# Mechanics of Fluid – CE 411 Assignment CE 4B

Solve the following and submit their solutions next meeting. Answers are given at the end of each problem for your guide. Don’t forget to carry out the units and show its cancellations. Refer to your notes for a further guide.

Problems:

1. Determine the total kilograms that can be made by mixing 2 liters of alcohol and 2 liters of water. Assume the densities of alcohol and water are 0.78 and 0.98 respectively. Ans. 3.520 kgs
1. Fluid A has a density of 600 kg/m3 is mixed with a liquid whose density is 1000 kg/m3 filling 1 m3 Find the respective quantities if the density of the mixture is 800kg/m3. Also, find the weight of the mixture if g = 9.8 m/sec2.

Ans.   A) m1 =  300 kgs, m2 = 500 kgs         b)         W = 800 kg f

1. Four kilograms of air at 270K are contained in a 0.3 m3 tank. Determine     a) pressure, kPa, b) Number of moles, kg moles, c) specific volume, m3/kg, d) specific volume of mass in a molal basis, m3/kg mol

For air, R= 0.287 kJ/kgK,                   M= 28.97 kg/kg mol,   use PV =mRT

Ans.  A) P = 1033.2 kPa  b) N  = 0.138 kg mol, c) 0.075 m3/kg  d) 2.17 m3/kg mol

4. Calculate how many stokes is kinematics viscosity of 2 ft / sec 2 ?

Ans.  v =   1859 stokes

1. Oxygen is at 50oC and 150 KPa abs. Calculate (a) density, (b) specific weight  (c) specific volume.

MW of oxygen                       = 32

Universal gas constant            = 8312 N m/ kg mole K

Note:

R  = 8312 / 32  = 0.26 kN m / kg K

Ans:  (a ) density , p = 1.79 kg/m3, ( b ) Specific Weight        = 17.54 N / m3

( c ) Specific Volume , v = 0.559 m3 /kg

Dr. Victor E. Odarve, BSME/MEP-ME/MAED/EDD-Lecturer

University of Immaculate Conception, Davao City, Philippines

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# Top 3 Performers in Engineering Math 1(EMT 201)

Shown below were the top 3 students’ performers in Engineering Mathematics 1 (EMT 201) for the First Semester 2015-16 Engineering 200 level. The Final exam was conducted last March 1, 2016, at Edeh’s Ark Exam Hall, Madonna University, Elele Campus, Nigeria, Africa. Their performance is based on their Cumulative Assessment (CA) and Final Exam result for the semester.

 Reg. Number CA(30% max) Final Exam(70%max) Total Score First Place CHE/14/034 26 65 91 PTE/14/107 26 65 91 Second Place CVE/14/115 25 65 90 EE/14/150 25 65 90 PTE/14/092 25 65 90 FST/14/012 25 65 90 Third Place PTE/14/099 24 65 89 EE/T/14/122 24 64 89 MECH/14/063 26 63 89

Congratulations! Keep up the good work.

VICTOR E. ODARVE – BSME/MEP-ME/MAED/EDD

Professor, Mechanical Engineering Department

# TOP 3 STUDENTS PERFORMERS- Probability and Statistics (EST 201)

Shown below were the top 3 students’ performers in Probability and Statistics (EST 201) for the First Semester 2015-16 Engineering 200 level. The Final exam was conducted last February 26, 2016, at Edeh’s Ark Exam Hall, Madonna University, Elele Campus, Nigeria, Africa. Their performance is based on their Cumulative Assessment (CA) and Final Exam result for the semester.

 Reg. Number CA(30% max) Final Exam(70%max) Total Score First Place CHE/14/034 26 65 91 CHE/14/045 26 65 91 MECH/14/095 26 65 91 EE/14/102 26 65 91 EE/14/150 26 65 91 PTE/14/092 26 65 91 PTE/14/143 26 65 91 FST/14/012 26 65 91 Second Place MECH/14/063 25 65 90 CVE/14/098 25 65 90 PTE/14/099 25 65 90 Third Place PTE/14/086 23 65 88

Congratulations! Keep up the good work.

