EXPERIMENT ON FRICTION IN PIPES

OBJECT :

To determine Darcy Friction Co-efficient of flow in a pipe and to

investigate the velocity for different diameters of pipe.

APPARATUS:

1. Pipe line of three different diameters of G.I.

2. U-Tube manometer with a stabilizing valve to measure the pressure

difference across the tapping, one at either end of the pipe line fitted with a

Ball Valve.

3. A constant steady supply of water with a means of varying the flow rate

using Centrifugal Pump.

4. Measuring tank to measure the flow rate.

5. Each pipe line is provided with separate control valve to conduct

experiment separately.

THEORY:

A closed circuit of any cross-section used for flow of liquid is known as a

pipe. In hydraulics, generally, pipes are assumed to be running full and of

circular cross section. Liquids flowing through pipes are encountered with

frictional resistance resulting in loss of head or energy of liquids. This

resistance is of two types depending upon the velocity of flow.

1. Viscous Resistance and

2. Frictional Resistance, due to different diameters.

The viscous resistance is due to the molecular attraction between the

molecules of the fluid. At low velocities, the fluid appeared to move in layer or

lamina, and hence the nature of this flow is termed laminar flow or Stream line.

If the velocity of the liquid is steadily increased, at certain velocity termed as

the lower critical velocity the parallel bands of liquid will become wavy. On

further increase in the velocity these instabilities will increase in intensity until a

velocity corresponding to the upper critical velocity is attained. The region of

flow bounded by the lower and upper critical velocities is termed the transition

zone. For all further increase in velocity of flow the streamline remains in a

diffused state and the nature of this type of flow is termed turbulent. In this

case the flow is restricted by the friction between the liquid and the pipe

surface which is known as frictional resistance.

DEFINITIONS :

Laminar Flow:

A flow is said to be laminar, when the various fluid particles appear to

move in layers (or laminae) with one layer of fluid sliding smoothly over an

adjacent layer. Thus in the development of laminar flow, the viscosity of the

fluids plays a significant role. Laminar flow occurs when the viscous forces

predominate over the inertia forces; it has been generally accepted now that if

Reynolds number is less than 2,000, Laminar flow is sustained in pipes.

Laminar flow is characterized by low velocity, narrow boundary and high

viscosity. The loss of head due to friction (hf) is directly proportional to

velocity (V) in laminar flow through pipes i.e., hf is proportional to V.

Turbulent Flow:

Turbulent flow is an irregular motion in which fluid particles move in an

entirely haphazard or disorderly manner that results in rapid and continuous

mixing of the fluid particle. It is characterized by high velocity and low

viscosity. Turbulent flow occurs when inertial forces predominate over viscous

forces; and generally turbulent flows are considered to occur in pipes at

Reynolds number more than 4,000. The loss of head due to friction (hf) in

turbulent pipe flows varies as Vn, where, V is the velocity of flow and n varies

from 1.72 to 2.0.

Transitional Flow:

The state of flow in between the laminar and turbulent flow is called as

Transitional Flow. That is, for pipe flows at Reynolds number between 2,000

and 4,000, transitional state of flow prevails, which is a region of uncertain

behavior. As change of state of flow cannot be abrupt, the transition from one

state of flow to another alternates back and forth between laminar and turbulent,

within the range of Re from 2,000 to 4,000.

Reynolds Number:

Reynolds number signifies the relative predominance of the inertia to the

viscous forces occurring in a flow system. Thus it is the key to decide whether

a flow is laminar or turbulent. It is defined as the ratio of inertia force to

viscous force and is given by, Reynolds number,

Inertia force V DRe = ---------------- or Re = ----- (for circular pipe)

Viscous force

Where V = average velocity of flowD = diameter of pipe = Kinematic viscosity coefficient of the fluid

= 1x10-6 m2/sec

It may hower be pointed out that Reynolds number is a function of

boundary geometry and for non-circular conduits, it is given by Re= VL/,

where L is a characteristic length defining the boundary geometry.

Critical Reynolds Number & Critical Velocity:

The concept of critical Reynolds number and critical velocity is used to

distinguish between the regions of laminar, turbulent and transitional state of

flow.

Critical state is occurs when flow changes from one state in to another.

Lower critical Reynolds number for flow of fluid in pipes is of greater

importance as it indicates a condition below which all turbulence entering the

flow from any source will damped out by viscosity and thus sets a limit below

which laminar flow will always occur.

Experimentally, the value of lower critical Reynolds number has been

found to be approximately 2,000 for flow through pipes.

Upper Critical Reynolds number and upper critical velocity are the

limiting Reynolds number and limiting velocity above which the flow will

always be turbulent, that is, it marks the upper limit of laminar flow. The upper

critical Reynolds number is indefinite, being dependent upon initial

disturbances affecting the flow, shape of entry to pipe, roughness of the

boundary etc. By carefully conducting the experiment, laminar flows have been

obtained at Reynolds number has high as 14,000. However the practical value

of upper critical Reynolds number may be considered to lie between 2,700 to

4,000 for pipe flows; the value of 4,000 is generally accepted as upper critical

Reynolds number, above which flow in pipes is considered to be turbulent.

Between Reynolds number of 2,000 and 4,000 the transitional region exists in

pipes.

Darcy - weisbach Friction Factor:

Darcy Weisbach equation is commonly used for computing the loss of head due to friction in pipes. It is given by,

LV2

hf = f -----------

D2gwhere ,

hf = loss of head due to friction

L = length of pipe D = diameter of pipe V = mean velocity of flow in the pipe f = Darcy Weisbach friction factor.

The above equation indicates that the loss of energy head varies directly with velocity head (V2/2g), pipe length L and inversely with pipe diameter (D). The constant of proportionality used in Darcy Weisbach equation, in the above form, f, is called friction factor.

PROCEDURE:

All the necessary instrumentations along with its accessories are readily

connected. It is just enough to follow the instructions below:

1. Fill-in the sump tank with clean water.

2. Keep the delivery valve closed.

3. Connect the power cable to 1 Ph, 220V, 10 Amps with earth connection.

4. Switch -ON the Pump & open the delivery valve.

5. Adjust the flow through the control valve of the pump.

6. Open the corresponding ball valves of the pipe line.

7. Note down the differential head reading in the Manometer (Expel if any

air is there by opening the drain cocks provided with the Manometer).

8. Operate the Butterfly Valve to note down the collecting tank reading

against the Known time and keep it open when the reading are not taken.

9. Change the flow rate & repeat the experiment for different diameter of

pipes.

PRECATIONS AND THINGS TO REMEMBER:

1. Do not start the pump if the voltage is less than 180 V.

2. Do not forget to give electrical neutral & earth connections correctly.

3. Frequently (at least once in three months) Grease / Oil the rotating parts.

4. Initially, put clean water free from foreign material, and change once in

three months.

At least every week, operate the unit for five minutes to prevent clogging of the moving parts. TABULAR COLUMN:

SL.NO.

TYPE OF PIPE FITTING

MANOMETER READING mm of Hg TIME TAKEN FOR

10cm RISE OF WATER,

t ‘s’

VALVE POSITION

h

1.1”

(Dia ) 27mm

FULL OPEN

¼ OPEN

2. ¾” (Dia ) 21mm

FULL OPEN

¼ OPEN

3. ½”(Dia ) 15mm

FULL OPEN

¼ OPEN

Table of Calculation:

FRICTION IN PIPES SET UP

VALVE POSITION

TYPE OF PIPE FITTING (d)

MANOMETER READING mm

of Hg

TIME TAKEN

FOR 10cm RISE OF

WATER t 's'

AREA (A) hf ReDischarge

(Q)V f

FULL OPEN 1" (DIA = 27mm)1/4

FULL OPEN 3/4" (DIA = 21mm)

1/4

FULL OPEN 1/2" (DIA = 15mm)

1/4

hf = Loss of Head due to Friction in mRe = Reynolds NumberQ = Discharge in m3/secV = Velocity Head in m/secf = Friction Factor

FORMULAE:

DATA:

* Area of Measuring Tank, “A” = 0.075m2

* Length of pipe, “L” = 1.3 m.* Kinematic viscosity, = 1.00 x 10-6 m2/sec* Acceleration due to gravity, “g’’ = 9.81 m/sec2

* Diameter of pipe, “d’’ = 27, 21, 15 mm, (G.I)

1) Loss of Head due to Friction (hf):

12.6 H hf = ----------- m. 1000

Where, H = Difference in Mercury Column in mm of Hg in double column Manometer.12.6 & 1000 are conversion factors.

