Engineering Measurements
Dr. Yasser Elhenawy
Y.Elhenawy Applications: Flow
Measurement
1.1
The general propose of this program
At the end of this program the students should be know and learn:
1- Fluid flow measurements
• Density and specific gravity measurements
• Viscosity measurements
• Pressure measurements, Head, Piezometer, U-tube Manometer
•
•
•
•
•
•
•
Mass flow rate
Flow mater
Venturi Tube
Pitot-Static Tube
Rotameter
Turbine Flowmeter
Hot Wire Anemometers, Leaser dropler Anemometers
Y.Elhenawy Applications: Flow
Measurement
1.1
1
‫‪The general propose of this program‬‬
‫‪At the end of this program the students should be know and learn:‬‬
‫‪2-Temperature measurements‬‬
‫‪• Thermometer‬‬
‫‪• Thermocuple‬‬
‫‪3-Flow Visualization‬‬
‫‪* Schlieren Method‬‬
‫‪* Shadowgraph Methods‬‬
‫‪1.1‬‬
‫‪Y.Elhenawy Applications: Flow‬‬
‫‪Measurement‬‬
‫اﻟﺗﻘﯾم ﺧﻼل اﻟﻔﺻل اﻟدراﺳﻲ‬
‫• * اﻟدرﺟﺔ اﻟﻛﻠﯾﺔ ‪ 100 :‬درﺟﺔ‬
‫•‬
‫•‬
‫•‬
‫•‬
‫•‬
‫•‬
‫•‬
‫‪2‬‬
‫* اﻣﺗﺣﺎن ﻧﺻف اﻟﻔﺻل اﻟدراﺳﻲ رﻗم ‪) 1‬اﻷﺳﺑوع اﻟﺛﺎﻣن (‬
‫‪ 10‬درﺟﺎت‬
‫* اﻣﺗﺣﺎن ﻧﺻف اﻟﻔﺻل اﻟدراﺳﻲ رﻗم ‪) 2‬اﻷﺳﺑوع اﻟﻌﺎﺷر(‬
‫‪ 5‬درﺟﺎت‬
‫‪ 10‬درﺟﺎت‬
‫* اﻣﺗﺣﺎن ﻋﻣﻠﻲ )اﻷﺳﺑوع اﻟﺛﺎﻧﻲ ﻋﺷر(‬
‫‪ 5‬درﺟﺎت‬
‫* اﻻﻣﺗﺣﺎن اﻟﺷﻔﮭﻲ‬
‫‪ 5‬درﺟﺎت‬
‫* ﺗﻘﺎرﯾر وأﺑﺣﺎث وﺗﻣﺎرﯾن‬
‫‪ 5‬درﺟﺎت‬
‫* اﻟﻐﯾﺎب‬
‫‪ 60‬درﺟﺔ‬
‫* اﻻﻣﺗﺣﺎن اﻟﻧﮭﺎﺋﻲ‬
Fluid flow measurement
Introduction
There would be a need to measure the physical entities such as
displacement, velocity, pressure, force, elapsed time etc. in the
operating devices and machines. In industry too, there is need
for the measurement and control of the physical conditions
required for mass production and high quality products.
Similarly in commercial organizations, the measurement to
water and electricity supplied to a consumer is a must.
Y.Elhenawy Applications: Flow
Measurement
1.1
Density and specific gravity measurements
In many process control situations in industry, measurement of
density and specific gravity is the best method of determining
and controlling the concentration of solution or a mixture.
Further, these fluid properties also provide a good means for
direct measurement of product quality. Most of the specific
gravity measurements for liquids are determined entirely on the
basis of the ratio of their masses to the mass of an equal
volume of water.
Y.Elhenawy Applications: Flow
Measurement
1.1
3
Density and specific gravity measurements
Pycnometer or specific gravity bottle method
The pycnometer is essentially a small flask or a straight walled glass tube of
definite volume fitted with a ground glass stopper containing a central overflow
hole. Measurements standards lay down the following sequence for specific
gravity determination.
