Flowmeters, Basic Hydraulics of Pipe Flow, Carrying Capacity and Continuity Equation Math for Water Technology MTH 082 Lecture 5 Hydraulics Chapter 7;

Flowmeters, Basic Hydraulics of Pipe Flow, Carrying Capacity and

Continuity Equation

Flowmeters, Basic Hydraulics of Pipe Flow, Carrying Capacity and

Continuity Equation

Math for Water TechnologyMTH 082Lecture 5

Hydraulics Chapter 7;(pgs. 319-341)

Math for Water TechnologyMTH 082Lecture 5

Hydraulics Chapter 7;(pgs. 319-341)

ObjectivesObjectives

• Review Flow meters

• Pipe flow

• Continuity Equation

• Finish Basic Hydraulics

• Review Flow meters

• Pipe flow

• Continuity Equation

• Finish Basic Hydraulics

A wall or plate placed in an open channel and used to measure flow:

Baf

fle W

eir

Par

shal

l Flu

me

Flo

w b

oard

25% 25%25%25%

1. Baffle

2. Weir

3. Parshall Flume

4. Flow board

1. Baffle

2. Weir

3. Parshall Flume

4. Flow board

Weirs are most often used to measure flows in

Tre

atm

ent p

lan...

Open

cha

nnels

Pip

elin

es

Under

grou

nd pi..

.

13%

0%0%

87%

1. Treatment plant intakes

2. Open channels

3. Pipelines

4. Underground pipes

1. Treatment plant intakes

2. Open channels

3. Pipelines

4. Underground pipes

http://images.google.com/imgres?imgurl=http://www.g-mwater.com.au/images/content/Goulburn_Weir1.jpg&imgrefurl=http://www.g-mwater.com.au/water-resources/storages/goulburnweir&usg=__TLVgKF0hf0epTSyKi_7sh4Ge5Ms=&h=1500&w=2187&sz=630&hl=en&start=1&tbnid=kAsBEDpZU7f59M:&tbnh=103&tbnw=150&prev=/images%3Fq%3Dweir%26gbv%3D2%26hl%3Den%26sa%3DG

Which of the following is not an example of a flow measuring

device?

Which of the following is not an example of a flow measuring

device?

Mag

netic

met

er

Par

shal

l flu

me

Wei

rs

Man

omet

er

Ven

turi

21%

0% 0%

71%

7%

1. Magnetic meter

2. Parshall flume

3. Weirs

4. Manometer

5. Venturi

1. Magnetic meter

2. Parshall flume

3. Weirs

4. Manometer

5. Venturi

A manometer measures pressure near atmospheric. The term manometer is often used to refer specifically to liquid column hydrostatic instruments. A manometer measures pressure near atmospheric. The term manometer is often used to refer specifically to liquid column hydrostatic instruments.

http://images.google.com/imgres?imgurl=http://nsm1.nsm.iup.edu/tsimmons/Environmental%2520Health%2520Photolibrary/Wastewater%2520Treatment%2520Plant%2520Photogallery/Wastewater_Treatment_Plant_Parshall_Flume.jpg&imgrefurl=http://nsm1.nsm.iup.edu/tsimmons/Environmental%2520Health%2520Photolibrary/ENVH_Photolibrary_Wastewater_Images.shtm&usg=__gT5dP1vk5ivOkXq1jxuW4DGirxQ=&h=752&w=500&sz=144&hl=en&start=2&um=1&tbnid=3LivmZunrSpErM:&tbnh=141&tbnw=94&prev=/images%3Fq%3Dparshall%2Bflume%26gbv%3D2%26hl%3Den%26sa%3DN%26um%3D1

Which of the following flow measuring devices is the most

accurate?

Which of the following flow measuring devices is the most

accurate?

Mag

netic

met

er

Par

shal

l flu

me

Wei

rs

Man

omet

er

Ven

turi

100%

0% 0%0%0%

1. Magnetic meter

2. Parshall flume

3. Weirs

4. Manometer

5. Venturi

1. Magnetic meter

2. Parshall flume

3. Weirs

4. Manometer

5. Venturi

“The in line type magnetic flow meters offer a higher accuracy. They can be as accurate as 0.5% of the flow rate. The insertion styles offer a 0.5 to 1% accuracy.”

