FLOW MEASURING APPARATUS
PAGE REF. NO.TU/ENG/LS-Y1S1
REV. DATE07-SEP-2011
FLOW MEASURING APPARATUS
OBJECTIVES:
1. To demonstrate the characteristics of several different
commonly used methods of measuring fluid flow rates.2. To determine
the head losses associated with each flow measuring methods.
APPARATUS:1) Flow measuring apparatus 2) Volumetric Hydraulic
Bench/Water3) Stop Watch1. INTRODUCTION
The flow measuring apparatus is designed to accustom students to
typical methods of measuring the discharge of an essentially
incompressible fluid, whilst at the same time giving applications
of the Steady Flow Energy Equation (Bernoulli's Equation). The
discharge is determined using a venturi meter, an orifice plate
meter and a rotameter. Head losses associated with each meter are
determined and compared as well as those arising in a rapid
enlargement and a 90-degree elbow. The unit is designed for use
with the Hydraulic Bench, which provides the necessary liquid
service and gravimetric evaluation of flow rate.
2. DESCRIPTION OF APPARATUSFigure 1 shows the Flow Measuring
Apparatus. Water from the Hydraulic Bench enters the equipment
through a venturi meter, which consists of a gradually-converging
section, followed by a throat, and a long gradually-diverging
section. After a change in cross-section through a rapidly
diverging section, the flow continues along a settling length and
through an orifice plate meter. This is manufactured in accordance
with BS1042 from a plate with a hole of reduced diameter through
which the fluid flows.
Following a further settling length and a right-angled bend, the
flow enters the rotameter. This consists of a transparent tube in
which a float takes up an equilibrium position. The position of
this float is a measure of the flow rate.
After the rotameter the water returns via a control valve to the
Hydraulic Bench and the weigh tank. The equipment has nine pressure
tapings as detailed in Fig. 2 each of which is connected to its own
manometer for immediate read out.
Figure 1. Flow Measuring Apparatus.
Figure 2. Explanatory diagram of flow measuring apparatus.
3. BACKGROUND
An effective way to measure the flowrate through a pipe is to
place some type of restriction within the pipe and measure the
pressure difference between the low-velocity, high-pressure
upstream section (1) and the high-velocity, low-pressure downstream
section (2) as shown in Fig. 3. So the principle is an increase in
velocity results in a decrease in pressure as the famous Bernoullis
equation states.
Figure 3. The steady-flow energy equation.
For steady, adiabatic flow of an incompressible fluid along a
stream tube, as shown in Fig. 3, Bernoulli's equation can be
written in the form;
(1)
wherep/(g
is termed the hydrostatic head.
is termed the kinetic head ( is the mean velocity i.e. the ratio
of
volumetric discharge to cross-sectional area of tube).
z
is termed potential head.
represents the total head.
The head loss (H12 may be assumed to arise as a consequence of
vorticity in the stream. Because the flow is viscous a wall shear
stress then exists and a pressure force must be applied to overcome
it. The consequent increase in flow work appears as increased
internal energy. Also, because the flow is viscous, the velocity
profile at any section is non-uniform. The kinetic energy per unit
mass at any section is then greater than and Bernoulli's equation
incorrectly assesses this term. The fluid mechanics entailed in all
but the very simplest internal flow problems is too complex to
permit the head loss (H to be obtained by other than experiment
means. Since a contraction of stream boundaries can be shown (with
incompressible fluids) to increase flow uniformity and a divergence
correspondingly decreases it, (H is typically negligibly small
between the ends of a contracting duct but is normally significant
when the duct walls diverge.
Principle of Rotameter
The cause of the pressure difference is the head loss associated
with the high velocity of water around the float periphery. Since
this head loss is constant then the peripheral velocity is
constant. To maintain a constant velocity with varying discharge
rate, the cross-sectional area through which this high velocity
occurs must vary. This variation of cross-sectional area will arise
as the float moves up and down the tapered rotameter tube.
From Fig. 4, if the float radius is Rf and the local bore of the
rotameter tube is 2Rt then,
= Cross sectional area
= Discharge / Constant peripheral velocity
Now ( = l(, where l is the distance from datum to the cross
section at which the local bore is Rt and ( is the semi-angle of
tube taper. Hence l is proportional to discharge. An approximately
linear calibration characteristic would be anticipated for the
rotameter.
Figure 4. Principle of the rotameter.
4. EXPERIMENTAL PROCEDURE
a) Close the apparatus valve fully then open it by 1/3 open with
the air purge closed.
b) Switch on the bench and slowly open its valve until the water
starts to flow, allow the apparatus to fill with water then
continue to open the bench valve until it is fully open.
c) Close the apparatus valve fully.
d) Couple the hand pump to the purge valve and pump down until
all the manometers read approximately 280 mm.
e) Dislodge entrained air from the manometers by gentle tapping
with the fingers.
f) Check that the water levels are constant. A steady rise in
levels will be seen if the purge valve is leaking.
g) Open the apparatus valve until the rotameter shows a reading
of about 10 mm. When a steady flow is maintained measure the flow
with the Hydraulic Bench as outlined in Fig. 2.h) During this
period, record the readings of the manometers in a table of the
form of Fig. 5.
i) Repeat this procedure for a number of equidistant values of
rotameter readings up to a maximum of approximately 220 mm.
