Fluid Flow measurement
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Transcript of Fluid Flow measurement
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First Law of Thermodynamics
Types of energy
3 ways that energy transferred to a system.
General Mechanical Energy Equation
3 types of non-flow work
Head form of Mechanical Energy Eqn
Bernoulli’s Equation
Application: Nozzle and diffuser
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Fdm
dW
2
ΔVzg
ρ
ΔP n.f
2
ggdm
dW
2g
ΔVΔz
ρg
ΔP n.f
2 F
02
Vzg
ρ
P 2
Toricelli’s equation
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Fluid Flow Measurement
Pitot tube
Pitot static tube
Venturi meter
Orifice meter
02
Vzg
ρ
P 2
Chapter 3 Week 4
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• A useful concept associated with Bernoulli’s equation deals with the stagnation and dynamic pressures.
• These pressures arise from the conversion of kinetic energy in a flowing fluid into a “pressure rise” as the fluid is brought to rest.
• Bernoulli’s equation can be rewritten as:
02
ρΔVρgΔzΔP
2
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• Static pressure.
– One could measure static pressure in a flowing fluid by drilling a hole on a flat surface, and attach a piezometer tube.
02
ρΔVρgΔzΔP
2
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• Hydrostatic pressure.
– not actually a pressure but does represent the change in pressure possible due to potential energy variations of the fluid as a result of elevation changes.
02
ρΔVρgΔzΔP
2
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• Dynamic pressure.
– Its interpretation can be seen in by considering the pressure at the end of a small tube inserted into the flow and pointing upstream.
02
ρΔVρgΔzΔP
2
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• Dynamic pressure.
– After the initial transient motion has died out, the liquid will fill the tube to a height of H as shown.
– The fluid in the tube, including that at its tip,(2),will be stationary
02
ρΔVρgΔzΔP
2
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• Applying Bernoulli’s equation between (1) and (2):
• Or, the sum of static and dynamic pressures is equal to stagnation pressure.
• V2 = 0 Stagnation point
2
ρVPP
2
112
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• Stagnation point:
– Exist in any solid body placed into a flowing fluid.
– For symmetrical objects stagnation point is clearly at the tip or front of the object.
– For nonsymmetrical objects the location of the stagnation point is not always obvious.
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• Knowledge of the values of the static and stagnation pressures in a fluid implies that the fluid speed can be calculated.
• This is the principle on which the Pitot-static tube is based.
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1) Static holes at appropriate distance from the tip of the tube.
2) Open tip of the tube.
3) Towards high pressure side.
4) Towards low pressure side
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P
V1
P2
V 1
• Instead of measuring static or stagnation pressures separately, it is customary to measure their difference with a transducer.
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Example
• Air is flowing in a duct. The pressure-difference gage attached to the pitot-static tube indicates a difference of 200 Pa. what is the air velocity? (air = 1.20 kg/m3)
• Solution:
s
m 28.81
2.1
2002
P2V 1
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• The primary disadvantage of Pitot tube is that it must be aligned with the flow direction, which is unknown.
• For yaw angles greater than 5o, there are substantial errors in both the static and stagnation pressures measurements.
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• Because of the slow response of the fluid filled tubes leading to the pressure sensors, it is not useful for unsteady flow measurements.
• The Pitot-static tube is useful in liquid and gases; for gases a compressibility correction is needed if the stream Mach number is high.
• It is not suitable for low-velocity measurement in gases because of the small pressure differences developed.
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Venturi meter
• Consist of:
– Truncated cone with decreasing cross sectional area
– Short cylindrical section (throat)
– Truncated cone with increasing cross sectional area
Perpendicular to the flow
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• From Bernoulli’s equation:
……………..(1)
• Friction is negligible then F is dropped
• From continuity equation, inserting into (1)
02
VV
ρ
PP2
1
2
212
A
A1
ρ
PP2
V
2
1
2
2
21
2
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Example
• The venturi meter has water flowing through it. The pressure difference P1 – P2 is 1 psi. The diameter at point 1 is 1 ft, and at point 2 is 0.5 ft. Determine the velocity through this meter.
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Solution
• Assumption: Water incompressible fluid, density constant
( = 62.4 Ibm/m3)
s
ft12.7
1
0.51
sIbf
ftIbm 32.2
ft
Ibm62.4
ft
in 144
in
Ibf1 2
A
A1
ρ
PP2
V
2
2
2
3
2
2
2
2
1
2
2
21
2
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• V2 that is obtained is the ideal V2
• In venturi, actual V2 is less than ideal
V2
• A correction factor is needed
A
A1
PP2
V
2
1
2
2
21
2
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• Correction factor Discharge Coefficient, Cv
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• The actual velocity, V2
• A reliable flow-measuring device
• Cause less pressure loss (F is small)
• Used for particularly large-volume liquid and gas flow
A
A1
PP 2
CV
2
1
2
1
2
2
21
vactual2,
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Orifice meter
• Venturi is expensive and complex to construct.
• To measure flow rate in small pipeline orifice meter
• Orifice meter cheap, easy to construct
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• Consist of flat orifice plate with circular hole drilled in it.
• Vena contracta contraction of flow occurs
• Cause actual outlet velocity less than ideal outlet velocity
Vena contracta
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• Correction factor Discharge Coefficient, Cv
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• From Bernoulli’s equation:
A
A1
PP 2
CV
2
1
2
1
2
2
21
vactual2,
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Example
The flow rate of methanol at20C (=788.4 kg/m3 and=5.85710-4 kg/ms) through4-cm-diamter pipe is to bemeasured with a 3-cm-diameter orifice meterequipped with a mercury(=13,600 kg/m3) manometeracross the orifice place (seefigure). If the differential of themanometer is read to be 11cm, determine the flow rate ofmethanol through the pipe andthe average flow velocity.