Fluid Engineering Mechanics - جامعة نزوى...Orifice 15 A standard orifice is one with a...

Chapter 5

Flow Measurement: Venturimeter, Orifices and

Mouthpieces, Pitot tube, Pitot static tube, Weirs and

notches.

Dr. Muhammad Ashraf Javid

Assistant Professor

1

Fluid Engineering Mechanics

Flow Measurement

2

Pipes (pressure conduits) Open channel (flumes, canals and

rivers etc)

1. Venturimeter

2. Orifices

3. Orifice meter

4. Mouth pieces/tubes

5. Nozzle

6. Pitot static tube

1. Notches (Rectangular notch, V-notch)

2. Weirs

Flow Measurement in Pipes by Venturi Meter

3

Venturi meters are flow

measurement instruments which use

a converging section of pipe to give

an increase in the flow velocity and a

corresponding pressure drop from

which the flowrate can be deduced.

They have been in common use for

many years, especially in the water

supply industry.

4


5

Venturimeter

According to Bernoulli's Equation

between section 1 and 2 we can write;

g

vz

P

g

vz

P

22

2

22

2

2

11

1

2121

2

2

2

1

21 22 zzgPP

gAA

AACQ dact

Figure shows a venturimeter in which

discharge Q is flowing,

Let, D1 is diameter, A1 is cross-section

area, P1 is pressure, z1 is elevation head V1

is velocity at section 1. Similarly D2 , A2, P2,

z2 & V2 are corresponding values at

section 2

D1, A1,

P1, Z1, V1

D2, A2,

P2, Z2, V2

2

1

2

22121 22 vvzzg

PPg

Datum

Direction of flow


Flow Measurements in Pipes

6

Venturimeter

2

1

2

2

2

2

2121 22

A

Q

A

Qzzg

PPg

2211 VAVAQ

2

2

1

2

2

2121 11

22 QAA

zzgPP

g

2

2

2

2

1

2

2

2

121

21 22 QAA

AAzzg

PPg

2121

2

2

2

1

2

2

2

12 22 zzgPP

gAA

AAQ

2121

2

2

2

1

21 22 zzgPP

gAA

AAQth

Datum

2121

2

2

2

1

21 22 zzgPP

gAA

AACQ dact

D1, A1,

P1, Z1, V1

D2, A2,

P2, Z2, V2


7

Venturimeter

thdact QCQ

2121

2

2

2

1

21 22 zzgPP

gAA

AACQ dact

Since

Where Cd is coefficient of discharge and is defined as ratio of actual

discharge to theoretical discharge .

Datum

2121

2

2

2

1

21 22 zzgPP

gAA

AACQ dact

D1, A1,

P1, Z1, V1

D2, A2,

P2, Z2, V2


8

Types of Venturimeter

a. Horizontal Venturimeter

b. Vertical Venturimeter


Figure shows a venturimeter

connected with a differential

manometer.

At section 1, diameter of pipe is D1,

and pressure is P1 and similar D2

and P2 are respective values at

section 2.

h

x y

1 2

According to gauge pressure equation

21 P

yhSxP

m

)()(21 hhSxyhSPP

mm


9


h

x y

1 2

21 P

yhSxP

m

HhS

SPP

hShhSxyhSPP

f

m

mmm

)1(

)1()()(

21

21

2121

2

2

2

1

21 22 zzgPP

gAA

AACQ dact

021 zz

gHAA

AACQ

PPg

AA

AACQ

dact

dact

2

2

2

2

2

1

21

21

2

2

2

1

21

For horizontal venturimeter,


pipewithinfluidflowinggravityspecificS

hS

SH

f

f

m

)1(


10

b. Vertical Venturimeter

h x

y

1

)()(

)()1(

22

11

1221

21

21

21

zP

zP

H

zzHzhS

SPP

hzhSPP

xyhSPP

PyhSx

P

f

m

m

m

m

Datum

Δz


zzz 12

yhzx

gHAA

AACHg

AA

AACQ

zP

zP

gAA

AACQ

ddact

dact

22

2

2

2

2

1

21

2

2

2

1

21

22

11

2

2

2

1

21

Numerical Problem 1

A venturimeter with a 150 mm diameter at inlet and 100 mm at throat is

laid with its axis is horizontal and is used for measuring the flow of oil

having specific gravity 0.9. The mercury differential manometer shows a

gauge difference of 200 mm. Calculate the discharge and take Cd = 0.90.

