Lab 2 Fluid Flow Rate.pdfMEE 491 Lab #2 Fluid Flow Rate .docx

Lab 2 Fluid Flow Rate.pdf
MEE 491 Lab #2: Fluid Flow Rate
The goal of the fluid flow lab is to become familiar with
measuring fluid pressure and flow rate
with orifice obstruction meters.
Reading: Beckwith pgs 489-576
Moran, Shapiro, Munson, and Dewitt (i.e. your thermofluids
book): Ch 11, 12 & 14
Introduction
This experiment introduces you to orifice obstruction meters,
which are a common tool used
to measure fluid flow rate. The experimental system includes
two types of orifice obstruction
meters: flow nozzles and orifice plates. The differential
pressure across the orifice obstruction
meter is needed to calculate flow rate, and so pressure
measuring devices are included to
measure a) the differential pressure across the flow nozzle and
b) the differential pressure across
the orifice plate. Figure 1 illustrates the experimental system
and its relevant components.
Air from the room enters the plenum chamber through the
nozzle. The air then flows through
flexible black tubing and into a transparent circular duct that is

instrumented with the orifice
plate. Lastly the air flow enters the vacuum pump via more
flexible black tubing and is returned
to the room via the vacuum pumps outlet. Variable air flow
through the system can be achieved
by a rheostat knob that controls the vacuum pump. We will
assume that any leaks in the system
are negligible. Since the obstruction meters are connected in
series, both obstruction meters
measure the same mass flow rate (i.e. conservation of mass).
In the case of the flow nozzles, two different sizes are provided.
Both nozzles are
standardized ASME long-radius flow nozzles with diameters of
1.265 cm and 2.530 cm for the
small and medium nozzles, respectively. The orifice plate has a
diameter of 0.795 in and is
located in a pipe with a diameter of 2 in.
Figure 1. Photograph of the experimental system and relevant
components for
part A of this lab
The discharge coefficient, CD, is a very important performance
parameter for an orifice
obstruction meter. The discharge coefficient tells you the ratio
of the actual orifice flow rate,
Qactual, to the ideal orifice flow rate, Qideal:
�! =

!!"#$!%
!!"#$%
[1]
The ideal flow rate corresponds to the flow rate as derived from
Bernoulli’s equation. Two of
the assumptions that Bernoulli’s equation makes are isentropic
and incompressible flow. While
these are good approximations in many engineering situations,
no real system is every truly
isentropic and incompressible. Hence the discharge coefficient
is always less than 1. In this lab
you will determine the discharge coefficient for the nozzles as
well as the orifice plate.
Procedure
• With the small nozzle measure at five different steady-state
(i.e. make sure pressures are
not changing with time) flow rates measure:
o The differential pressure across the flow nozzle.
o The differential pressure across the orifice plate with the most
sensitive pressure
measurement instrument possible for that flow rate.
• With the large nozzle measure at five different steady-state
(i.e. make sure pressures are
not changing with time) flow rates measure:
o The differential pressure across the flow nozzle.
o The differential pressure across the orifice plate with the most
sensitive pressure
measurement instrument possible for that flow rate.

Note: You should have a total of 10 steady-state flow rate
measurements (5 for the small nozzle
and 5 for the medium nozzle) with differential pressures
measured across the flow nozzle and
orifice plate for each.
Analysis
• Calculate the mass flow rate of the system (see appendix) for
each of the 10 flow rate
measurements.
• Based on conservation of mass, the discharge coefficient for
the orifice plate can be
calculated using the mass flow rate through the nozzle.
Calculate the discharge
coefficient of the orifice for each flow rate. Do these values
agree with Fig.4 in the
appendix?
• Construct a calibration curve for the orifice plate. Plot the
system’s mass flow rate versus
pressure drop across the orifice plate on a log – log scale (i.e.
the x- and y-axes should be
on a log-log scale (i.e. the x- and y-axes should be on a log10
scale).
• Determine the constant k and the exponent n in the general
equation: ( )nPkm Δ= *!
Appendix
Calculation procedure to determine the mass flow rate in the
flow nozzle in part A

1. Infer the air velocity upstream of the nozzle (Hint: the
“diameter” upstream of the nozzle
is very large).
2. Calculate the air velocity at the nozzle’s exit using
Bernoulli’s equation and the pressure
drop across the nozzle.
3. Calculate the Reynolds number, Re=ρVD/µ, where ρ is the
density, µ is the dynamic
viscosity, and V is the average velocity, A the cross-sectional
area at the nozzle’s exit.
4. Calculate the discharge coefficient, CD, of the nozzle using
the empirical equation1:
( )[ ] ( )[ ] ( )[ ]32
Reln00020903.0Reln0097785.0Reln152884.019436.0 +−+=DC
[2]
5. To calculate the actual volumetric flow rate, Qactual, the
volumetric flow rate of an ideal
orifice obstruction meter, Qideal, must first be calculated:
( )
( )
ρ
P
AA
A
Qideal