DR. VICTOR E. ODARVE, BSME/MEP-ME/MAED/EDD

Mayana, Jagna, Bohol, Philippines

The result can also be viewed at the blog site, “http://tagamayana.blogspot.com&#8221;

Congratulations! Keep up the good work.

1. VICTOR E. ODARVE – BSME/MEP-ME/MAED/EDD

Professor, Mechanical Engineering Department

# Competent Math Lecturer, Please!

By Vic Odarve

“I hate math. It gives a headache every time I enter the class. The lecturer just copies a problem and its answer in a textbook and do little discussion, then complete the lecture period”, muttered one student after two- hour talk. A common complaint among students!

Math students doing seatwork

Unlike other courses where memory counts with a little class discussion, math lecturers must solve problems using mathematical calculations, discuss in a readable and compact manner, and persuade students to contemplate and enjoy math. Computation is a lifeblood in problem solving; hence math calculation skill of a teacher is needed. Further a teacher must have a deep understanding to enable a detailed step by step discussions as to whys the actions are done. Communication prowess allows the lecturers to organize the teaching methods in an efficient manner without much complication to students’ understanding. An amazing picture inside the schoolroom! That’s how a competent math lecturer teaches.

Math students

As solving math problems and exercises form part most of the activities in the classroom, lecturers must possess an outstanding skill in math computation techniques.  Math calculations are the primary elements in problems solving and most students struggle in pain over this country; hence math lecturers must have an extended knowledge in math.  Without this skill, course content roadmap may suffer; often part of the topics may not be discussed on what is supposed to be completed in a semester.

Math qualifications play an important role as lecturer

Ability to discuss well every step of the math calculation facilitates attentiveness of the students. Sensing that students fail to grasp the manner how the steps are done, the lecturer will slowly expound the subject matter and occasionally review the ways in every solution step. Lecturers must explain the principles and theorems succinctly and clearly; draw some parallel application to our everyday lives. A little review in a discussion that initially baffled them will all of a sudden make sense. Failure to understand the steps as to whys they are done results to poor math foundation. Then impending disaster awaits on the next level math course, as poor preparation takes its toll.

Lecturer at work

With competent lecturer, students experience a quite different teaching approach and style. The picture inside the classroom is clear: smooth sailing discussion, where all eyes will be on the board and ears to the lecturers and topics appear easy and simple. Relax and confident, lecturers can explain the course topics in a detailed manner; repeat the discussion as if they know what students are asking for.

Math courses are indeed difficult, but with competent lecturers, students who traditionally struggle math begin to build confidence. Math becomes a relevant and never a boring course. So, with a vibrant, expert, and competent math lecturer mathematics is simple and interesting. Good lecturers have the power to change the students’ negative attitude towards math.!

Students must enjoy and love math. Mathematics does have a purpose and a meaning. Being the language of nature, math unfolds the secrets of our universe… from dark matter to the gravitational waves – what are sometimes referred to as ripples in the curvature of space-time. In math competent lecturers really matter!

# Top Five(5) Performers MEC 232-Strength of Materials

Top Five (5) Performers  MEC 232-Strength of Materials

Second Semester 2014-2015

Below are the top 5 performers of Strength of Materials for the Second Semester 2014-2015 of Madonna University, Elele Campus, River State, Nigeria. Final Exam was given last July 31,2015. Final Score consists of Cumulative Assessment (CA) (30%) and Final exam (70%). There are 230 students in a class in MEC 232.

 Reg. Number CA Final Exam Total Score Top 1 SC/13/309 SC/13/385 27 25 65 67 92 92 Top 2 SC/13/437 25 65 92 Top 3 SC/13/409 23 65 90 Top 4 SC/13/411 SC/13/500 SC/13/516 27 22 27 60 65 60 87 87 87 Top 5 SC/13/279 SC/13/533 26 26 60 60 86 86

CONGRATULATIONS. KEEP UP THE GOOD WORKS!

Happy vacation for all!

1. VICTOR E. ODARVE, BSME, MEP-ME,MAED, EDD, PHILIPPINES, ASIA

Final Exam Strength of Materials

# MEC 232 Strength of Materials Final Exam Review

Strength of Materials Final Exam Review. Try solving the problems below in preparation of the exam. Similar problems will come out. Bring individual calculator.