Solution to Numerical Problem 1

sec/276.0

)82.281.92()00785.0()0176.0(

)00785.0)(0176.0(9.0

82.21000

200)1

9.0

56.13()()1(

00785.0)1.0(4

0176.0)15.0(4

)2(

3

22

22

2

22

1

2

2

2

1

21

mQ

xxQ

oilofmxmgofhS

SH

mA

mA

gHAA

AACQ

act

act

oil

m

dact

Numerical Problem

13

Find the flow rate in venturimeter as shown in

figure if the mercury manometer reads h=10cm.

The pipe diameter is 20cm and throat diameter is

10 cm and Δz =0.45m. Assume Cd=0.98 and

direction of flow is downward.

h x

y

1 Datum

Δz

yhzx

gHAA

AACQ dact 2

2

2

2

1

21

)()1( mgofhS

SH

f

m

Orifice

14

An orifice is an opening (usually circular) in wall of a tank or in plate

normal to the axis of pipe, the plate being either at the end of the pipe or

in some intermediate location.

An orifice is characterized by the fact that the thickness of the wall or plate

is very small relative to the size of opening.

Orifice

15

A standard orifice is one with a sharp edge as in Fig (a) or an absolutely square shoulder (Fig. b) so that there in only a line contact with the fluid

Those shown in Fig. c and d are not standard because the flow through them is affected by the thickness of plate, the roughness of surface and radius of curvature (Fig. d).

Hence such orifices should be calibrated if high accuracy is desired.

Classification of Orifice

16

According to size

1. Small orifice

2. Large orifice

An orifice is termed as small when its size is small compared to head causing flow. The velocity does not vary appreciably from top to bottom edge of the orifice and is assumed to be uniform. D < H/5

The orifice is large if the dimensions are comparable with the head causing flow. The variation in the velocity from top to bottom edge is considerable. D > H/5

According to shape

1. Circular orifice

2. Rectangular orifice

3. Square orifice

4. Triangular orifice

According to shape of

upstream edge

1. Sharp-edged orifice

2. bell-mouthed orifice

According to discharge

condition

1. Free discharge orifice

2. Submerged orifice

Coefficients

17

Coefficient of contraction: It is the

ratio of area Ac of jet, to the area Ao of

the orifice or other opening.

Coefficient of velocity: It is ratio of

actual velocity to ideal velocity

Coefficient of discharge: It is the ratio

of actual discharge to ideal discharge.

occ AAC /

th

actv

V

VC

cv

thth

actact

th

actd CC

AV

AV

Q

QC

Vena-Contracta is section of

jet of minimum area. This section

is about 0.5Do from upstream

edge of the opening, where Do is

diameter of orifice

Jet: It is a stream of liquid

issuing from a orifice,

nozzle, or tube.

Orifice

18

Small orifice (D<H/5)

Figure shows a tank having small orifice

at it bottom. Let the flow in tanks is

steady.

Let’s take section 1 (at the surface) and

2 just outside of tank near orifice.

According to Bernoulli’s equation

Datum

Z1

Z2

Outflow

inflow

Cross-

sectional area

1

2

g

vz

P

g

vz

P

22

2

22

2

2

11

1

g

vzz

2000

2

221

H

gHv

Hzzg

v

th 2

221

2

2

Where, H is depth of water above orifice

Orifice

19

Small orifice

Datum

Z1

Z2

Outflow

inflow

Cross-sectional

area, A

1

2

H

gHvth 2

Where, A0 is cross-sectional are of orifice

and Cd is coefficient of discharge.

gHACvACQ

gHAvAQ

dthdact

thth

2

2

00

00

Numerical Problem

20

A jet discharges from an orifice in a vertical plane under a head of 3.65m.

The diameter of orifice is 3.75 cm and measured discharge is 6m3/s. The co-

ordinates of centerline of jet are 3.46m horizontally from the vena-

contracta and 0.9m below the center of orifice.

