Bernoulli Theorem Lab
pdf
keyboard_arrow_up
School
The University of Sydney *
*We aren’t endorsed by this school
Course
2611
Subject
Mechanical Engineering
Date
Jan 9, 2024
Type
Pages
8
Uploaded by EarlMoon5843
CIVL2611 Introductory Fluid Mechanics
Bernoulli Theorem Lab Report
SID: 510460929
Lab conducted on:
Submitted:
9th of September, 2022
26th of September, 2022
1. Aim
To determine whether the horizontal steady flow of water through a divergent tube, experiencing
an increase in velocity is accompanied by a decrease in pressure, as stated in Bernoulli’s
Theorem. It will also determine if the total pressure head of a flow is constant along a streamline,
due to a negligible difference in elevation between two points, stated in Bernoulli’s Theorem.
2. Apparatus
Figure 1.1:
F1-15 Bernoulli Theorem Demonstration Unit Labelled Apparatus
Figure 1.2:
Isolated Test Section of F1-15 Bernoulli Theorem Demonstration Unit
Figure 1.3:
Venturi Tube Dimensions of F1-15 Bernoulli Theorem Demonstration Unit
1
Figure 1.4:
Labelled Apparatus of F1-10 Hydraulics Bench
2.1 F1-10 Hydraulics Bench
The Armfield F1-10 Hydraulics Bench depicted in figure 1.4, draws water from a sump tank in
the lower section of the bench, which then enters the test section and venturi tube and returns
back into the sump tank. The flow control valve regulates the flow rate of the water, which is
also accompanied by a sight gauge and level scale which shows the instantaneous water level in
litres. The hydraulics bench has a plug which enables the filling of the volumetric tank which
generates a change in the total pressure head.
2.2 F1-15 Bernoulli Theorem Demonstration Unit
The Armfield F1-15 Bernoulli Theorem Demonstration Unit (BTDU) includes wall tappings
which display the static pressure head in tappings 1 to 6 for the specific locations in the venturi
tube as depicted at points A to F in figure 1.3. These tappings are visualised by the manometer
tubes in figure 1.1. The total pressure head is depicted in the rightmost manometer tube, in
tapping 8. Water flows through the test section venturi tube depicted in figure 1.2. A hypodermic
probe is present within the venturi tube which when moved to a specific location of A to F, will
display the total pressure head at chosen point in the connected tapping 8. There is an air bleed
screw which can empty the water into the sump tank if needed. The BTDU is fitted with a flow
control valve to regulate the water flow through the venturi tube test section.
3. Procedures
3.1 Initial Set-up of Apparatus
To begin the experiment, the F1-10 Hydraulics Bench and the F1-15 Bernoulli Theorem
Demonstration Unit must be properly set up and levelled. The BTDU is to be placed horizontally
on the Hydraulics Bench, and levelled properly. To do so, the air bubble on the BTDU must be
centred with regards to the circular indicator. Adjust the legs of the BTDU to centre the bubble if
it is not level.
2
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
3.2 Flow of water into test section, hydraulics bench and manometer
Turn on the power switch on the hydraulics bench and open the bench valve to initiate the flow
of water into the hydraulic bench. Use the flow control valve on the bench and the test section to
initiate a flow into the venturi tube. Fill the entire tube with water by adjusting the valves. Turn
off the flow control valve on the venturi tube and slowly open the air bleeding screw which will
start to fill the manometer tubes with water. Once they have filled, slowly open the air bleeding
screws so that the manometer tubes start to lose volume of water and close the screw once the
water in all of the tubes are within the scale of the tubes.
3.3 Static and Total Pressure Head readings, and volumetric flow rate
Try to maximise the total pressure head in tapping 8 by adjusting the flow valves on the
hydraulic bench and test section. Once the water has stabilised within the manometers, take the
readings at each tapping from 1 to 6, which are the static pressure head at the corresponding
points. Move the probe to each point for each tapping and record the reading at tapping 8 for the
total pressure head at each point the probe is placed. The flow rate will be measured through the
sight gauge. Plug the hole in the hydraulics bench using the ball valve. Set an incremental
volume to be filled and start a timer as soon as the bench starts to fill. Measure the time it takes
for each increment to be filled. (e.g finding time taken for every 7 Litres filled in the bench,
record at v = 7, 14, 21). Record times until the third increment.
