flowmeters, basic hydraulics of pipe flow, carrying capacity and continuity equation math for water...
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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
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.
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
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.”
“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
4. A venturi restriction
1. An orifice plate
2. A Parshall flume
3. A v-notched weir
4. A venturi restriction
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
Carrying CapacityCarrying Capacity
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
Carrying CapacityCarrying 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 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)?
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)
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
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)?
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)?
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)
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
DRAW:
Given: D1= 4”=0.33ft;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 (.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
3. Flow is not impacted
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
________________
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
3. Flow is not impacted
1. Increases, 9 fold
2. Decreases it 9 fold
3. Flow is not impacted
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.”
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
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
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/secV2= ?ft/sec
d2=8 ind2=8 in
D=diameter (8 inches)Convert! (8in)(1ft/12in)D=0.67 ft
D=diameter (8 inches)Convert! (8in)(1ft/12in)D=0.67 ft
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.
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
•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.
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
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
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=diameter (3 inches)Convert! (3in)(1ft/12in)DC=0.25 ft
dC=3 indC=3 in
Example 11. Different velocities & Continuity Rule (ft/time) Determine the velocities at the different points (A,B, and C)in ft/sec.
Example 11. Different velocities & Continuity Rule (ft/time) Determine the velocities at the different points (A,B, and C)in ft/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
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
•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.
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.•CR-states that flow (Q) entering a system must equal flow that leaves a system.
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
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
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=diameter (3 inches)Convert! (3in)(1ft/12in)DC=0.25 ft
dC=3 indC=3 in
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
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
Example 11. Different velocities & Continuity Rule (ft/time) Determine the velocities at the different points (A,B, and C)in ft/sec.
Example 11. Different velocities & Continuity Rule (ft/time) Determine the velocities at the different points (A,B, and C)in 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
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
•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.
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