Δ
−
=
2
*
1 212
2
[3]
where A1 is the area upstream of the meter, A2 is the area of
the orifice, ΔP = P1 – P2, P1
is the pressure upstream, P2 is the pressure downstream, and ρ
is the fluid density (Hint:
since the “diameter” upstream of the nozzle is very large, so is
the “area” upstream of the
nozzle).
6. The actual volumetric flow rate, Qactual, can then be
calculated as:
idealDactual QCQ *= [4]
7. The mass flow rate, m! , can then by calculated as:
actualQm ρ=! [5]
Note: For a given system with a known CD the actual
volumetric flow rate can be expressed as:

where γ is a constant for the meter that includes ρ, A1, A2, and
CD (note that equation [1] in lab 3
handout is exactly of this mathematical form).
PQactual Δ=γ
References:
[1] Robert P. Benedict, “Most Probable Discharge Coefficients
for ASME Flow Nozzles,”
Journal of Basic Engineering, 88, 734 (1966)
Figure 4 – Discharge coefficient vs. Reynolds number for an
orifice plate (from NACA TM 952). Where d2/d1 is
the ratio of the orifice diameter to the pipe diameter.
lab 2.docx
Surname 1
Maithah al-ali
Tutor’s Name
Class Information
Date of Submission
MEE 491 Lab #2
Fluid Flow Rate
Introduction

Fluid flow is a significant part of several processes, such as
material transportation from one point to the other, chemical
reactions, and material mixing. Determination of fluid flow
rates involves investigating flow in a network of pipes, and
exploring different methods, such as, rotameters, and venturi
meters for the flow measurement. The fluid flow through a pipe
network has several engineering applications. The systems such
as the turbines, heat exchangers, heat pumps, air conditioners,
and wind tunnels are some of the few examples. The proper
choice and use of the experimental instrumentations used in
characterizing the fluid flow rates is essential component of
verification of a design process Moreover, the properties of
fluid flow measurement in a process is, in most cases, needed
for producing and controlling the required products. The
experiment also involves exploration of the impacts of the
configuration of the pipe network, skin friction, pipe fittings,
such as elbows, trees; and the drop in pressure across the pipe.
This laboratory experiment introduces a student to the use of
orifice obstruction meters, which are common tools used in
measuring the rate of fluid flow. The experimental setup
involved the use of flow nozzles, orifice plates, and two
different orifice obstruction meters. The pressure difference
across the meter is required to determine the fluid flow rates.
Therefore, the devices for measuring pressure are also included
for measuring the pressure difference across the nozzle and the
orifice plate.
Theory
The mass conservation is an essential concept of engineering.
Within some domain, the quantity of mass normally remains
constant. According to the principle of conservation of mass,
mass is neither created nor destroyed. The mass of any matter
is simply the product of its density and the volume it occupies.
For a gas or liquid, the volume, shape, and density can change
with time within the domain. There is no mass destruction or
accumulation through any pipe or tube carrying the matter. For
a fluid in a tube, at any given plane that is perpendicular to the

tube’s middle line, the same quantity of mass will pass through.
The quantity of matter through the plane is known as mass flow
rate. The mass conservation, also known as continuity is a proof
of the fact that quantity of matter passing through a section of
fluid is constant. The value of the mass flow can be determined
from the conditions of the flow. Mass flow is defined as the
quantity of mass passing through a given cross-section area of a
tube per unit time. From mass flow, volume flow can be
determined easily.
If a fluid passes through a tube of cross-section area A at a
speed V, the volume flow is defined as the volume of fluid
passing through a pipe per unit time. Mathematically, the
volume flow is expressed as follows:
Volume = Area * Velocity * time.
The question many people have been asking is how the
scientists and engineers apply the concepts of mass and
volumetric flow rates in real life situations. From the
Newton's Second Law of Motion, the forces of aerodynamic
acting on an aircraft, such as drag and lift, are directly
proportional to the rate of change of a gas momentum.
The momentum can be defined as a product of mass of an object
and its velocity. Therefore, the aerodynamic forces are expected
to depend upon the rate of mass flow past an object. The thrust
generated by a propulsion system is also a function of the rate
of change of momentum of working gas. The thrust force is
directly proportional to the rate of mass flow. For flow in a
tubular section, the rate of mass flow is always constant. For
constant-density fluid flow, if the velocity can be set at some
known area, the velocity for any other known area can be
determined easily. If a fluid velocity at a given time is required
at a certain region, the area of that region must be calculated
first. The fluid velocity is calculated from the general equation
below:
=
The equation is commonly known as the equation of continuity
and is very useful in the design of wind tunnels. Considering