3.4 Repeating the Tests, and Turning of the machine
Once the measurements for one flow rate has been found, reset the manometers by opening the
air bleeding screw and draining the water from the test section. Repeat steps 3.2 to 3.3 but
choosing different flow rates for each different test. The flow rates can be changed through the
flow control valves on the hydraulics bench and test section. Repeat the experiments a total of 5
times, and close the valves after the final experiment. Turn off the power switch on the
hydraulics bench.
4. Results
By using the tabulated raw data from appendix 1, the following flow velocities can be calculated
through the following relationships:
,
?
?
=
𝑉 (???? ??????)
?
? (???? ?????𝑖??)
=
?
?
𝐴
Since incremental volumes were set for each test, the volume will stay constant in calculation.
The volumes are converted from litres to
by dividing found litre volumes by 1000. Time
?
3
periods are averaged out of the three incremental recordings for each test. The following flow
rates were calculated for each test:
3
Test #
V,
Incremental
Volume collected
(
)
?
3
(Average time to
?
,
collect volume in
seconds) (s)
?
?
=
𝑉
?
(Volumetric Flow
Rate) (
/s)
?
3
Test 1
0.01
73
0.000137
Test 2
0.07
68.7
0.000102
Test 3
0.07
73
0.000096
Test 4
0.0102
74
0.000138
Test 5
0.09
64.3
0.000140
Table 1.1:
Volumetric Flow Calculated from Raw Data
Cross sectional area is calculated for each point of A to F, with the diameters provided in figure
1.3. The cross sectional area of the venturi tube is a circle,
. Using the volumetric flow
1
4
π?
2
rates found above, the flow velocities for each test are calculated through the given formula and
tabulated below.
Points
Diameter
(m)
Cross
Sectional
Area
A
,
?
2
v, flow
velocity,
(m/s)
Test 1
v, flow
velocity,
(m/s)
Test 2
v, flow
velocity,
(m/s)
Test 3
v, flow
velocity,
(m/s)
Test 4
v, flow
velocity,
(m/s)
Test 5
A
0.025
4.91
E
-4
0.28
0.21
0.2
0.28
0.29
B
0.0139
1.52
E
-4
0.9
0.67
0.63
0.91
0.92
C
0.0118
1.0
E
-4
1.37
1.02
0.96
1.38
1.4
D
0.0107
8.99
E
-5
1.52
1.13
1.07
1.54
1.56
E
0.010
7.85
E
-5
1.75
1.3
1.22
1.76
1.78
F
0.025
4.91
E
-4
0.28
0.21
0.2
0.28
0.29
Table 1.2:
Flow Velocities at each point for each test
Using the relationship
, in which h, static pressure head, is equal to static pressure,
P
,
ℎ =
?
ρ?
divided by (g, gravitational acceleration multiplied by
, density of water). Gravitational
ρ
4
acceleration is taken as 9.81 m/
and density of water as 998 kg/
. By rearranging this
?
2
?
3
relationship to make P the subject the following static pressures are calculated through the use of
experimental static pressure heads. Using the static pressure findings, the total pressure head at
each point can be calculated using the calculated flow velocities and experimental static pressure
heads, with the relationship
. The following static and total pressure heads were
ℎ
?
= ℎ +
𝑉
2
2?
found:
Points
Test 1
, total
ℎ
?
pressure
head, (m)
Test 2
, total
ℎ
?
pressure
head, (m)
Test 3
, total
ℎ
?
pressure
head, (m)
Test 4
, total
ℎ
?
pressure
head, (m)
Test 5
, total
ℎ
?
pressure
head, (m)
A
0.269
0.272
0.209
0.229
0.239
B
0.268
0.273
0.210
0.228
0.233
C
0.261
0.283
0.216
0.244
0.243
D
0.263
0.273
0.208
0.226
0.216
E
0.243
0.266
0.195
0.203
0.186
F
0.174
0.217
0.152
0.119
0.109
Lab Total Head
Readings
0.267
0.275
0.232
0.252
0.290
Table 1.3:
Calculated Total Pressure Heads at Points A-F
Points
Test 1 Static
Pressure
P
(Pa)
Test 2 Static
Pressure
P
(Pa)
Test 3 Static
Pressure
P
(Pa)
Test 4 Static
Pressure
P
(Pa)
Test 5 Static
Pressure
P
(Pa)
A
2594.5
2643.4
2026.6
2202.8
2300.7
B
2222.4
2447.6
1860.2
1821.0
1860.2
C
1615.4
2251.8
1664.4
1439.2
1400.0
D
1419.6
2036.4
1468.6
1028.0
900.7
E
851.7
1762.3
1174.8
440.6
244.8
F
1664.4
2104.9
1468.6
1125.9
1028.0
Table 1.4:
Calculated Static Pressures at Points A-F
5
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Figure 1.5:
Static Pressures vs. Flow Velocity
5. Error Analysis
Experimental errors may have occurred through:
●
Manometer Readings
As seen in table 3, the recorded total heads in the physical lab are not exactly corresponding with
the calculated values of total head. This can be attributed to an error of reading the scales of
manometers for either the static and/or total head pressures.The following error analysis is done
in accordance with test 5 at point F and point E, with the largest visible error.