“The in line type magnetic flow meters offer a higher accuracy. They can be as accurate as 0.5% of the flow rate. The insertion styles offer a 0.5 to 1% accuracy.”

Magnetic flow meters work on which of the following principles of

operation?

Magnetic flow meters work on which of the following principles of

operation?

The

volu

me

of w

ater

...

The

reduct

ion in

mag

...

Mag

netic

induct

ion w

...

The

volu

me

of w

ater

t...

25%

6%

63%

6%

1. The volume of water required to separate two magnets.

2. The reduction in magnetic pull as the volume of water separates a magnet and plug.

3. Magnetic induction where voltage is generated in a magnetic field and converted to a velocity.

4. The volume of water that can be moved by an electromagnet.

1. The volume of water required to separate two magnets.

2. The reduction in magnetic pull as the volume of water separates a magnet and plug.

3. Magnetic induction where voltage is generated in a magnetic field and converted to a velocity.

4. The volume of water that can be moved by an electromagnet.

“The operation of a magnetic flowmeter or mag meter is based upon Faraday's Law, which states that the voltage induced across any conductor as it moves at right angles through a magnetic field is proportional to the velocity of that conductor.”

“The operation of a magnetic flowmeter or mag meter is based upon Faraday's Law, which states that the voltage induced across any conductor as it moves at right angles through a magnetic field is proportional to the velocity of that conductor.”

A thin plate with a hole in the middle used to measure flow is

called _________.

A thin plate with a hole in the middle used to measure flow is

called _________.

An o

rific

e pl

a...

A p

arsh

all f

lu...

A p

inhole

wei

r

A v

entu

ri re

st...

79%

0%

14%7%

1. An orifice plate

2. A parshall flume

3. A pinhole weir

4. A venturi restriction

1. An orifice plate

2. A parshall flume

3. A pinhole weir


“Orifices are the most popular liquid flowmeters in use today. An orifice is simply a flat piece of metal with a specific-sized hole bored in it. Most orifices are of the concentric type, but eccentric, conical (quadrant), and segmental designs are also available.”

“Orifices are the most popular liquid flowmeters in use today. An orifice is simply a flat piece of metal with a specific-sized hole bored in it. Most orifices are of the concentric type, but eccentric, conical (quadrant), and segmental designs are also available.”

The effluent weir of a sedimentation basin should be level

in order to prevent:

The effluent weir of a sedimentation basin should be level

in order to prevent:

Clo

gging o

f th...

Corro

sion o

f t...

Unev

en fl

ows

a...

They

nee

d not

...

31%

23%

38%

8%

1. Clogging of the “V notch”

2. Corrosion of the weir material

3. Uneven flows and short circuiting

4. They need not be kept level

1. Clogging of the “V notch”

2. Corrosion of the weir material

3. Uneven flows and short circuiting

4. They need not be kept level

What calibrated device developed for measuring flow in an open

channel consists of a contracting length, a throat with a sill, and an

expanding length?

What calibrated device developed for measuring flow in an open

channel consists of a contracting length, a throat with a sill, and an

expanding length?

An o

rific

e pl

a...

A P

arsh

all f

lu...

A v

-notc

hed w

e...

A v

entu

ri re

st...

25% 25%25%25%

1. An orifice plate

2. A Parshall flume

3. A v-notched weir


1. An orifice plate

2. A Parshall flume

3. A v-notched weir


The difference in pressure between high- and low-pressure taps is

proportional to the square of the flow rate through the Venturi.

Therefore, a differential-pressure sensor with a square root output

signal can be used to indicate flow.

Tru

e

Fal

se

0%

100%

1. True

2. False

1. True

2. False

A centrifugal untreated raw water pump starts pumping at 25

gal/min and has a maximum pumping capacity of 100 gal/min. A Venturi flowmeter can be used to measure flow from this pump.

Tru

e

Fal

se

43%

57%

1. True

2. False

1. True

2. False

Venturi flowmeters can measure flow when partially full of liquid.