Weight the clean and carefully dired empty pycnometer with stopper on a
sensitive analytical balance (weight w1)
Fill the pycnometer with boiled distilled water at the desired temperature. Insert
the stopper and wipe off the excess water which is forced out through the
stopper hole. Weight again (weight, w2).
Empty the pycnometer and refill it with the process liquid. Weight it after
inserting the stopper and wiping off the excess liquid (weight, w3)
Specific gravity of the process liquid is then determined from the relation:
Sp. Gr. = (w3-w1)/(w2-w1)
Y.Elhenawy Applications: Flow
Measurement
1.1
Density and specific gravity measurements
Hydrometer
The operation of a hydrometer is based on the principle of
buoyancy. The unit consists of a weighted-float with a graduated
stem of constant diameter. The float is weighted at the bottom so
that it floats upright when immersed in the liquid under test. Since
the buoyant force (equal to the weight of the hydrometer) is
constant, the hydrometer floats deeper or shallow depending on
specific weight of the liquid. Consequently, graduations on the
stem corresponding to different depths of submergence can be
made to indicate directly the specific weight or specific gravity of
the liquid.
Y.Elhenawy Applications: Flow
Measurement
1.1
4
Liquid level measurement
Liquid level refers to the position or height of a liquid surface
above a datum line. Level measurements are made to ascertain the
quantity of the liquid held in a container. Level affects both the
pressure and rate of flow in and out of the container and as such its
measurement is an important function in a variety of process.
Y.Elhenawy Applications: Flow
Measurement
1.1
Liquid level measurement
Sight glass and float gauges
The task of liquid level measurement is accomplished by a direct method
wherein the varying level is the means to obtain the measurement.
A sight glass is a graduated glass tube mounted on the side of the liquid
container, and it provides visual indication of the liquid level. The rise or fall of
the liquid level in the tank results in a corresponding change of level in the tube.
Float gauges follow the change in liquid level due to buoyancy effects. The float
is connected by means of flexible tap or cable to a drum or pulley which
communicates with the indicating or recording mechanism. The counter weight
keeps the tap taught as the float rise or falls with changes in the liquid level.
Y.Elhenawy Applications: Flow
Measurement
1.1
5
Liquid level measurement
Hydrostatic pressure device
The hydrostatic head created by a liquid is directly related to the height of the
liquid column (p = ρgh). Therefore, a pressure gauge installed near the bottom
of the tank will record a pressure p proportional to height h of the liquid level.
An increase in liquid level would cause corresponding increase in the pressure
which would be indicated by the pressure gauge. The scale of the pressure gauge
can be calibrated in terms of the height h of the liquid column, i.e., the liquid
level.
Y.Elhenawy Applications: Flow
Measurement
1.1
Viscosity measurements
Measurement of viscosity is desirable because the viscosity of lubricating and fuel oils plays
an important role in the effective operation of processes such as:
•Fluid film lubrication requires high viscous lubricating oils for greater load carrying capacity.
•High viscosity, however, entails much greater power requirements.
Proper combustion in a period low viscosity fuel oils so that they can be properly atomized, i.e.,
broken into very small droplets.
Y.Elhenawy Applications: Flow
Measurement
1.1
6
Viscosity measurements
Viscosity measurements are made with devices known as
viscosimeter or viscometers which may employ relationships for
force balance, torque balance, and the fact that a constant flow
rate of fluids of fixed viscosity requires a definite pressure
differential. The operation of all the viscometers depends upon the
existence of laminar flow under certain controlled and
reproducible conditions. Capillary tube viscometer , Fig.14.5,
represents the basic principle of a capillary tube viscosity wherein
the viscosity measurements are based on Poiseuilli's relation:
For laminar flow conditions in a circular pipe. Here Q is the flow rate
of the liquid of specific weight, γ,
hf is the head loss over the length l of a capillary tube of diameter d.
Y.Elhenawy Applications: Flow
Measurement
1.1
Flow rate.
Mass flow rate
• If we want to measure the rate at which water is flowing along a pipe.