?
?𝑎?
=
0.109+0.181
0.186−0.104
= 3. 54
?
?𝑖?
=
0.109−0.181
0.186+0.104
=− 0. 25
6. Discussion and Conclusion
Figure 1.5 alongside table 1.2 and table 1.4 it is observed that the gradual increase in flow
velocity from points A - E is accompanied with a decrease in static pressures at the respective
points. When the fluid reaches point F, it returns back into a cross sectional area that was equal to
its origin point, and thus the velocity reduces once more, and is accompanied by an increase in
static pressure. These findings have confirmed Bernoulli’s Theorem which states the inversely
proportional relationship between flow velocity and pressure. In table 1.3, the total head
pressures that were calculated through points A - E were in close proximity with each other, with
slight differences which can be to errors regarding the reading of manometer scales. Through the
physical experiment, it was assumed that total pressure heads between tappings 1 to 5,
corresponding to points A - E, were constant, which is validated through the calculated total
pressure heads. Since the differences are only slight, it can be assumed that the total pressure
head is indeed constant, thus also proving the validity of Bernoulli’s Theorem.
In conclusion, the experiments have proven the validity of Bernoulli’s Theorem of constant total
head pressure and the inverse relationship between flow velocity and pressure.
6
7. References
Lei, C.
2022,
Information for Bernoulli Theorem Lab
, The University of Sydney
-
Page 4 and 5:
Apparatus figures
-
Page 12:
Appendix B: Guide for Error Analysis
Armfield, 2011,
Hydraulics Bench,
https://www.kaznu.kz/content/files/pages/folder4371/F1-10%20Issue%2011%20Instruction%20
Manual.pdf
, Armfield Limited.
8. Appendix
Appendix 1:
Raw Data from Physical Experiment
7
Related Documents
Related Questions
Please solve the following
arrow_forward
follow the format to answer the question
arrow_forward
5) A cylindrical bucket 150 mm in diameter and 200 mm high contains 150 mm of
water. A boy swings the bucket on a vertical plane so that the bottom of the bucket describes a circle of radius 1 m. how fast should it be rotated so that no water will
be spilled?
Answer: 31.13rpm
Subject: Fluid Mechanic
Lesson: Relative Equilibrium of Liquids
Fundamentals of Fluid Flow
arrow_forward
1) At any time, approximately 20 volcanoes are actively erupting on the Earth, and 50–70
volcanoes erupt each year. Over the past 100 years, an average of 850 people have died
each year from volcano eruptions. As scientists and engineers study the mechanics of lava
flow, accurately predicting the flow rate (velocity) of the lava is critical to saving lives
after an eruption. Jeffrey's equation captures the relationship between flow rate and
viscosity as:
Flow
V = Pgt sin(@)
28 сm
10
where p is the density of the lava, g is gravity, t is the flow thickness, a is the slope, and u
is the lava viscosity. Typical values are given as follows for the flow rate:
u= 4x103 kg/(m.s) ±1%
p= 2.5 g/cm³ ±1%
t= 28 cm +0.5 cm
a= 10° +1 °
g= 9.81 m/s?
Determine the likely maximum possible error in the calculated value of the flow rate.
arrow_forward
The property of a fluid called viscosity is related to its internal friction and
resistance to being deformed. The viscosity of water, for instance, is less than that
of molasses and honey, just as the viscosity of light motor oil is less than that of
grease. A unit used in mechanical engineering to describe viscosity is called the
poise, named after the physiologist Jean Louis Poiseuille, who performed early
experiments in fluid mechanics. The unit is defined by 1 poise = 0.1 (N s)/m2.
Show that 1 poise is also equivalent to 1 g/(cm · s).