Tru

e

Fal

se

93%

7%

1. True

2. False

Carrying CapacityCarrying Capacity

Carrying Capacity = (D2)2

(D1)2

Carrying Capacity = (D2)2

(D1)2

Capacity ratio = (new pipe diameter)2

(old pipe diameter)2

Capacity ratio = (new pipe diameter)2

(old pipe diameter)2

Capacity ratio = (Big pipe diameter)2

(Little pipe diameter)2

Capacity ratio = (Big pipe diameter)2

(Little pipe diameter)2


Capacity ratio = (D2)2

(D1)2

Capacity ratio = (D2)2

(D1)2

Capacity ratio = (12 in)2

(6 in)2

Capacity ratio = (12 in)2

(6 in)2

Capacity ratio = 144 in2

36 in2

Capacity ratio = 144 in2

36 in2

Capacity ratio = 4 times moreCapacity ratio = 4 times more

A = 0.785 (Diameter)2 ; Q= VA or V=Q/AA = 0.785 (Diameter)2 ; Q= VA or V=Q/A

Assuming the same flow rate and velocity. A 12 inch pipe carries how much more water then a six inch pipe?

Assuming the same flow rate and velocity. A 12 inch pipe carries how much more water then a six inch pipe?

When the flow rate increases (Q) the flow velocity increases (V)

and so does the friction or resistance to flow caused by the

liquid viscosity and the head loss

Tru

e

Fal

se

50%50%

1. True

2. False

Q = V A


When the inside diameter is **made larger** the flow area increases and the liquid velocity and head loss for a given

capacity is reduced

When the inside diameter is **made larger** the flow area increases and the liquid velocity and head loss for a given

capacity is reduced

When the inside diameter is made smaller the flow area decreases and the

liquid velocity and head loss for a given capacity is increased

When the inside diameter is made smaller the flow area decreases and the

liquid velocity and head loss for a given capacity is increased

Determine the relationship between carrying capacity and flow rate. What is the velocity (ft/min) in a pipe that is 12 inches in diameter and currently

has a flow rate of 50 gal/min (gpm)?



8.5

FT/M

IN

5.2

FT/M

IN

39.

2 Ft/M

in

64

Ft/M

IN

25% 25%25%25%

1. 8.5 FT/MIN

2. 5.2 FT/MIN

3. 39.2 Ft/Min

4. 64 Ft/MIN

1. 8.5 FT/MIN

2. 5.2 FT/MIN

3. 39.2 Ft/Min

4. 64 Ft/MIN

DRAW:

Given: D1= 1ft ; Q= 50 gpm conversions: (1ft3/7.48 gal)

Formula: A = 0.785 (Diameter)2 ; Q/A= V

Solve: Q= 50 gal/min (1ft3/7.48 gal)=6.68 ft3/min

A = 0.785 (Diameter)2

A = 0.785 (1ft)2

A= 0.785 (1ft2)

A= 0.785 ft2

Q/A= V

V= (6.68FT3/MIN)/(0.785 FT2)= 8.5 FT/MIN

DRAW:

Given: D1= 1ft ; Q= 50 gpm conversions: (1ft3/7.48 gal)




A = 0.785 (1ft)2

A= 0.785 (1ft2)

A= 0.785 ft2

Q/A= V

V= (6.68FT3/MIN)/(0.785 FT2)= 8.5 FT/MIN





4.2

5FT/M

IN

0.5

8 FT/

MIN

588

FT/M

in

79

FT/M

IN

25% 25%25%25%

DRAW:

Given: D1= 4”=0.33ft;Q= 50 gpm

Conversions: (1ft3/7.48 gal)




A = 0.785 (.33ft)2

A= 0.785 (.11ft2)

A= 0.085 ft2

Q/A= V

V= (6.68FT3/MIN)/(0.085 FT2)= 78.6 FT/MIN

DRAW:

Given: D1= 4”=0.33ft;Q= 50 gpm

Conversions: (1ft3/7.48 gal)




A = 0.785 (.33ft)2

A= 0.785 (.11ft2)

A= 0.085 ft2

Q/A= V

V= (6.68FT3/MIN)/(0.085 FT2)= 78.6 FT/MIN

1. 4.25FT/MIN

2. 0.58 FT/MIN

3. 588 FT/Min

4. 79 FT/MIN

1. 4.25FT/MIN

2. 0.58 FT/MIN

3. 588 FT/Min

4. 79 FT/MIN

Assuming both are flowing full at the same FLOW RATE (Q). The velocity in a 4 inch pipe relative

to a 12 inch pipe is?????