1. A piston rod of a reciprocating water pump is 18 mm diameter and 100 cm long. If maximum elongation is not to exceed 3 mm and E = 206,785 x 10 3 kpa, determine the allowable load, KN.
2. Determine the diameter of the steel rod which is stretched between two walls if the allowable stress is not to exceed 138 MPa at – 20 . The rod carries a tensile load of 5000 N at 20 C. Assume coefficient of thermal expansion 12.1 m/m and E = 196 GPa.
3. A concrete column 280 mm in diameter is reinforced with steel to support an axial compressive load of 700 kN. Determine the area of the reinforcing steel if allowable stresses are 8 MPa and 130 MPa for concrete and steel, respectively. E for concrete = 14 GPa and E for steel = 200 GPa.
4. A machinery, solid shaft 4 inches in diameter is driven by a 36 inch gear and rotating at 120 rpm. If the allowable shearing stress is 10 ksi, determine the transmitted horsepower.
5. A concrete column 250 mm in diameter is reinforced with steel to support an axial compressive load of 600 kN. Determine the area of the reinforcing steel if allowable stresses are 8 MPa and 130 MPa for concrete and steel, respectively. E for concrete = 14 GPa and E for steel = 200 GPa.
6. A rod whose unit mass is 3800 kg/ m3 has a cross sectional area of 390 mm2 and 250 meters long. If the load of 40 kN is applied at its end and E = 200 x 10 3 MPa, determine,a) elongation due to its own weight, mm b) elongation due to the applied load, mm c) total elongation , mm
7. A petrochemical plant uses a cylindrical vessel as storage for its chlorine gas requirement. The storage is 90 mm diameter, 4 mm thick, 4 meters length. Determine the maximum internal pressure in the tank can hold if the maximum allowable longitudinal stress is 28 MPa and maximum circumferential stress is 12 MPa.
8.      Calculate the maximum allowable pressure of a sphere 100 mm diameter with a wall 0.6mm thick if allowable stress is 2 MPa.
9. A steel tank at the Boy’s hostel is open at the top, ¼ in thick, 24 feet in diameter and 48 feet high is filled with water. Determine the maximum circumferential stress. Ans. 11980.0 psi
10. A concrete beam 20 meters long and weighing 2 t0ns is carried by a steel and bronze cable shown on page 36 (workbook). Determine the smallest areas of bronze and steel cable if the maximum allowable stress for bronze is 100 MPa and steel is 150 MPa.
11. A wooden uniform beam AB is 72 meters long, weighs 120 kg and loaded as shown. At what point must the beam be supported so that it may rest horizontally? Let the resultant of these forces passes through point D. Refer to page 23 in your workbook in the diagram.
12. A beam shown on page 22 (Workbook) has a uniformly distributed load of 10 kN/m. If the span is 20 meters long, find the reactions at A and B. Use equilibrium and virtual work method.
13. A 30 m –beam of the bridge is loaded as shown in page 22 Workbook. Determine Ra and Rb. Use the equilibrium and virtual work method.
14. A steel rod is to withstand a pull of 10,000 pounds. If the ultimate stress is 50,000 psi and a factor of safety of 4 is used, determine the diameter of the rod.
1. What force is necessary to punch a ¾ “diameter hole in a ½ “ thick plate? Ultimate shear strength of the steel plate is 50,000 psi.

1. The beams are loaded as shown in example 1 page 127 and example 2 page 131 in our workbook. Study how to draw the load, shear, and moment diagram.

1. A rectangular steel bar 1 /2 “ wide by 1/8 “ thick and 80 inches long  is bent by applying forces at the ends. Midpoint deflection is 2 “. Determine the bending stress in the bar if E = 29 x 10 6
1. Determine the maximum flexural or bending stress developed on a belt 10 mm wide by 0.20 mm thick running over a pulley 400 mm in diameter. Assume E = 100 GPa.

# EMT 202 Engineering Math 2 Quiz 2

Our second quiz will be on Monday, June 22, 2015. Please review the following matrix methods in solving unknowns for sets of linear equations.