%3D
arrow_forward
You are employed as a mechanical engineer within an unnamed research center, specializing in the development
of innovative air conditioning systems. Your division is tasked with providing computer-based modeling and
design solutions using computational fluid dynamics through ANSYS software. Your primary responsibilities
involve the analysis of horizontal channel dynamics to meet specific criteria. Under the guidance of your
immediate supervisor, you have been assigned unique responsibilities within an ongoing project. As a member of
the research team, your role includes constructing an appropriate model and executing a sequence of simulation
iterations to explore and enhance channel performance. Figure 1 provides a visualization of the horizontal channel
under consideration. Consider 2D, incompressible, steady flow in a horizontal channel at a Reynolds number of
150. The schematic below illustrates the channel flow, not drawn to scale. For simplicity, neglect gravity. The
channel's…
arrow_forward
Fluid Mechanics Problem:
Assume all fluids are 20oC.
arrow_forward
Can I have a detailed, step-by-step explanation for the following question? Thank you!
The answer is given as, q = sqrt [ (2*sigma*g*h)/(rho) ], which is not the answer I got.
Can someone clarify?
arrow_forward
SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer
arrow_forward
% ParametersD = 0.1; % Diameter of the tube (m)L = 1.0; % Length of the tube bundle (m)N = 8; % Number of tubes in the bundleU = 1.0; % Inlet velocity (m/s)rho = 1.2; % Density of the fluid (kg/m^3)mu = 0.01; % Dynamic viscosity of the fluid (Pa.s)
% Define the grid size and time stepdx = D/10; % Spatial step size (m)dy = L/10; % Spatial step size (m)dt = 0.01; % Time step size (s)
% Calculate the number of grid points in each directionnx = ceil(D/dx) + 1;ny = ceil(L/dy) + 1;
% Create the velocity matrixU_matrix = U * ones(nx, ny);
% Perform the iterationsfor iter = 1:100 % Calculate the velocity gradients dUdx = (U_matrix(:, 2:end) - U_matrix(:, 1:end-1)) / dx; dUdy = (U_matrix(2:end, :) - U_matrix(1:end-1, :)) / dy; % Calculate the pressure gradients dpdx = -mu * dUdx; dpdy = -mu * dUdy; % Calculate the change in velocity dU = dt * (dpdx / rho); % Update the velocity matrix U_matrix(:, 2:end-1) = U_matrix(:, 2:end-1) + dU; % Apply…
arrow_forward
please show steps with explanation of the formulas and calculs for more understanding. Thank you!
arrow_forward
Hi, Please help me with this question and please show the full solution. Thank you very much
arrow_forward
b) A student team is to design a human-powered submarine for a design competition. The
overall length of the prototype submarine is 4.85 m, and its student designers hope that it
can travel fully submerged throoh water at 0.440 m/s. The water is freshwater (a lake) at
a temperature, T=15°C, p=999.1 kg/m² and dynamic viscosity, µ = 1.138 x 103 kg/m's.
The design team builds a one-fifth scale moder to test in their university's wind tunnel
(Figure 10). A shield surrounds the drag balance strut so that the aerodynamic drag of the
strut itself does not influence the measured drag. The air in the wind tunnel is at 25°C and
at one standard atmosphere pressure having p = 1.184 kg/m³ and µ = 1.849 x 10-$ kg/m's.
Determine the air speed required to run the wind tunnel in order to achieve similarity.
Wind tunnel test section
Model
FD
V
P P
Strut
Shield
Drag balance
Figure 10
arrow_forward
The Reynold's number of a sphere falling in air is 1E6. If the sphere's radius is 1ft, what is its velocity? Density of air is 0.00234 slug/ft³ and viscosity of air is 3.8E-7 lbf-sec/ft²A. 2.5 ft/sB. 5.1 ft/sC. 40.6 ft/sD. 81.2 ft/s
arrow_forward
ENGINEERING FLUID MECHANICS. ANSWER SHOULD BE SAME AS THE OTHER PICTURE.
arrow_forward
Biotransport Phenomena
arrow_forward
Needs Complete typed solution with 100 % accuracy.
arrow_forward
( computational fluid dynamics question)
Question:  If the calculations lag behind the flow of fluid, what factor of the simulation gets affected?
Circle Final answer or State it clearly
arrow_forward
In fluid mechanics, which of the following are true:
(a) Fluid mechanics is the branch of science concerned with stationary fluids
(b) Fluids like water posses only potential energy
(c) The field of fluid mechanics is infinite and endless
(d) It is a branch of physics which concerns the study of liquids and the ways in which they interact with forces
(e) It is a sience concerned with the response of fluids to forces exerted upon them,
(f) the fluid which is in state of rest is called as static fluid and its study is called as statics.
arrow_forward
Requesting, I want answers for a,b,c,d (all)
arrow_forward
I need help correcting this problem (incorrect attempts are attached). Please step-by-step.