~9

times

fast

e...

~3

times

fast

e...

~63

2 tim

es fa

s...

The

sam

e ra

te

25% 25%25%25%

A 12 in pipe with a Q of 50 (gpm) has a velocity of 8.5 ft/min. A smaller 4 inch pipe with the same Q (50 gpm) has a velocity of 79 ft/min. Thus water is moving (79/8.5= 9 times faster).

A 12 in pipe with a Q of 50 (gpm) has a velocity of 8.5 ft/min. A smaller 4 inch pipe with the same Q (50 gpm) has a velocity of 79 ft/min. Thus water is moving (79/8.5= 9 times faster).

1. ~9 times faster

2. ~3 times faster

3. ~632 times faster

4. The same rate

The flow velocity in a 6-in. diameter pipe is twice that in a 12-in diameter pipe if both are carrying 50 gal/min of water.

Tru

e

Fal

se

47%

53%1. True

2. FalseV= Q/A = 50 gpm/.785 = 64V=Q/A = 50 gpm/0.19 = 255Decreasing the pipe diameters increases the flow velocity if all else is held equal. Going from a 12 inch to a 6 inch pipe speeds up the water 4 times.

V= Q/A = 50 gpm/.785 = 64V=Q/A = 50 gpm/0.19 = 255Decreasing the pipe diameters increases the flow velocity if all else is held equal. Going from a 12 inch to a 6 inch pipe speeds up the water 4 times.

“The bigger the pipe the more water it can carry. Increase the pipe size increase the carrying capacity. For a double in pipe size you increase its carrying capacity 4 fold.”

“The bigger the pipe the more water it can carry. Increase the pipe size increase the carrying capacity. For a double in pipe size you increase its carrying capacity 4 fold.”

“If two pipes have the same flow rate (Q) the smaller diameter pipe has a faster flow velocity (V). You are moving the same flow volume of (Q) water through a smaller hole so it goes faster.”

“If two pipes have the same flow rate (Q) the smaller diameter pipe has a faster flow velocity (V). You are moving the same flow volume of (Q) water through a smaller hole so it goes faster.”

Increasing this To this Increases the capacity

pipe diameter diameter by a factor of

(inches) (inches)

4 6 2.25

4 8 4.00

6 8 1.78

6 10 2.78

6 12 4.00

8 10 1.56

8 12 2.25

8 15 3.52

10 12 1.44

10 15 2.25

12 15 1.56

Job Interview Clean Water Service ?:

“A 12 inch pipeline is flowing full of water and is necked down to a four inch pipeline, does the flow velocity

of the water in the 4 inch line increase or decrease?

Incr

ease

s

Dec

reas

es

Flo

w is

not i

m...

33% 33%33%

1. Increases

2. Decreases

3. Flow is not impacted

1. Increases

2. Decreases



“A 12 inch pipeline is flowing full of water and is necked down to a four inch pipeline, does the velocity of

the water in the 4 inch line increase or decrease and by a factor of

________________

Incr

ease

s, 9

...

Dec

reas

es it

9...

Flo

w is

not i

m...

33% 33%33%

1. Increases, 9 fold

2. Decreases it 9 fold


1. Increases, 9 fold

2. Decreases it 9 fold



“You need to replace a 4 inch sewer pipe with a 6 inch sewer pipe. If

velocity is the same in both pipes the new pipe will be able to carry

2.25 times as much material.”

Tru

e

Fal

se

Can

not d

eter

mi..

.

33% 33%33%

1. True

2. False

3. Cannot determine with the info given.

1. True

2. False

3. Cannot determine with the info given.

DRAW:•Given: D1= 1ft ; (CC or CR)=2; D2=?•Formula:•Solve:

DRAW:•Given: D1= 1ft ; (CC or CR)=2; D2=?•Formula:•Solve:

A 12 in water main must be replaced with a new main that has double the carrying capacity. What is the diameter of the new main, rounded to the nearest

inch?

