Flowmeters, Basic Hydraulics of Pipe Flow, Carrying Capacity and Continuity Equation

1
Flowmeters, Basic Hydraulics of Pipe Flow,
Carrying Capacity and Continuity Equation

• Math for Water Technology
• MTH 082
• Lecture 5
• Hydraulics Chapter 7
• (pgs. 319-341)

2
Objectives

• Review Flow meters
• Pipe flow
• Continuity Equation
• Finish Basic Hydraulics

3
A wall or plate placed in an open channel and
used to measure flow

1. Baffle
2. Weir
3. Parshall Flume
4. Flow board

4
Weirs are most often used to measure flows in

1. Treatment plant intakes
2. Open channels
3. Pipelines
4. Underground pipes

5
Which of the following is not an example of a
flow measuring device?

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.
6
Which of the following flow measuring devices is
the most accurate?

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.
7
Magnetic flow meters work on which of the
following principles of operation?

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.
8
A thin plate with a hole in the middle used to
measure flow is called _________.

1. An orifice plate
2. A parshall flume
3. A pinhole weir
4. A venturi restriction

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.
9
The effluent weir of a sedimentation basin
should be level in order to prevent

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

10
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?

1. An orifice plate
2. A Parshall flume
3. A v-notched weir
4. A venturi restriction

11
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.

1. True
2. False

12
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.

1. True
2. False

13
Venturi flowmeters can measure flow when
partially full of liquid.

1. True
2. False

14
Carrying Capacity
Carrying Capacity (D2)2
(D1)2
Capacity ratio (new pipe diameter)2
(old pipe
diameter)2
Capacity ratio (Big pipe diameter)2
(Little pipe
diameter)2
15
Carrying Capacity
Assuming the same flow rate and velocity. A 12
inch pipe carries how much more water then a six
inch pipe?
Capacity ratio (D2)2
(D1)2
Capacity ratio (12 in)2
(6 in)2
Capacity ratio 144 in2
36 in2
Capacity ratio 4 times more
A 0.785 (Diameter)2 Q VA or VQ/A
16
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
Q V A

1. True
2. False

17
Carrying Capacity
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
18
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)?
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

1. 8.5 FT/MIN
2. 5.2 FT/MIN
3. 39.2 Ft/Min
4. 64 Ft/MIN

19
Determine the relationship between carrying
capacity and flow rate. What is the velocity
(ft/min) in a pipe that is 4 inches in diameter
and currently has a flow rate of 50 gal/min (gpm)?
DRAW Given D1 40.33ftQ 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 (.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

20
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?????

1. 9 times faster
2. 3 times faster
3. 632 times faster
4. The same rate

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).
21
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.

1. True
2. False

V Q/A 50 gpm/.785 64 VQ/A 50
gpm/0.19 255 Decreasing 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.
22
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.
23
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
24
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?

1. Increases
2. Decreases
3. Flow is not impacted

25
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 velocity
of the water in the 4 inch line increase or
decrease and by a factor of ________________

1. Increases, 9 fold
2. Decreases it 9 fold
3. Flow is not impacted

26
Job Interview Clean Water Service ? 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.

1. True
2. False
3. Cannot determine with the info given.

27
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?
New

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

CR2
D112 in 1 ft
Capacity ratio D22/D12 D12 (CR)D22 D12
(2)D22 (12in)2 (2)D22 144in2(2)D22 288
in2D22 v288 in2D 16.97 inches D
D2 ??
Old

1. 12 inches
2. 15 inches
3. 17 inches
4. 24 inches

28
Definitions

• Continuity rule states that flow (Q) entering a
  system must equal flow that leaves a system.
• Q1Q2
• Or
• A1V1A2V2
• 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.

29
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?
Q1 Q2 and A1V1A2V2 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
V2 ? ft/sec
d110 in
d28 in
Ddiameter (8 inches) Convert! (8in)(1ft/12in) D0
.67 ft
V1 3.5 ft/sec
Ddiameter (10 inches) Convert!
(10in)(1ft/12in) D0.83 ft
V1 3.5 ft/sec
V2 ?ft/sec
A1V1A2V2 V2 A1V1/A2 (0.54ft2)(3.5
ft/sec)/(0.35ft2) 5.37 ft/sec
30
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?

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

Q2 0.14 m3/sec
Q1 Q2 Q3 Q3 Q1 Q2 Q3 0.25 m3/sec- 0.14
m3/sec Q30.11 m3/sec
Q1 0.25 m3/sec
Q3 ? m3/sec
31
Example 11. Different velocities Continuity
Rule (ft/time) Determine the velocities at the
different points (A,B, and C)in ft/sec.

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

Qa Qb Qc Qc Qa Qb Qc 910 gpm- 620
gpm Qc290 gpm
B
Q2 0.14 m3/sec
dB4 in
A
V620 gpm
V910 gpm
DBdiameter (4 inches) Convert!
(4in)(1ft/12in) DB0.33 ft
dA6 in
DAdiameter (6 inches) Convert!
(6in)(1ft/12in) DA0.5 ft
C
dC3 in
V??? gpm
DCdiameter (3 inches) Convert!
(3in)(1ft/12in) DC0.25 ft
32
Example 11. Different velocities Continuity
Rule (ft/time) Determine the velocities at the
different points (A,B, and C)in ft/sec.

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

Convert gpm to ft3/sec Qa 910 gpm (1min/60 sec)
(1 ft3 /7.48 gal) 2.03 ft3/sec Qb 620
gpm(1min/60 sec) (1 ft3 /7.48 gal) 1.38
ft3/sec Qc290 gpm(1min/60 sec) (1 ft3 /7.48
gal) 0.65 ft3/sec
33
Example 11. Different velocities Continuity
Rule (ft/time) Determine the velocities at the
different points (A,B, and C)in ft/sec.

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

Pipe Area 0.785 (diameter)2 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
B
Q2 0.14 m3/sec
dB4 in
A
V620 gpm
V910 gpm
DBdiameter (4 inches) Convert!
(4in)(1ft/12in) DB0.33 ft
dA6 in
DAdiameter (6 inches) Convert!
(6in)(1ft/12in) DA0.5 ft
C
dC3 in
V??? gpm
DCdiameter (3 inches) Convert!
(3in)(1ft/12in) DC0.25 ft
34
Example 11. Different velocities Continuity
Rule (ft/time) Determine the velocities at the
different points (A,B, and C)in ft/sec.

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

Solve QVA at Each Point Va Qa/Aa 2.03
ft3/sec/ (0.19 ft2)10.34 ft/sec Vb Qb/Ab1.38
ft3/sec/ (0.09 ft2) 16.14 ft/sec Vc Qc /Ac
0.65 ft3/sec/ (0.05 ft2) 13.25 ft/sec
35
What is the Continuity Equation?

• Flow in flow out

Q1 Q2 and A1V1A2V2
Q1 Q2 Q3
36
Syllabus Objective Flowmeters, Flow rates and
the continuity equation were discussed this
evening?

1. Strongly Agree
2. Agree
3. Neutral
4. Disagree
5. Strongly Disagree