A very simple way of doing this is to catch all the water coming out of
the pipe in a bucket over a fixed time period. Measuring the weight of
the water in the bucket and dividing this by the time taken to collect
this water gives a rate of accumulation of mass. This is know as the
mass flow rate.
•
For example an empty bucket weights 2.0kg. After 7 seconds of
collecting water the bucket weights 8.0kg,
7
Flow rate
•
Performing a similar calculation, if we know the mass flow is 1.7kg/s,
how long will it take to fill a container with 8kg of fluid?
Volume Flow rate
•
More commonly we need to know the volume flow rate - this is more
commonly know as discharge. (It is also commonly, but inaccurately,
simply called flow rate). The symbol normally used for discharge is Q.
The discharge is the volume of fluid flowing per unit time. Multiplying
this by the density of the fluid gives us the mass flow rate.
Consequently, if the density of the fluid in the above example is 850
kgm3 then:
8
Continuity
•
•
Matter cannot be created or destroyed - (it is simply changed in to a
different form of matter). This principle is know as the conservation of
mass and we use it in the analysis of flowing fluids. The principle is
applied to fixed volumes, known as control volumes (or surfaces), like
that in the figure below:
An arbitrarily shaped control volume.
For any control volume the principle of conservation of mass says
9
Some example applications
We can apply the principle of continuity to pipes with cross sections
which change along their length. Consider the diagram below of a
pipe with a contraction:
A liquid is flowing from left to right and the pipe is narrowing in the
same direction. By the continuity principle, the mass flow rate must
be the same at each section - the mass going into the pipe is equal to
the mass going out of the pipe. So we can write:
10
11
Applications: Flow Measurement (Bernoulli’s equation)
The Bernoulli equation can be applied to several commonly
occurring situations in which useful relations involving pressures,
velocities and elevations may be obtained.
1.2
12
•
From the Bernoulli's equation we can calculate the pressure at this point. Apply
the Bernoulli’s equation along the central streamline from a point upstream where
the velocity u1 and pressure p1 to the stagnation point of the blunt body where
the velocity is zero, u2=0. Also, z1=z2
An example of the use of the Bernoulli equation
13
Applications: Pitot tube
If a stream of uniform velocity flows into a blunt body, the stream lines take a
pattern similar to this:
Note how some of the move to the left and some to the right. But one, in the centre, goes to the tip
of the blunt body and stops. It stops because at this point the velocity is zero - the fluid does not
move at this one point. This point is known as the stagnation point.
1.3
14
15
The Pitot-Static Tube
P1 is a Static pressure: It is
measured by a device (static
tube) that causes no velocity
change to the flow. This is
usually accomplished by drilling
a small hole normal to a wall
1
P1,V1
along which the fluid is flowing.
P2 2
P2 is a Stagnation pressure: It
Stagnation
Point V2=0
is the pressure measured by an
open-ended tube facing the flow
direction. Such a device is called
a Pitot tube.
1.4
Y.Elhenawy Applications: Flow
Measurement
Pitot-Static tube
Bernoulli equation (5.3) between 1 and 2:
P2  P1 
1
r V12
2
( P2  P1 ) ( V22  V12 )

0
r
2
Stagnation Pressure is higher than
Static Pressure
(Recall that position 2 is a stagnation point: V2= 0)
 2 ( P2  P1 ) 
V1  

r


1/ 2
We can measure pressures P1 and P2 using hydrostatics:
P1=Patm + rgh1, P2=Patm + rgh2
or using a Pressure Gauge
Y.Elhenawy Applications: Flow
Measurement
1.5
16
The Pitot-Static Tube
Pitot-static tube
The static and Pitot tube are often combined into the one-piece
Pitot-static tube.
Y.Elhenawy Applications: Flow
Measurement
1.6
17
Example:
An airplane flies at an elevation of 3,000 m in standard atmosphere.
The pressure difference indicated by the Pitot-static probe attached to
the fuselage is 1.5 bar . What is the velocity of the airplane? (The
density of air at this altitude is 1.05kg/m3)
Y.Elhenawy Applications: Flow
Measurement
1.7
Orifice, Nozzle and Venturi meters
Basic principle: Increase in velocity causes a decrease
in pressure.