the equation of the rate of mass flow, it appears that for a given
area, the rate of mass flow can be made as large as possible by
setting the fluid velocity high. Nevertheless, in the actual
fluids, compressibility normally limits the velocity at which
fluid flow can be forced through a region. In the events that
there is a small constriction within the pipe, The Mach number
of the flow through the constriction must be less than one. This
phenomenon is commonly known as flow choking. It is
important that one have a clear understanding of the flow
structure in any tubular section before conducting an
experiment. This will enable one to predict the experimental
values.
Objectives
This experiment aims to demonstrate the measurement of rates
of fluid flow using devices such as the orifice obstruction
meters, which are common tools used in measuring the rate of
fluid flow for incompressible flow in tubes. Moreover, energy
losses in the devices will also be determined using the
necessary equations, such as the steady-state energy equation
and Bernoulli equation.
Experimental Setup
The setup for the experiment is as shown in figure 1 shown
below.
Figure 1: The experimental system and some necessary
components for the lab
The air from the lab enters the plenum-chamber via the flow
nozzle. The air then flows via the flexible black tube onto the
transparent circular duct connected with the orifice plate.
Finally, the air flows into the vacuum pump through a more
flexible black tube and is then returned to the laboratory room
through the outlets of the vacuum pumps. The variable flow of
air via the system can be realized by the use of a rheostat knob.
The knob is used in controlling the vacuum pumps. In this
laboratory experiment, it was assumed that any leakages in the

system are negligible. Because the obstruction meters are
instrumented in series, both the meters measure the same rate of
mass flow. For the case of the nozzles, two different sizes are
given. Both the nozzles are standardized ASME long radius
nozzles, with their diameters ranging from 1.265 cm to 2.530
cm. The diameter of the orifice plate is 0.795 inch and is
instrumented within a pipe of diameter 2 inches.
The coefficient of discharge, Cd is an essential performance
parameter for the orifice obstruction meter. It is defined as the
ratio of the actual flow to the ideal flow rate. The ideal rate of
flow is normally the flow rate that is derived from the
Bernoulli’s equation. The assumptions made while deriving an
ideal flow rate is that the flow is incompressible and isentropic.
Whereas these are good estimations in any scientific or
engineering situations, it is not possible to realize a system that
is completely incompressible and isentropic. Due to this fact,
the coefficient of discharge is normally less than one. In this
laboratory experiment, the discharge coefficient for the orifice
plate, as well as the flow nozzles, were determined.
Procedure
1. With the small flow nozzle at five dissimilar steady-state
flow rates the following were measured;
a. The pressure difference across the nozzle.
b. The pressure difference across the orifice plate using the
most sensitive pressure measurement device possible for that
particular flow rate.
2. With the larger nozzle, the following were measured at five
different steady-states:
a. The pressure difference across the nozzle.
b. The pressure difference across the orifice plate using the
most sensitive pressure measurement device possible for that
particular flow rate.
A total of ten steady-state flow measurements were taken, i.e.,
five for small flow nozzle and five for large flow nozzle.

Results and Calculations
The rate of mass flow of the system for the ten measurements
are:
[Insert the values as per your results]
Based on the conservation of mass, the orifice plate coefficient
of discharge can be calculated with the use of the rate of mass
flow through the flow nozzle. The coefficient of discharge for
each flow can be calculated as follow:
[Calculte as per your results]
The calibration curve for the orifice plate is as shown below:
[Construct the calibration curve as per your values]
The table of system’s mass flow versus the change in pressure
across the orifice plate on a log – log scale is as shown below:
The values are as shown in the table below:
Change in Pressure, Δp ( Pascal)
Log Δp
Mass Flow Rate ṁ (Kg/s)
Log ṁ

[Plot a the system graph here, the x and y-axes must be on a log
10 scale]
From the graph, the values of the constant k and the exponent n
are calculated as follows:
Using the general formula, ṁ = k(Δp)n, where ṁ is the rate of
mass flow,
Δp is the differential pressure across the orifice plate, and k and
n are constants whose values can be calculated as follows:
From the general formula, ṁ = k(Δp)n, we can take log on both
sides of the equation as follows:
Log ṁ = log { k(Δp)n}
This can be further expressed as:
Log ṁ = nlog Δp + logk and comparing with a standard equation
of a straight line graph, y = mx +c, n is the gradient of the
graph, and log is the y-intercept of the graph. The value of k is
now the antilog of y-intercept.
Conclusion
{This part is dependent on the experimental results. It is in
order to supply the experimental result so as to draw a
conclusion from them}