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Related Questions
- Please solve the followingarrow_forwardfollow the format to answer the questionarrow_forward5) A cylindrical bucket 150 mm in diameter and 200 mm high contains 150 mm of water. A boy swings the bucket on a vertical plane so that the bottom of the bucket describes a circle of radius 1 m. how fast should it be rotated so that no water will be spilled? Answer: 31.13rpm Subject: Fluid Mechanic Lesson: Relative Equilibrium of Liquids Fundamentals of Fluid Flowarrow_forward
- 1) At any time, approximately 20 volcanoes are actively erupting on the Earth, and 50–70 volcanoes erupt each year. Over the past 100 years, an average of 850 people have died each year from volcano eruptions. As scientists and engineers study the mechanics of lava flow, accurately predicting the flow rate (velocity) of the lava is critical to saving lives after an eruption. Jeffrey's equation captures the relationship between flow rate and viscosity as: Flow V = Pgt sin(@) 28 сm 10 where p is the density of the lava, g is gravity, t is the flow thickness, a is the slope, and u is the lava viscosity. Typical values are given as follows for the flow rate: u= 4x103 kg/(m.s) ±1% p= 2.5 g/cm³ ±1% t= 28 cm +0.5 cm a= 10° +1 ° g= 9.81 m/s? Determine the likely maximum possible error in the calculated value of the flow rate.arrow_forwardThe property of a fluid called viscosity is related to its internal friction and resistance to being deformed. The viscosity of water, for instance, is less than that of molasses and honey, just as the viscosity of light motor oil is less than that of grease. A unit used in mechanical engineering to describe viscosity is called the poise, named after the physiologist Jean Louis Poiseuille, who performed early experiments in fluid mechanics. The unit is defined by 1 poise = 0.1 (N s)/m2. Show that 1 poise is also equivalent to 1 g/(cm · s). %3Darrow_forwardYou are employed as a mechanical engineer within an unnamed research center, specializing in the development of innovative air conditioning systems. Your division is tasked with providing computer-based modeling and design solutions using computational fluid dynamics through ANSYS software. Your primary responsibilities involve the analysis of horizontal channel dynamics to meet specific criteria. Under the guidance of your immediate supervisor, you have been assigned unique responsibilities within an ongoing project. As a member of the research team, your role includes constructing an appropriate model and executing a sequence of simulation iterations to explore and enhance channel performance. Figure 1 provides a visualization of the horizontal channel under consideration. Consider 2D, incompressible, steady flow in a horizontal channel at a Reynolds number of 150. The schematic below illustrates the channel flow, not drawn to scale. For simplicity, neglect gravity. The channel's…arrow_forward
- Fluid Mechanics Problem: Assume all fluids are 20oC.arrow_forwardCan I have a detailed, step-by-step explanation for the following question? Thank you! The answer is given as, q = sqrt [ (2*sigma*g*h)/(rho) ], which is not the answer I got. Can someone clarify?arrow_forwardSOLVE CAREFULLY!! Please Write Clearly and Box the final Answerarrow_forward
- % ParametersD = 0.1; % Diameter of the tube (m)L = 1.0; % Length of the tube bundle (m)N = 8; % Number of tubes in the bundleU = 1.0; % Inlet velocity (m/s)rho = 1.2; % Density of the fluid (kg/m^3)mu = 0.01; % Dynamic viscosity of the fluid (Pa.s) % Define the grid size and time stepdx = D/10; % Spatial step size (m)dy = L/10; % Spatial step size (m)dt = 0.01; % Time step size (s) % Calculate the number of grid points in each directionnx = ceil(D/dx) + 1;ny = ceil(L/dy) + 1; % Create the velocity matrixU_matrix = U * ones(nx, ny); % Perform the iterationsfor iter = 1:100 % Calculate the velocity gradients dUdx = (U_matrix(:, 2:end) - U_matrix(:, 1:end-1)) / dx; dUdy = (U_matrix(2:end, :) - U_matrix(1:end-1, :)) / dy; % Calculate the pressure gradients dpdx = -mu * dUdx; dpdy = -mu * dUdy; % Calculate the change in velocity dU = dt * (dpdx / rho); % Update the velocity matrix U_matrix(:, 2:end-1) = U_matrix(:, 2:end-1) + dU; % Apply…arrow_forwardplease show steps with explanation of the formulas and calculs for more understanding. Thank you!arrow_forwardHi, Please help me with this question and please show the full solution. Thank you very mucharrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY