Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 2, Problem 77CP
To determine
The ball which reaches the bottom first when one ball is released in water and the other ball is released in oil.
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If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass.
Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image.
Discuss the positive definiteness of V (x, x_dot).
Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of thesystem based on the information we gain from ̇V_dot .
In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 1.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
Homework#5
Chapter 2 Solutions
Fluid Mechanics Fundamentals And Applications
Ch. 2 - For a substance, what is the difference between...Ch. 2 - What is the difference between intensive and...Ch. 2 - What is specific gravity? How is it related to...Ch. 2 - The specific weight of a system is defined as the...Ch. 2 - Prob. 5CPCh. 2 - Under what conditions is the ideal-gas assumption...Ch. 2 - What is the difference between R and Ru? How are...Ch. 2 - A fluid that occupies a volume of 24 L weighs 22 N...Ch. 2 - Prob. 9PCh. 2 - A mass of 1-Ibm of argon is maintained at 200 psia...
Ch. 2 - What is the specific volume of oxygen at 40 psia...Ch. 2 - The air in an automobile tire with a volume of...Ch. 2 - The pressure in an automobile tire depends on the...Ch. 2 - A spherical balloon with a diameter of 9 m is...Ch. 2 - Prob. 16PCh. 2 - Prob. 18EPCh. 2 - Does water boil at higher temperatures at higher...Ch. 2 - Prob. 22CPCh. 2 - What is cavitation? What causes it?Ch. 2 - What is vapor pressure? How is it related to...Ch. 2 - Prob. 24EPCh. 2 - A pump is used to transport water to a higher...Ch. 2 - Prob. 26PCh. 2 - The analysis of a propeller that operates in water...Ch. 2 - What is flow energy? Do fluids at rest possess any...Ch. 2 - How do the energies of a flowing fluid and a fluid...Ch. 2 - Prob. 30CPCh. 2 - Prob. 31CPCh. 2 - List the forms of energy that contribute to the...Ch. 2 - How are heat, internal energy, and thermal energy...Ch. 2 - Using average specific heats, explain how internal...Ch. 2 - Prob. 35CPCh. 2 - Saturated water vapor at 150°C (enthalpy...Ch. 2 - Prob. 37CPCh. 2 - What does the coefficient of volume expansion of a...Ch. 2 - Can the coefficient of compressibility of a fluid...Ch. 2 - Water at 15°C and 1 atm pressure is heated to 95°C...Ch. 2 - Prob. 41PCh. 2 - Prob. 42PCh. 2 - Water at 1 atm pressure is compressed to 400 atm...Ch. 2 - The volume of an ideal gas is to be reduced by...Ch. 2 - Saturated refrigerant-134a liquid at 10C is cooled...Ch. 2 - Prob. 46PCh. 2 - Prob. 47PCh. 2 - The density of seawater at a free surface where...Ch. 2 - Prob. 49EPCh. 2 - Prob. 50EPCh. 2 - Prob. 51PCh. 2 - The ideal gas equation of state is very simple,...Ch. 2 - A frictionless piston-cylinder device contains 10...Ch. 2 - Reconsider Prob. 2-48. Assuming a bear pressure...Ch. 2 - Prob. 55CPCh. 2 - Prob. 56CPCh. 2 - Prob. 57CPCh. 2 - Prob. 58CPCh. 2 - Prob. 59CPCh. 2 - Prob. 60CPCh. 2 - Is then sonic ve1ocity a specified medium a fixed...Ch. 2 - The Airbus A-340 passenger plane has a maximum...Ch. 2 - Carbon dioxide enters an adiabatic nozzle at 1200...Ch. 2 - Prob. 64PCh. 2 - Assuming ideal gas behavior, determine the speed...Ch. 2 - Prob. 66PCh. 2 - Steam flows through a device with a pressure of...Ch. 2 - Prob. 69EPCh. 2 - Air expands isentropically from 2.2 MPa 77C to 0.4...Ch. 2 - Repeat Prob. 2-66 for helium gas.Ch. 2 - Prob. 72PCh. 2 - What is viscosity? What is the cause of it is...Ch. 2 - Prob. 74CPCh. 2 - How does the kinematic viscosity of (a) liquids...Ch. 2 - Prob. 76CPCh. 2 - Prob. 77CPCh. 2 - The viscosity of a fluid is to be measured by a...Ch. 2 - Consider the flow of a fluid with viscosity ...Ch. 2 - A thin 30cm30cm flat plate is pulled at 3 m/s...Ch. 2 - A rotating viscometer consists of two concentric...Ch. 2 - The dynamic viscosity of carbon dioxide at 50°C...Ch. 2 - For flow over a plate, the variation of velocity...Ch. 2 - In regions far from the entrance, fluid flow...Ch. 2 - Repeat Prob. 2-83 for umax=6m/s .Ch. 2 - A frustum-shaped body is rotating at a constant...Ch. 2 - A rotating viscometer consists of two concentric...Ch. 2 - A large plate is pulled at a constant speed of U =...Ch. 2 - A cylinder of mass m slides down from rest in a...Ch. 2 - A thin plate moves between two parallel,...Ch. 2 - Prob. 95PCh. 2 - What is surface tension” What is its cause? Why is...Ch. 2 - Prob. 97CPCh. 2 - What is the capillary effect? What is its cause?...Ch. 2 - Prob. 99CPCh. 2 - Is the capillary rise greater in small- or...Ch. 2 - Prob. 101PCh. 2 - A2.4-in-diameter soap bubble is to be enlarged by...Ch. 2 - Prob. 103PCh. 2 - Determine the gage pressure inside a soap bubble...Ch. 2 - A 0.03-in-diameter glass tube is inserted into...Ch. 2 - Prob. 106PCh. 2 - A capillary tube of 1.2 mm diameter is immersed...Ch. 2 - Prob. 108PCh. 2 - Contrary to what you might expect, a solid steel...Ch. 2 - Nutrients dissolved in water are carried to upper...Ch. 2 - Prob. 111PCh. 2 - Consider a 55-cm-long journal bearing that is...Ch. 2 - Prob. 113PCh. 2 - Prob. 114PCh. 2 - A rigid tank contains an ideal gas at 300kPa and...Ch. 2 - The absolute pressure of an automobile tire is...Ch. 2 - The composition of a liquid with suspended solid...Ch. 2 - Prob. 119PCh. 2 - A 10-m3 tank contacts nitrogen at 25C and 800kPa....Ch. 2 - Prob. 123PCh. 2 - Although liquids, in general, are hard to...Ch. 2 - Prob. 125PCh. 2 - Prob. 126PCh. 2 - Prob. 127PCh. 2 - Reconsider Prob. 2-120. The shaft now rotates with...Ch. 2 - A 10-cm diameter cylindrical shaft rotates inside...Ch. 2 - Some rocks or bricks contain small air pockets in...Ch. 2 - Prob. 131PCh. 2 - Prob. 132PCh. 2 - Prob. 133PCh. 2 - Prob. 134PCh. 2 - Liquid water vaporizes into water vaper as it ?aws...Ch. 2 - In a water distribution system, the pressure of...Ch. 2 - Prob. 137PCh. 2 - The difference between the energies of a flowing...Ch. 2 - Prob. 139PCh. 2 - An ideal gas is compressed isothermally from...Ch. 2 - Prob. 141PCh. 2 - Prob. 142PCh. 2 - Prob. 143PCh. 2 - Water is compressed from 100 kPa to 5000 kPa at...Ch. 2 - Prob. 145PCh. 2 - The dynamic viscosity of air at 20C and 200kPa is...Ch. 2 - A viscometer constructed of two 30-cm -long...Ch. 2 - Prob. 148PCh. 2 - Prob. 149PCh. 2 - Prob. 150PCh. 2 - Prob. 151PCh. 2 - Prob. 152PCh. 2 - Prob. 153PCh. 2 - Prob. 154PCh. 2 - Evan though steel is about 7 to 8 times denser...
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- If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass. Using linear stability analysis, show that the system is asymptotically stable. Hint: stability of a linear system z_dot = Az is characterized by the eigenvalues of A.arrow_forwardWhat would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like?arrow_forward### What would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like, with a counter, in the fluidsim?arrow_forward
- You are asked to design a unit to condense ammonia. The required condensation rate is 0.09kg/s. Saturated ammonia at 30 o C is passed over a vertical plate (10 cm high and 25 cm wide).The properties of ammonia at the saturation temperature of 30°C are hfg = 1144 ́10^3 J/kg andrv = 9.055 kg/m 3 . Use the properties of liquid ammonia at the film temperature of 20°C (Ts =10 o C):Pr = 1.463 rho_l= 610.2 kf/m^3 liquid viscosity= 1.519*10^-4 kg/ ms kinematic viscosity= 2.489*10^-7 m^2/s Cpl= 4745 J/kg C kl=0.4927 W/m CCalculate the surface temperature required to achieve the desired condensation rate of 0.09 kg/s( should be 688 degrees C) a) Show that if you use a bigger vertical plate (2.5 m-wide and 0.8 m-height), the requiredsurface temperature would be now 20 o C. You may use all the properties given as an initialguess. No need to iterate to correct for Tf. b) What if you still want to use small plates because of the space constrains? One way to getaround this problem is to use small…arrow_forwardA differential element on the bracket is subjected to plane strain that has the following components:, Ɛx = 300 × 10-6, Ɛy = 150 × 10-6, Ɛxy = -750 x 10-6. Use the strain-transformation equations and determine the normal strain Ɛx in the X/ direction on an element oriented at an angle of 0 = 40°. Note, a positive angle, 0, is counter clockwise. x Enter your answer in micro strain to a precision of two decimal places. eg. if your answer is 300.15X106, please enter 300.15.arrow_forwardIf the 50 mm diameter shaft is made from brittle material having an ultimate strength of σult=595 MPa for both tension and compression, determine the factor of safety of the shaft against rupture. The applied force, F, is 140 kN. The applied torque T, is 5.0 kN⚫m. Enter your answer to a precision of two decimal places. T Farrow_forwardЗіс 1 mH 10 Ω m 16 cos 2.5 × 104 A Lic 592 10 Ω 1 μFarrow_forwardHomework#5arrow_forwardHomework#5arrow_forwardOxygen (molar mass 32 kg/kmol) expands reversibly in a cylinder behind a piston at a constant pressure of 3 bar. The volume initially is 0.01 m3 and finally is 0.03 m3; the initial temperature is 17°C. Calculate the work input and the heat supplied during the expansion. Assume oxygen to be an ideal gas and take cp = 0.917 kJ/kg K. For 1 bonus mark explain why (using your understanding of thermodynamics) that oxygen is used in this context rather than water vapour.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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