D1=12 in=1 ftD1=12 in=1 ftCapacity ratio = D2

2/D12

D12 (CR)=D2

2

D12 (2)=D2

2

(12in)2 (2)=D22

144in2(2)=D22

288 in2=D22

√288 in2=D16.97 inches =D

Capacity ratio = D22/D1

2

D12 (CR)=D2

2

D12 (2)=D2

2

(12in)2 (2)=D22

144in2(2)=D22

288 in2=D22

√288 in2=D16.97 inches =D

OldOld

NewNew

D2= ??D2= ??

CR=2CR=2

1. 12 inches

2. 15 inches

3. 17 inches

4. 24 inches

1. 12 inches

2. 15 inches

3. 17 inches

4. 24 inches

DefinitionsDefinitions• Continuity rule states that flow (Q) entering a system

must equal flow that leaves a system.

Q1=Q2

Or

A1V1=A2V2

• Flow of water in a system is dependant on the amount of force causing the water to move.

• Pressure is the amount of force acting (pushing) on a unit area.

• Continuity rule states that flow (Q) entering a system must equal flow that leaves a system.

Q1=Q2

Or

A1V1=A2V2

• Flow of water in a system is dependant on the amount of force causing the water to move.

• Pressure is the amount of force acting (pushing) on a unit area.

Example 9. Different diameter pipe & velocities (ft/time)

If the velocity in the 10 in diameter section of pipe is 3.5 ft/sec, what is the ft/sec velocity in the 8 in diameter section?

Example 9. Different diameter pipe & velocities (ft/time)

If the velocity in the 10 in diameter section of pipe is 3.5 ft/sec, what is the ft/sec velocity in the 8 in diameter section?

D=diameter (10 inches)Convert! (10in)(1ft/12in)D=0.83 ft


V1= 3.5 ft/secV1= 3.5 ft/sec

A1V1=A2V2 V2= A1V1/A2 = (0.54ft2)(3.5 ft/sec)/(0.35ft2)=5.37 ft/sec

A1V1=A2V2 V2= A1V1/A2 = (0.54ft2)(3.5 ft/sec)/(0.35ft2)=5.37 ft/sec

V1= 3.5 ft/secV1= 3.5 ft/sec

d1=10 ind1=10 in

Q1= Q2 and A1V1=A2V2

Pipe Area = 0.785 (diameter)2

Area1 (pipe)= 0.785 (0.833ft)2= 0.54 ft2

Area2 (pipe)= 0.785 (0.67ft)2= 0.35 ft2

Q1= Q2 and A1V1=A2V2


Area1 (pipe)= 0.785 (0.833ft)2= 0.54 ft2

Area2 (pipe)= 0.785 (0.67ft)2= 0.35 ft2

V2= ?ft/secV2= ?ft/sec

d2=8 ind2=8 in



V2= ? ft/secV2= ? ft/sec

Example 10. Different flows & Continuity Rule (ft3/time)

A flow entering the leg of a tee connection is 0.25 m3/sec. If the flow is 0.14 m3/sec in one branch what is the flow through the other branch?

Example 10. Different flows & Continuity Rule (ft3/time)

A flow entering the leg of a tee connection is 0.25 m3/sec. If the flow is 0.14 m3/sec in one branch what is the flow through the other branch?

Q1= Q2 + Q3

Q3= Q1 – Q2

Q3 =0.25 m3/sec- 0.14 m3/secQ3=0.11 m3/sec

Q1= Q2 + Q3

Q3= Q1 – Q2

Q3 =0.25 m3/sec- 0.14 m3/secQ3=0.11 m3/sec

Q1= 0.25 m3/secQ1= 0.25 m3/sec

Q2= 0.14 m3/secQ2= 0.14 m3/sec

Q3= ? m3/secQ3= ? m3/sec

•CR-states that flow (Q) entering a system must equal flow that leaves a system.•CR-states that flow (Q) entering a system must equal flow that leaves a system.

Example 11. Different velocities & Continuity Rule (ft/time) Determine the velocities at the different points (A,B, and C)in ft/sec.


