION

Sl

No

Rotameter

reading LPH

Full length h (mm) Half length h(mm)

Forward Reverse Forward Reverse

123

8910

CALCULATION TABLE

Sl

No

Q V

m/s

Re fr Fp(half) Fp(full) ∆P/l(half) ∆P/l(full)

MODEL CALCULATION

RESULT

Pressure drop per unit length of the bed was calculated

Plotted the log –log graph for friction factor and modified Reynolds number

REASONING

FLUIDISED BED APPARATUS

AIM

To study the flow through fluidized bed and tom determine pressure drop per unit length of bed.

THEORY

Fluidization is one of the methods available for contacting granular solids with fluids. A fluidized

bed provides a higher interfacial surface area of contact of higher transfer rates .When a fluid is passed

upward through bed of solids ,there will be certain pressure drop across the bed to maintain the fluid

flow .Depending up on the bed geometry , fluid velocity and particle characteristics the following

phenomenon occurs with gradual increase in fluid velocity .

At law velocities there is a pressure drop across the bed but the solid bed is static (curve AB) as

the fluid velocity is reached the bed starts expanding .At this point the pressure drop across the bed

equals to the mass per unit area of the bed .This point is known as point of incipient fluidization .Once

the particle are separated , pressure require to maintain fluidization is less. As the velocity is further

increased ,the pressure drop remains constant until the bed assume a loosest form of packing

If froude’s number , f >1 aggregative fluidization

.f < 1 particulate fluidization

Pressure drop across a fixed bed is given by Erguns equation

∆Pε Dp/ ρL(1-ε)V2 = 150 (1-ε)µ/ DpVp ------------------1

. ε =ZA – WS/ρ /ZA= 1- WS/ZAρ

At the onset of fluidization pressure drop across the bed equals the weight or bed per unit area of

cross section.

∆P/z = ρ(ρp- ρ)( 1-ε)-----------------------3

From equation 1 and 3

The minimum fluidization velocity Vmf = Dp2g (ρp- ρ) ε3mf / 150(1- εmf ) µ

Fluidization efficiency = GF-Ge/ Ge

Porosity of static bed

Take some solids in a granulated cylinder and note it’s initial volume (v1). Add a known

volume (v2) of water & note the final volume. The porosity of static bed is given by,

ε0 =V1+V2-V3/V1

PROCEDURE

Note height of bed in column .start with minimum flow of water in the column at a constant

rate .Note the flow rate ,bed height(z) and pressure drop across the column after the steady state is

reached .Gradually increase the flow rate of water steadily and repeat the above step for 8-10 different

rate of flow continue till the bed is fluidized and finally becomes turbulent.(ie, there is no appreciate

change in pressure drop indicated by manometer .)Now decrease the flow rate back to zero and record

the same data.

FORMULAE

Velocity of water =v = Q x 10-3/3600A

Pressure drop per unit length of bed ∆P/Z = h x 9.81N/m3

Porosity of fluidized bed ε = 1-z0/z1 (1- ε0)

Wen and Yu equation (NRe)mf =(A2+BNar)1/2-A

Nar = (dp) 3 x ρH2O (Pρ- ρH2O) ρ /µH2O2

OBSERVATION

SL

No

Q (LPH) Forward reverse

Z(cm) h(mm) Z(cm) h(mm)

1

2

3

9

10

CALCULATION TABLE

Sl No Flow rate Q m3/s

Height(10-2m) V m/s

Pressure drop, ∆P/z (N/m2)

Porosity (ε) NRe

forward reverse forward reverse forward reverse

1.

RESULT

Minimum fluidization velocity from Pressure drop curve for forward = m/s

Minimum fluidization velocity from Pressure drop curve for reverse = m/s

Minimum fluidization velocity from porosity graph =

Minimum fluidization velocity from Wen & Yu equation =

REASONING

DRAG COEFFICIENT

AIM

To study the drag coefficient of a falling sphere for the given fluid To determine the settling velocity of particle for the given fluid To plot graph for logarithmic Reynold’s number vs logarithmic CD

To verify the stok’s law

THEORY

When a sphere falls through a liquid at terminal settling velocity , the drag coefficient can be

determined as a function of NRe .At law NRe , Stoke’s law prevails as the initial forces are negligible

and drag is a function of viscosity

When the particle is at a sufficient distance from the boundary of the containers and from all

other particle (no particle or solid boundary should be either 20 times the diameter of the particle ), so

that is motion is not affected by them,the process is called free settling .Now the forces acting on the

particle are the gravitational force, buoyant force and the drag force .The resultant force on the

particle is equal to fg-fb- fd.At terminal settling velocity ,the resultant force are equal to zero.

CD = 4 DP (lp-l1)g / 3Ut2 l1

Ut = g DP2 (lp-l1) / 18µ

At low Reynold’s no ie, NRe<1, fd.= 3πUtDPµ, This is stoke’s law,in this range ,

CD = 24/ NRe ie , is a graph of log CD vs log NRe will be a straigtht line with slope 1

PROCEDURE

The equipment consist of two long columns filled with glycerin solution and gingelly oil .

Two points are marked in the column , one near the top ( at a distance of about 20 cm from the top) and the other near the bottom .It is assured that by the time a particle reaches the first mark it would have reached terminal velocity . The distance between the marks is measured A spherical particle is taken and its diameter is measured using screw gauge. The particle 1 is first dropped at the center of the column with zero velocity and the time taken to travel the distance is noted. The experiment is repeated with particles of different diameter and material. The same procedure is repeated for the fluid in the second column. The observations are tabulated and log CD vs log NRe is plotted. Precautions should be taken that the particle should have no initial velocity and the particle should be dropped exactly at the centre of the column.

FORMULAE

UF =Height /time taken (m/s)

NRe = (DPUt l1) /µ1

Ut = g DP2 (ρp- ρ1) / 18µ

CD = 4 DP (ρp- ρ1)g / 3Ut2 l1

Dp – diameter of the spherical particle, m

Ut – Terminal settling velocity, m/s

µl - Viscosity of the fluid, Nm/s2

ρp – density of the particle ,kg/m3

ρ1 – density of the fluid, kg/m3

g- Gravity force, m/ s2

fD –Drag force

DATA

Viscosity of glycerin =1.25 poise =1.25 kg/ms

Viscosity of gingelly oil = 8.5 poise = 0.85 kg/ms

Density of glycerin = 1261 kg/m3

Density of gingelly oil = 920 kg/m3

OBSERVATION

Sl no. Spherical particle used(Glass beads)

Diameter of particle, m

Density of particle, kg/m3

Distance travelled by the particle, m

Time taken, s

Gingelly oil 1

2

3

4

5

Glycerine 1

2

3

4

5

CALCULATION TABLESl no. Spherical

particle used(Glass beads)

Exp Velocity, V=Distance/time, m/s

Predicted velocity, m/s

NRe CD Log NRe

Log CD

Gingelly

oil

1

2

3

4

5

Glycerine 1

2

3

4

5

MODEL CALCULATION

RESULT

1. Slope of logarithmic Reynold’s number vs logarithmic CD(gycerine) is =

2. Slope of logarithmic Reynold’s number vs logarithmic CD(oil) is =

3. Stoke’s law is verified.

REASONING