Find the coefficient of discharge, velocity and contraction.

gHAQC

gHACAvCQ

actd

dthdact

2/

2

yH

x

gH

ygx

v

vC

th

actv

42

2

2

vdc CCC /

Outflow

inflow

1

2

H

x=3.46m

y=0.9m

tvx act

2

2

1gty ygxVact 2/2

Numerical Problem

21

Outflow

inflow

1

2

H

x=3.46m

y=0.9m

673.0954.0

642.0

954.065.39.04

46.3

4

642.01034.9

106

sec/1034.9

65.381.92)0375.0(4

2

)0375.0(4

sec/106sec/6

3

3

33

2

0

2

33

v

dc

v

d

th

act

C

CC

xxyH

xC

x

xC

mx

xxghAQ

orificeofArea

mxlitQ

Discharge through large orifice

D

h2

▼

h

b

dh

h1

)(23

2

)(23

2

)(3

22

.2

..2

2..

.

2/3

1

2/3

2

2/3

1

2/3

2

2/3

1

2/3

2

2

1

2

1

hhgbCQ

hhgbQ

hhgbQ

dhhgbdQ

dhhgb

hgdhb

VdAdQ

dth

th

th

h

h

th

thth

Problem

▼

h

b

dh

h1

A rectangular orifice of 1.5 m wide and 0.5 m deep is discharging water

from a tank, if the level in the tank is 3 m above the top edge of an orifice

fixed. Find the discharge through orifice and take Cd = 0.6 .

Solution:

sec/59.3

)35.3(81.925.13

26.0

5.1,5.3,3

)(23

2

3

2/32/3

21

2/3

1

2/3

2

m

xxxxQ

mbmhmh

hhgbCQ

act

dact

Discharge through submerged orifice

Consider a submerge orifice in the wall common to two tank.

Let h1 head over orifice in tank (1) and h2 head in tank (2) and Δh is the difference of head over orifice in two tanks.

Consider two points “A” and “B” such that point “A” is at the surface of liquid in tank (1) and point ‘B’ is at the orifice.

Applying the Bernoulli's equation between “A” and “B”.

▼

▼ h1

h2

Δh

A

B

1

2

Datum line

Discharge through submerged orifice

A submerge orifice 1.5 m wide and

0.5 m deep is provided in the wall of

two tanks. Find the discharge of the

orifice if the difference of water level

in two tanks is 4m and Cd = 0.64.

Solution:

hgACQ

hgAQ

hgV

hhhg

V

h

g

Vh

p

g

VZ

p

g

VZ

dact

th

B

B

B

BBB

AAA

2

2

2

2

2000

22

0

0

21

2

2

2

1

22

sec/252.4

462.195.05.164.0

3m

xxxxQact

Mouthpieces/tubes

26

A tube/mouth piece is a short pipe whose length is not more than

two or three times diameters.

There is no sharp distinction between a tube and a thick walled

orifices.

A tube may be uniform diameter or it may diverge.

Figure: types and coefficients of tubes/mouthpieces

Problem

27

A re-entrant mouthpiece of 50 mm diameter is provided on one side of a

tank containing water up to a height of 3 m above the center line of the

mouthpiece.

Find the discharge if the mouth piece is running free.

Solution:

sec/00753.0

381.92)05.0(4

5.0

3,50,5.0

2

3

2

m

xxQ

mhmmdC

ghACQ

act

d

dact

Nozzle

28

Figure shows a nozzle. At section 1,

diameter of pipe is D1, and pressure

is P1 and similar D2 and P2 are

respective values at section 2.

1 2 g

v

g

vP

200

20

2

2

2

11

1

2

1

2

2

22

P

g

v

g

v

A nozzle is a tube of changing diameter, usually converging as shown in figure if used for liquids.

2211

21

VAVAQ

QQQ

According to continuity eq.

1

2

1

2

2

2

2

2P

gA

Q

A

Q

g

vz

P

g

vz

P

22

2

22

2

2

11

1

Nozzle

29

1 2

2211

21

VAVAQ

QQQ

According to continuity eq.

1

2

1

2

2

2

2

2P

gA

Q

A

Q

1

2

2

2

1

21

1

2

1

2

2

2

2

211

Pg

AA

AAQ

Pg

AAQ

th

1

2

2

2

1

21 2P

gAA

AACQ dact

Jet

Jet: It is a stream of liquid issuing from a orifice, nozzle, or tube.