1. Cramer’s rule. This method makes use of the determinants in finding the solutions. Using the minor’s method, determinants can be solved easier. Very important for the minor’s method is the use of the conventional signs. Any rows or columns can be utilized as long as conventional signs are observed. Then use the formulas for the unknowns.

2. Gaussian Elimination method. This is the most used among the upper triangular matrix system in solving sets of linear equation. Of course transform first three sets of equation into the augmented matrix form. Any legitimate row operations can be used to achieve the required upper triangular matrix. Then, finally, back substitution will solve the unknowns.

3. Gauss Jordan. This method is just a continuation from Gaussian elimination by making the diagonal line into 1’s and zeros upper and lower matrices. Row operations are used to attain the form. Since the diagonal elements are 1’s, unknowns can be solved readily.

4. Inverse Method. This is derived from the AX= b equation. Of course, A is a coefficient matrix, X represents the unknowns, and b, are the constants. Transforming such equation into X = A -1b, may solve the equation where A -1 is the inverse of A.

Try the sets of linear equations below. Solve the following sets of equations by

a) Cramer’s rule b) Gaussian elimination

c) Gauss Jordan method d) Inverse method

2x – y + 2z       = 7

x + 3y -3z        = 10

3x – 2y + 3z    = 5

Answers:        x = 1                y= 11               z= 8

1. Victor E. Odarve, BSME/MEP-ME, MAED, EDD

Mayana, Jagna, Bohol, Philippines, Southeast Asia

# Math Examples that Keep Students Challenge

By Vic Odarve

Solving math examples in different methods but yield the same answer is itself a challenge.  And it works; keeping students at bay!

This approach allows the students to learn the principles of each method of solving same examples and develop mastery. As they master the different methods, students can readily compare the results with ease and build confidence. As confidence builds up, they challenge math problems by doing themselves; hence math becomes easier and simpler.

Solving math problems by different methods can surprise many      students, even the stupid ones. Math teachers, an expert in this field and speak with a power of persuasion, keep students’ eyes, glue to the board; ears listen to every discussion, and silence throughout the classroom. For example, in Algebra, find the value of x in a quadratic equation by factoring, by completing the square, and by the use quadratic formula. These three methods of finding the solution work differently but yields the same answer. This way the students learn three math principles in just one example. Furthermore, they can spot the differences, and mimic the teacher’s steps in arriving the final answer. Students feel great, satisfied, and enjoyed by learning three different approaches. This develops mastery of the course. Of course, a surprise and challenge!

Working Examples

Solving single math problem and obtain the same result using different methods also allows students to check and compare the final answer; hence the process builds up their confidence. Students turn this great opportunity to learn more methods; thus, increasing their math knowledge. These environments keep them changing, growing, and learning more math; thus becoming them to be an expert. Since all the methods yield the same results, they are motivated and making great grades… one of the top class math performers. The approach does build their confidence. Henceforth, as confidence develops, students challenge themselves in solving math exercises and problems.

What were the results? Some students came to the office smiling and showed their solutions confidently; others wanted to discuss how they got their final answer. Sounds great and fulfilling! It all begins with single math example that keeps the student’s challenge.

# Copy Blindly and Understand Later

By  Vic  Odarve

Failed to understand and behind in a math discussion? Just copy blindly and understand your notes later.

Math lecturer

This is an engineering student’s way of life – abounds of mathematical theorems, formulas, principles, transformations, and a lot more. What a life! So, anybody would like to become an Engineer? And adding to the pain, once students behind in a discussion, teachers just told them boldly,” Just copy blindly and understand it later”. Copying without understanding? That’s it. This is the picture painted inside the classroom. The lecturer did no longer explain the details of the steps on how the previous course of mathematical

Copy blindly and understand later

principles and techniques are done. “These steps are supposed to be learned in your previous course, and the class is running out of time,” lecturer told the students. That’s why students who did poorly in the previous math are frustrated. Sounds hopeless? Not at all; just copy blindly and understand the notes later!