2) Discharge (Q):

A x RQ = ------------ in m3/sec

100 x tWhere, A = Area of Collecting tank = 0.075 m2

R = Rise of water in collecting tank in mt = time taken for ‘R’ rise of water in collecting tank in sec.

3) Velocity Head(V):

Discharge QV = --------------------- = ------ in m/sec.

Area of inlet section a

Where, Q = from formulae 2. a = area of pipe (π d2/4) in m2.

4) Friction Factor (f):

Loss of Headf = ------------------

Velocity Head

2 g d hf

f = ---------- 4 L V2

Where,hf = The loss of head due to friction = Formulae (1)g = Specific gravity = 9.81 m/sec2

d = diameter of pipe in m.L = The length of the pipe (Manometer tapping distance) in m.= 1.3 mf = Friction factor or co-efficient.V = Velocity Head = Formulae (3).

5) HYDRAULIC MEAN DEPTH (m)

d m = -----

4

d = diameter of pipe in m.

6) CHEZYS CONSTENT ©

V © = --------------------

hf

m × ----- L

V = Velocity Head = Formulae (3).m = Hydraulic mean depth

hf = The loss of head due to friction = Formulae (1)L = The length of the pipe (Manometer tapping distance) in m.= 1.3 m

7) MANNINGS CONSTENT (h)

m2 hf /L h = ----- × -----------

3 V

m = Hydraulic mean depthhf = The loss of head due to friction = Formulae (1)

L = The length of the pipe (Manometer tapping distance) in m.= 1.3 m V = Velocity Head = Formulae (3).

8) Reynolds Number (Re):

Inertia force V DRe = ---------------- or Re = ----- (for circular pipe)

Viscous force

Where, V = average velocity of flowD = diameter of pipe = Kinematic viscosity coefficient of the fluid(water)

1x10-6 m2/sec

AREA OF INLET

TYPE OF PIPE

FITTING

VALVEPOSITI

ON

MANOMET

ERREADING

mm of Hg

TIME TAKENFOR 10

cmRISE OF WATER

't' sec

AREA (A)

LOSS OF HEAD DUE

TO FRICTION

hf

DISCHARGE(Q)

VELOCITY

HEAD,V

DARCYS CONSTAN

T (f)

HYDRAULIC

MEAN DEPTH

(m)

CHEZYS CONSTEN

T ©

MANNINGS CONSTENT

(h)

FRICTION

FACTOR,f

REYNOLD'S

NUMBER,Re

0.00061"

(DIA = 27 mm)

FULL OPEN

5 12.28 0.075 0.063 0.000611 1.067249 0.0225387 0.00675 59.00859 3.44816E-07 0.005635 28815.72

0.0006 3/4th 4 13.01 0.075 0.0504 0.000576 1.007365 0.0202384 0.00675 62.27178 2.92251E-07 0.00506 27198.85

0.0006 1/2th 3 14.91 0.075 0.0378 0.000503 0.878995 0.019936 0.00675 62.74228 2.51199E-07 0.004984 23732.87

0.0006 1/4th 1 15.06 0.075 0.0126 0.000498 0.87024 0.0067797 0.00675 107.5904 8.45755E-08 0.001695 23496.48

0.00033/4"

(DIA = 21 mm)

FULL OPEN

4 12.75 0.075 0.0504 0.000588 1.699193 0.0071132 0.00525 119.1021 1.04812E-07 0.001383 35683.06

0.0003 3/4th 3 14.19 0.075 0.0378 0.000529 1.526759 0.006608 0.00525 123.5711 8.74873E-08 0.001285 32061.95

0.0003 1/2th 2 18.32 0.075 0.0252 0.000409 1.182572 0.0073429 0.00525 117.2247 7.53004E-08 0.001428 24834.01