Qa= Qb + Qc

Qc= Qa – Qb

Qc =910 gpm- 620 gpmQc=290 gpm

Qa= Qb + Qc

Qc= Qa – Qb

Qc =910 gpm- 620 gpmQc=290 gpm


Q2= 0.14 m3/secQ2= 0.14 m3/sec

AA

BB

CC

dB=4 indB=4 in

DB=diameter (4 inches)Convert! (4in)(1ft/12in)DB=0.33 ft


V=620 gpmV=620 gpm

V=??? gpmV=??? gpm

V=910 gpmV=910 gpmdA=6 indA=6 in

DA=diameter (6 inches)Convert! (6in)(1ft/12in)DA=0.5 ft


DC=diameter (3 inches)Convert! (3in)(1ft/12in)DC=0.25 ft


dC=3 indC=3 in



Convert gpm to ft3/sec

Qa =910 gpm (1min/60 sec)(1 gal/7.48 ft3)=2.03 ft3/sec

Qb= 620 gpm(1min/60 sec)(1 gal/7.48 ft3)= 1.38 ft3/sec

Qc=290 gpm(1min/60 sec)(1 gal/7.48 ft3)= 0.65 ft3/sec

Convert gpm to ft3/sec

Qa =910 gpm (1min/60 sec)(1 gal/7.48 ft3)=2.03 ft3/sec

Qb= 620 gpm(1min/60 sec)(1 gal/7.48 ft3)= 1.38 ft3/sec

Qc=290 gpm(1min/60 sec)(1 gal/7.48 ft3)= 0.65 ft3/sec





Q2= 0.14 m3/secQ2= 0.14 m3/sec

AA

BB

CC

dB=4 indB=4 in



V=620 gpmV=620 gpm

V=??? gpmV=??? gpm

V=910 gpmV=910 gpmdA=6 indA=6 in





dC=3 indC=3 in


Areaa (pipe)= 0.785 (0.5ft)2= 0.19 ft2

Areab (pipe)= 0.785 (0.33ft)2= 0.09 ft2

Areac (pipe)= 0.785 (0.25ft)2= 0.05 ft2


Areaa (pipe)= 0.785 (0.5ft)2= 0.19 ft2

Areab (pipe)= 0.785 (0.33ft)2= 0.09 ft2

Areac (pipe)= 0.785 (0.25ft)2= 0.05 ft2



Solve Q=VA at Each Point

Va =Qa/Aa =2.03 ft3/sec/ (0.19 ft2)=10.34 ft/sec

Vb= Qb/Ab=1.38 ft3/sec/ (0.09 ft2)= 16.14 ft/sec

Vc= Qc /Ac= 0.65 ft3/sec/ (0.05 ft2)= 13.25 ft/sec

Solve Q=VA at Each Point

Va =Qa/Aa =2.03 ft3/sec/ (0.19 ft2)=10.34 ft/sec

Vb= Qb/Ab=1.38 ft3/sec/ (0.09 ft2)= 16.14 ft/sec

Vc= Qc /Ac= 0.65 ft3/sec/ (0.05 ft2)= 13.25 ft/sec


What is the Continuity Equation?•Flow in = flow out•Flow in = flow out

Q1= Q2 and A1V1=A2V2Q1= Q2 and A1V1=A2V2

Q1= Q2 + Q3Q1= Q2 + Q3

Syllabus Objective: Flowmeters, Flow rates and the continuity equation were discussed this

evening?

Syllabus Objective: Flowmeters, Flow rates and the continuity equation were discussed this

evening?

Stro

ngly A

gree

Agre

e

Neu

tral

Dis

agre

e

Stro

ngly D

isag

ree

20% 20% 20%20%20%

1. Strongly Agree

2. Agree

3. Neutral

4. Disagree

5. Strongly Disagree

1. Strongly Agree

2. Agree

3. Neutral

4. Disagree

5. Strongly Disagree

Documents

Flowmeters, Basic Hydraulics of Pipe Flow, Carrying Capacity and Continuity Equation Math for Water Technology MTH 082 Lecture 5 Hydraulics Chapter 7;