•
Fluid is accelerated by forcing it to flow through a constriction,
thereby increasing kinetic energy and decreasing pressure
energy. The flow rate is determined by measuring the pressure
difference between the meter inlet and a point of reduced
pressure.
•
Desirable characteristics of flow meters:
– Reliable, repeatable calibration
– Introduction of small energy loss into the system
– Inexpensive
– Minimum space requirements
Y.Elhenawy Applications: Flow
Measurement
1.8
18
Generalized flow obstruction in a pipe
1
2
V1
P
P
1
2
Q  A1V1  A 2 V2
Continuity equation between 1 and 2:
Bernoulli equation between 1 and 2:
V 2 , ideal 
( P2  P1 ) ( V22  V12 )

0
r
2
2 ( P1  P 2 )
r [1 - (A 2 / A 1 ) 2 ]
1.9
Y.Elhenawy Applications: Flow
Measurement
Generalized flow obstruction in a pipe
• In eq. (5.6) frictional losses have not been taken into
account
• To account for frictional losses we use a “discharge”
coefficient, C:
V 2  C  V 2 , ideal
V2  C 
2 ( P1  P 2 )
r [1 - (A 2 / A 1 ) 2 ]
(5.7)
• The volumetric flow rate can be easily calculated:
Q  V2 A 2
Y.Elhenawy Applications: Flow
Measurement
19
Orifice Meter
This type of meter consists of a thin flat plate with a circular hole drilled
in its center. It is very simple, inexpensive and easy to install, but it can
cause significant pressure drops.
1
2
Front view of
orifice plate
V1
P
P
1
2
Where the discharge coefficient,
V2  C 
2 ( P1  P 2 )
r [1 - (A 2 / A 1 ) 2 ]
C =f(Re, D2/D1), can be found
in Figure 5.14, textbook (5.12
2nd edition)
1.10
Y.Elhenawy Applications: Flow
Measurement
Nozzle Meter
The nozzle meter uses a contoured nozzle. The resulting flow pattern
for the nozzle meter is closer to ideal.
V2  C 
P
P
1
2
2 ( P1  P 2 )
r [1 - (A 2 / A 1 ) 2 ]
Where the nozzle discharge
coefficient, C =f(Re, D2/D1),
can be found in textbooks and
is higher than the orifice
discharge coefficient.
Chee 223
1.11
20
Venturi Meter
This device consists of a conical contraction, a short cylindrical throat
and a conical expansion. The fluid is accelerated by being passed
through the converging cone. The velocity at the “throat” is assumed to
be constant and an average velocity is used. The venturi tube is a
reliable flow measuring device that causes little pressure drop. It is used
widely particularly for large liquid and gas flows.
P
P
1
2
V2  C 
2 ( P1  P 2 )
r [1 - (A 2 / A 1 ) 2 ]
Y.Elhenawy Applications: Flow
Measurement
Where the discharge
coefficient, C =f(Re), can
be found in Figure 5.11,
textbook (5.9 2nd edition)
1.12
Example 1: Flow through an orifice meter
A lubricating oil flows through a 5” Schedule 40 steel pipe (which
corresponds to 0.128m ID) at 6000 Lit/min. A sharp-edged orifice is
inserted into this pipe and attached to a mercury manometer. At the flow
temperature the oil has a specific gravity of 0.87 and a viscosity of 0.02
N sec/sq m. What manometer reading is expected if the manometer is
positioned vertically and the orifice diameter is 0.09m?
Y.Elhenawy Applications: Flow
Measurement
1.13
21
Example 1
C
Y.Elhenawy Applications: Flow
Measurement
1.14
Example 2: Flow through an orifice meter
An orifice meter like that shown in the previous page is used to monitor
the water flow rate in a 10 cm diameter pipe. Determine the volumetric
flow rate if the orifice has a diameter of 2 cm and the manometer shows
a 30 cm difference in mercury.
Y.Elhenawy Applications: Flow
Measurement
1.15
22
Example 3: Flow through pipe contraction
Example 4: Flow through pipe contraction
23