Copying blindly simply means noting down whatever the steps the lecturer has

Engineering students after the class

done in the classroom, even without complete understanding on what you have copied. This is the common scenarios in an engineering classroom. The lecturer is a lecturer and nothing more. He knows how to weigh things, whether to review or not, otherwise he will be behind or may not complete the topic before the semester ends. So as a result “just copy blindly “. It is the students’ initiative; teaching them that to become an engineer is not a bed of roses. Math professors like Einstein, works and solves worded problems lightning speed that only few can fully understand. Since math is like a ladder and if students had poor performance in their previous courses, this time it takes its toll. As a result, students just copy without understanding. But this is a significant step…first step to develop how the students can catch up the tremendous pressure to pass the course.

However, this scenario is not so horrible. This message” copy blindly and study later” encourages the students to study more. This means that students must revisit their notes and lessons after the class. The phrase “understand later” lingers in their memory urging them to review on what happen to their notes or else next meeting they do the same…. Copy blindly and completed the bachelor’s degree in six to eight years instead of five. Most often students will find that after a little review in a discussion that initially baffled them will all of a sudden make sense. Thus, like a gravitational pull exerted by dark energy in the expanding universe, “copying blindly and understand later” drags and challenges the students to study.

Subsequently, the students develop a habit of opening the notes and review everything there on what was discussed by the teacher every after the classroom session. Believe it or not, that slowly and surely, the students develop the habits of doing these practices every after the class session. The turn of events is now clear: students find themselves loving and embracing mathematics!

The phrase “copy blindly and understand later” becomes the things of the past.

# EMT 201 Engineering Math 1 Review Final Exam

Final exam emt 201 review. Study the following problems. Similar exercises will be given on final exam.

1. A 4 kg mass suspended to a coiled spring with k = 484 N/m, initially displaced a distance of 1 meter from equilibrium position, and released with zero velocity and subjected to no damping or external forces. Determine a) the equation of motion using Ordinary DE and Laplace transform solutions b) amplitude c) natural frequency d) period of motion e) graph the equation.

2. How much will be left after 500 years for a radioactive element which has a half life of 2000 years if the initial amount is 40 grams? Solve by a) Ordinary DE solution b) Laplace transform.

3. Solve the non-homogeneous differential equation y” + 2y’ – 8y = e 3x by undetermined coefficient method.

4. A tank contains 200 liters of water. A sweetener containing 2 kg/liter of sugar enters the tank at the rate of 4 liters/min and runs out at 3 liters/min. The tank has a paddle that keeps on stirring in order to keep the mixture uniform. Find the amount of sugar in the tank after 25 minutes.

5. A university canteen serves a cup of tea at 83℃ to an Engineering student. After 2 minutes, the tea has cooled to 73℃. If the canteen temperature is 23℃, how many minutes that the student must wait to cool the tea to 54℃ ?

6. A football superstar was found dead at 6 pm in a room temperature of 22 C. His dead body temperature was 28C upon discovery. If a person’s temperature was 37C and cools down to 35 C after 2 hours after death, determine what time the murder was committed? Use Newton’s law of cooling. Solve by an ordinary differential equation method.

7. Solve DE y’ – y = 0, y(0) = 1. Find y (0.8) using a) ordinary DE method b) Laplace transform c) Power series d) Euler’s method with n= 4.

8. A Petro chemical company uses 900 m3 wastewater tank to control the flow of toxic wastes to its treatment pond. The tank initially has a 160m3 of wastewater containing 1 kg toxic wastes per m3 wastewater. A wastewater containing 1.5 kg toxic wastes per m3 enters the tank at 40 m3/hr and simultaneously released to the treatment pond at 20 m3/hr. A tank has paddle to keep the mixture uniform. Determine the rate, kg toxic/m3 wastewater at which it is released after 5 hours. Solve by ordinary DE method.

9. A tank contains 200 liters of water. A sweetener containing 2 kg/liter of sugar enters the tank at the rate of 4 liters/min and runs out at 3 liters/min. The tank has a paddle that keeps on stirring in order to keep the mixture uniform. Find the amount of sugar in the tank after 25 minutes. Solve by Ordinary DE.

10. A student deposited N300, 000.00 at an annual rate of 8.25 % compounded continuously, how long will it take the account to double in value? Solve by ordinary DE.

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