Nozzle

30

1 2

h

hSxP

hSxP

m

m

1

1 0


Numerical Problems

31

Discharge and head loss in nozzle are

20L/s and 0.5m respectively. If dia of

pipe is 10cm and dia of nozzle is 4cm,

determine the manometric reading.

Manometric fluid is mercury.

1 2

h

5.02

002

0

22

2

2

2

11

2

22

2

2

11

1

g

v

g

vP

Hg

vz

P

g

vz

PL

mh

h

hSxP

m

97.0

*56.1305.022.13

1

Solution:

1

2

2

2

1

21

1

2

2

2

1

21

2/

2

Pg

AA

AAQC

Pg

AA

AACQ

actd

dact

5cm

Q = 20 x 10-3 m3/s

A1 = 0.00785 m2

V1 = 2.54 m/s

A2 = 0.00125 m2

V2 = 16 m/s

Pitot Tube and Pitot Static Tube

32

Pitot Tube: It measures sum of velocity

head and pressure head

Piezoemeter: It measures pressure

head

Pitot-Static tube: It is combination of

piezometer and pitot tube. It can

measure velocity head in pressure

conduits.

Notches and Weirs

33

Notches and Weirs

34

Notches and Weirs

35

Notch. A notch may be defined as an opening in the side of a tank or vessel such that the liquid surface in the tank is below the top edge of the opening.

A notch may be regarded as an orifice with the water surface below its upper edge. It is generally made of metallic plate. It is used for measuring the rate of flow of a liquid through a small channel of tank.

Weir: It may be defined as any regular obstruction in an open stream over which the flow takes place. It is made of masonry or concrete. The condition of flow, in the case of a weir are practically same as those of a rectangular notch.

Nappe: The sheet of water flowing through a notch or over a weir

Sill or crest. The top of the weir over which the water flows is known as sill or crest.

Note: The main difference between notch and weir is that the notch is smaller in size compared to weir.

Classification of Notches/Weirs

36

Classification of Notches

1. Rectangular notch

2. Triangular notch

3.Trapezoidal Notch

4. Stepped notch

Classification of Weirs

According to shape

1. Rectangular weir

2. Cippoletti weir

According to nature of

discharge

1. Ordinary weir

2. Submerged weir

According to width of weir

1. Narrow crested weir

2. Broad crested weir

According to nature of crest

1. Sharp crested weir

2. Ogee weir

Discharge over Rectangular Notch/Weir

37

Figure: Flow over rectangular notch/weir

gLHCQ dact 23

2 2/3

Note: The expression of discharge (Q) for rectangular weir and sharp crested

weirs are same.

H = Head over crest

L = Length of crest = width of notch

Numerical Problems

38

A rectangular notch 2m wide has a constant head of 500mm. Find

the discharge over the notch if coefficient of discharge for the notch

is 0.62.

Numerical Problems

39

A rectangular notch has a discharge of 0.24m3/s, when head of water

is 800mm. Find the length of notch. Assume Cd=0.6

Discharge over Triangular Notch (V-Notch)

40

2/52/tan215

8HgCQ dact

Numerical Problems

41

Find the discharge over a triangular notch of angle 60o, when head

over triangular notch is 0.2m. Assume Cd=0.6

Numerical Problems

42

During an experiment in a laboratory, 0.05m3 of water flowing over a right

angled notch was collected in one minute. If the head over sill is 50mm

calculate the coefficient of discharge of notch.

Solution:

Discharge=0.05m3/min=0.000833m3/s

Angle of notch, θ=90o

Head of water=H=50mm=0.05m

Cd=?

Numerical Problems

43

A rectangular channel 1.5m wide has a discharge of 0.2m3/s, which is

measured in right-angled V notch, Find position of the apex of the notch

from the bed of the channel. Maximum depth of water is not to exceed 1m.

Assume Cd=0.62

Width of rectangular channel, L=1.5m

Discharge=Q=0.2m3/s

Depth of water in channel=1m

Coefficient of discharge=0.62

Angle of notch= 90o

Height of apex of notch from bed=Depth of water in channel-height of

water over V-notch

=1-0.45= 0.55m

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