5. RESULTS AND CALCULATIONS
1) Calculations of Discharge
The venturi meter, the orifice meter and the rotameter are all
dependent upon Bernoullis equation for their principal of
operation.
a) Venturi meterSince is negligibly small between the ends of a
contracting duct, the z terms, can be omitted from Eq. (1) between
stations (A) and (B).
From continuity,
(2)
The discharge, (m3/s)
(3)
Taking the density of water as 1000 kg/m3, the mass flow rate
will be
(kg/s)
(4)Figure 5. Form of results table.Manometric levels
(mm)Rota-
meter
(cm)Water
mass m (kg)Time
t (s) (k/s)H/inlet kinetic head
Test No.ABCDEFGHIVenturi
(4)Orifice
(8)Rota-meter
Calibration curveWeigh tank
m/tVenturi*
(10)/(11)Orifice
(12)/(13)Rota-meter
(15)/(16)Diffuser
(18)/(19)Elbow
(21)/(22)
* Numbers between brackets refer to the equation numbers
b) Orifice MeterFrom Fig. 6 between tapping (E) and (F), in Eq.
(1) is by no means negligible. Rewriting the equation with the
appropriate symbols
(5)
i.e. the effect of the head loss is to make the difference in
manometric height (hE-hF) less than it would otherwise be.
An alternative expression is
(6)where the coefficient of discharge, K, is given by previous
experience in BS1042 (1943) for the particular geometry of the
orifice meter. For the apparatus provided K is given as 0.601.
The expression for the discharge of the orifice meter can be
obtained in exactly the same way as for venturi meter,
The discharge,
(7)Again the density of water is 1000 kg/m3, the mass flow rate
will be
(kg/s)
(8)
Figure 6. Construction of the orifice meter.
c) RotameterThe mass flow rate is plotted as a function of
rotameter scale reading as shown in Fig. 7. An approximate linear
calibration characteristic would be anticipated.
Figure 7. Typical rotameter calibration curve.2) Calculations of
Head LossBy reference to Eq. (1) the dimensionless head loss
associated with each meter can be evaluated.
a) Venturi meterApplying the equation between pressure tappings
(A) and (C), the head loss is expressed as;
(9)
i.e.
(10)This can be made dimensionless by dividing it by the inlet
kinetic head,
Thus
(11)b) Orifice MeterApplying Eq. (1) between (E) and (F) by
substituting kinetic and hydrostatic heads would give an elevated
value to the head loss for the meter. This is because at an
obstruction such as an orifice plate, there is a small increase in
pressure on the pipe wall due to part of the impact pressure on the
plate being conveyed to the pipe wall. BS1042 (Section 1.1.1981)
gives an approximate expression for finding the head loss and
generally this can be taken as 0.83 times the measured head
difference.
Therefore
(mm)
(12)The orifice plate diameter is approximately twice the
venturi inlet diameter, therefore the orifice inlet kinetic head is
approximately 1/16 that of the venturi. Thus
(13)
The dimensionless head loss can be calculated by dividing it by
the inlet kinetic head of orifice meter which is based on the
venturi's inlet kinetic head.
c) RotameterFor this meter, application of Eq. (1) gives
(14)Then as shown in Fig. 8:
(15)
Figure 8. Rotameter head loss.Since the connecting tube has a 26
mm bore the inlet kinetic head is as it is with the venturi
meter.
Thus
(16)
d) Wide-Angled DiffuserThe inlet to the diffuser may be
considered to be at (C) and the outlet at (D).
Applying Eq. (1),
(17)
(18)
Since the area ratio, inlet to outlet, of the diffuser is 1:4,
the outlet kinetic head is onesixteenth of the venturi's inlet
kinetic head.
Thus
(19)
e) Right-Angled BendThe inlet to the bend is at (G) where the
pipe bore is 51 mm and outlet is at (H) where the bore is 26 mm.
Applying Eq. (1);
(20)
(21)
The outlet kinetic head is now approximately sixteen times the
venturi's inlet kinetic head.
Thus
(22)
6. DISCUSSION OF RESULTS
Comment on the fluid discharge, head loss of various methods of
measuring fluid flow rate.
REFERENCES:1. Massey, B.S. (1989). Mechanics of Fluids. 6th Ed,
Chapman & Hall.
2. White F.M. (1994). Fluid Mechanics. 3rd Ed., McGraw-Hill.
3. Van Dyke M. (1982). An Album of Fluid Motion. Parabolic
Press.
4. Coulson, J.M.; and Richardson, J.F. Chemical Engineering,
Volume 1., 6th Ed., Butterworth-Heinemann.Last updated on 8/2009 by
Dr. Abdulkareem Sh. Mahdi
Last updated on 9/2009 by Dr. Abdulkareem Sh. Mahdi
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