0.0003 1/4th 1 23.41 0.075 0.0126 0.00032 0.925447 0.005995 0.00525 129.7354 4.81108E-08 0.001166 19434.39

0.00021/2"

(DIA = 15 mm)

FULL OPEN

7 13.13 0.075 0.0882 0.000571 3.234032 0.0034364 0.00375 202.7525 4.91691E-08 0.000668 48510.49

0.0002 3/4th 4 15.02 0.075 0.0504 0.000499 2.827087 0.0025696 0.00375 234.466 3.2141E-08 0.0005 42406.3

0.0002 1/2th 3 19.14 0.075 0.0378 0.000392 2.218539 0.0007824 0.00375 212.4601 3.0718E-08 0.000609 33278.09

0.0002 1/4th 1 23.22 0.075 0.0126 0.000323 1.828719 0.0003838 0.00375 303.3316 1.2422E-08 0.000299 27430.78

GUIDANCE FOR CALCULATION:DATA:* Area of Measuring Tank, “A” = 0.075m2

* Length of pipe, “L” = 1.3 m.* Kinematic viscosity, = 1.00 x 10-6 m2/sec* Acceleration due to gravity, “g’’ = 9.81 m/sec2

* Diameter of pipe, “d’’ = 27, 21, 15 mm, (G.I)

1) Loss of Head due to Friction (hf):- For 1” pipe

12.6 H hf = ----------- m. 1000

12.6 x 5= ---------- = 0.063 m.

1000Where, H = Difference in Mercury Column in mm of Hg in double column Manometer.12.6 & 1000 are conversion factors.

2) Discharge (Q):

A x RQ = ------------ in m3/sec

100 x t

0.075 x 10= -------------- = 0.000611 m3/sec

100 x 12.28

Where, A = Area of Collecting tank = 0.075m2

R = Rise of water in collecting tank t = time taken for ‘R’ rise of water in collecting tank in sec.

3) Velocity Head(V):

Discharge QV = --------------------- = ------ in m/sec.

Area of inlet section a

0.000611 ----------- = 1.067249 m/sec 0.0006

Where, Q = From formulae 2. = 0.0051 m3/sec a = area of pipe (π d2/4) in m2 = 0.0006 m2

4) Friction Factor (f):

Loss of Headf = ------------------

Velocity Head

2 g d hf 2 x 9.81 x 0.027 x 0.063f = ---------- = --------------------------------

4 L V2 4 x 1.3 x 1.067249^2

f = 0.0225387

Where,hf = The loss of head due to friction = Formulae (1)g = Specific gravity = 9.81 m/sec2

d = diameter of pipe in m.L = The length of the pipe (Manometer tapping distance) in m.= 1.3 mf = Friction factor or co-efficient.V = Velocity Head = Formulae (3).

5) HYDRAULIC MEAN DEPTH (m)

d 0.027 m = ----- = ----------- = 0.00675 m

4 4

d = diameter of pipe in m.

6) CHEZYS CONSTENT ©

V © = --------------------

hf

m × ----- L

1.067249 = ---------------------------- = 59.00859

0.063 0.00675 × --------

1.3

V = Velocity Head = Formulae (3).m = Hydraulic mean depth

hf = The loss of head due to friction = Formulae (1)L = The length of the pipe (Manometer tapping distance) in m.= 1.3 m

7) MANNINGS CONSTENT (h)

m2 hf /L h = ----- × -----------

3 V

0.006752 0.063 /1.3 h = ------------ × ------------------ = 3.44816E-07

3 1.067249

m = Hydraulic mean depthhf = The loss of head due to friction = Formulae (1)

L = The length of the pipe (Manometer tapping distance) in m.= 1.3 m V = Velocity Head = Formulae (3).

8) Reynolds Number (Re):

Inertia force V DRe = ---------------- or Re = ----- (for circular pipe)

Viscous force

1.067249x 0.027= ---------------------- = 28815.72

1.00 x 10-6

Where, V = average velocity of flowd = diameter of pipe = Kinematic viscosity coefficient of the fluid(water)

1x10-6 m2/sec