Appendix: Procedure on Determination of the Mass Flow Rate
The following steps were followed in determining the various
values of mass flow rate.
1. The air velocity was inferred upstream of the flow nozzle.
2. The exit velocity of air was calculated by using the
Bernoulli’s equation and the change in pressure across the
nozzle.
3. The third step is the determination of the Reynolds number.
The number is calculated as follow:
Re = ρVA/µ ------------------------------------------------------------
----------------------------------- (1)
Where ρ is the density, V is the velocity, A is the nozzle exit
cross-section area, and µ is the dynamic viscosity.
4. The nozzle coefficient of discharge, Cd is then calculated by
the use of the equation below:
Cd = 0.19436 + 0.152884[In (Re)] – 0.0097785 [In (Re)]2 +
0.00020903[In(Re)]3 -----------(2)
5. The ideal orifice obstruction meter, Q ideal, is calculated
first before calculating the actual volumetric flow. The ideal
volumetric flow is calculated as follow:
Q ideal = . -------------------------------------------------------------
------------ (3)
Where A1 is the meter's area upstream and is the orifice area,
Δp = P1 – P2; P1 is the upstream pressure, P2 is the downstream
pressure, and ρ is the density of the fluid.
6. The actual volumetric flow is calculated as follows:
Qactual = CD x Qactual-----------------------------------------------
---------------------------------------- (4)
The rate of mass flow is calculated as follows:

ṁ = ρQactual ----------------------------------------------------------
-------------------------------------- (5)
Note: For a system with a known value of CD, the value of
Qactual can be expressed as follow:
Qactual = γ ------------------------------------------------------------
-------------------------------- (7)
Where γ is the meter’s constant and is a function of the cross-
section areas, the density, and the discharge coefficient.
Works Cited
Cotton, K. C. 'Discussion: ‘Most Probable Discharge
Coefficients for ASME Flow Nozzles’ (Benedict, Robert P.,
1966, ASME J. Basic Eng., 88, Pp. 734â€“744)'. Journal of
Basic Engineering 88.4 (1966): 744. Web.
This assignment provides you with an opportunity to read an
article and then to share your thoughts about the article by

critiquing the details, including the decisions made. Access an
Academic OneFile database. This article includes details and
assertions about the ethical choices/decisions made by Edward
J. Snowden, a former National Security Agency (NSA)
contractor. Here is the reference citation for the article:
Securing our liberty. (2013). Commonweal, 140(12), 5.
After reading the article, draft a two-page response by
discussing the U.S. government’s decision to acquire phone and
internet data without disclosing its intentions to citizens. For
this assignment, consider the NSA as an organization (i.e.,
business) and Snowden as a manager. How have the decisions of
this event impacted the fairness of the U.S. government, its
citizens, and Snowden? How did ethics, perhaps, influence
Snowden’s decision to leak information? In this event, what is
the greater good and also the consequences/sacrifices of that
greater good? Based on the details of this event, what can we
learn about making important decisions as a leader and
manager? This event was covered by several news and media
organizations, so there should be plenty of articles in the
library. Conduct a bit more research in the online library related
to this event involving Edward Snowden and the U.S.
government—see what else you can discover about the event to
determine an appropriate punishment, if any, for Snowden’s
conduct. Include at least one additional source from the library
in your response. The purpose of this assignment is for you to
think critically about managers (and other leaders) making
important decisions, and the process managers use to make
important decisions. Consider how important it is to collect all
of the facts before making an important decision, such as those
involving fairness and ethics. Use APA Style to format your
response. Proofread your work, and submit it in Blackboard for
grading
Original work only
ATT00001

ATT00002
ATT00003
ATT00004
ATT00005
ATT00006
ATT00007
ATT00008
ATT00009
ATT00010
Sent from my iPhone
IMG_2518.JPG
IMG_2519.JPG
IMG_2520.JPG

Lab 2 Fluid Flow Rate.pdfMEE 491 Lab #2 Fluid Flow Rate .docx

Recommended

Recommended

More Related Content

Similar to Lab 2 Fluid Flow Rate.pdfMEE 491 Lab #2 Fluid Flow Rate .docx

Similar to Lab 2 Fluid Flow Rate.pdfMEE 491 Lab #2 Fluid Flow Rate .docx (20)

More from DIPESH30

More from DIPESH30 (20)

Recently uploaded

Recently uploaded (20)

Lab 2 Fluid Flow Rate.pdfMEE 491 Lab #2 Fluid Flow Rate .docx