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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). Objectives. Review Flow meters Pipe flow Continuity Equation Finish Basic Hydraulics.
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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)
Objectives • Review Flow meters • Pipe flow • Continuity Equation • Finish Basic Hydraulics
A wall or plate placed in an open channel and used to measure flow: • Baffle • Weir • Parshall Flume • Flow board
Weirs are most often used to measure flows in • Treatment plant intakes • Open channels • Pipelines • Underground pipes
Which of the following is not an example of a flow measuring device? • Magnetic meter • Parshall flume • Weirs • Manometer • Venturi 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? • Magnetic meter • Parshall flume • Weirs • Manometer • 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.”
Magnetic flow meters work on which of the following principles of operation? • The volume of water required to separate two magnets. • The reduction in magnetic pull as the volume of water separates a magnet and plug. • Magnetic induction where voltage is generated in a magnetic field and converted to a velocity. • 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.”
A thin plate with a hole in the middle used to measure flow is called _________. • An orifice plate • A parshall flume • A pinhole weir • 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.”
The effluent weir of a sedimentation basin should be level in order to prevent: • Clogging of the “V notch” • Corrosion of the weir material • Uneven flows and short circuiting • 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? • An orifice plate • A Parshall flume • A v-notched weir • 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. • True • 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. • True • False
Venturi flowmeters can measure flow when partially full of liquid. • True • False
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
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 V=Q/A
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 • True • False Q = V A
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
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/MIN • 5.2 FT/MIN • 39.2 Ft/Min • 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
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= 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 • 4.25FT/MIN • 0.58 FT/MIN • 588 FT/Min • 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 faster • ~3 times faster • ~632 times faster • 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).
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. • True • False V= Q/A = 50 gpm/.785 = 64 V=Q/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.
“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.”
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? • Increases • Decreases • 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 ________________ • Increases, 9 fold • Decreases it 9 fold • 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.” • True • False • Cannot determine with the info given.
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: • 12 inches • 15 inches • 17 inches • 24 inches CR=2 D1=12 in =1 ft Capacity ratio = D22/D12 D12 (CR)=D22 D12 (2)=D22 (12in)2 (2)=D22 144in2(2)=D22 288 in2=D22 √288 in2=D 16.97 inches =D D2= ?? Old
Definitions • 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? 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/sec d1=10 in d2=8 in D=diameter (8 inches) Convert! (8in)(1ft/12in) D=0.67 ft V1= 3.5 ft/sec D=diameter (10 inches) Convert! (10in)(1ft/12in) D=0.83 ft V1= 3.5 ft/sec V2= ?ft/sec A1V1=A2V2V2= A1V1/A2 = (0.54ft2)(3.5 ft/sec)/(0.35ft2) =5.37 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? • 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 Q3=0.11 m3/sec Q1= 0.25 m3/sec Q3= ? m3/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. Qa= Qb+ Qc Qc= Qa– Qb Qc =910 gpm- 620 gpm Qc=290 gpm B Q2= 0.14 m3/sec dB=4 in A V=620 gpm V=910 gpm DB=diameter (4 inches) Convert! (4in)(1ft/12in) DB=0.33 ft dA=6 in DA=diameter (6 inches) Convert! (6in)(1ft/12in) DA=0.5 ft C dC=3 in V=??? gpm DC=diameter (3 inches) Convert! (3in)(1ft/12in) DC=0.25 ft
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 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
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 dB=4 in A V=620 gpm V=910 gpm DB=diameter (4 inches) Convert! (4in)(1ft/12in) DB=0.33 ft dA=6 in DA=diameter (6 inches) Convert! (6in)(1ft/12in) DA=0.5 ft C dC=3 in V=??? gpm DC=diameter (3 inches) Convert! (3in)(1ft/12in) DC=0.25 ft
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 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 Q1= Q2 and A1V1=A2V2 Q1= Q2+ Q3
Syllabus Objective: Flowmeters, Flow rates and the continuity equation were discussed this evening? • Strongly Agree • Agree • Neutral • Disagree • Strongly Disagree