Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 11, Problem 73CP
To determine
The reason of contribution of viscous effect to lift usually negligible for airfoils.
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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.
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Chapter 11 Solutions
Fluid Mechanics Fundamentals And Applications
Ch. 11 - Which bicyclist is more likely to go faster: one...Ch. 11 - Consider laminar flow over a flat plate. How does...Ch. 11 - Define the frontal area of a body subjected to...Ch. 11 - Define the planform area of a body subjected to...Ch. 11 - Prob. 5CPCh. 11 - Prob. 6CPCh. 11 - What is the difference between streamlined and...Ch. 11 - Prob. 8CPCh. 11 - What is drag? What causes it? Why do we usually...Ch. 11 - Prob. 10CP
Ch. 11 - During flow over a given body, the drag force, the...Ch. 11 - During flow over a given slender body such as a...Ch. 11 - What is terminal velocity? How is it determined?Ch. 11 - What is the difference between skin friction drag...Ch. 11 - What is the effect of surface roughness on the...Ch. 11 - Prob. 16CPCh. 11 - What is flow separation? What causes it? What is...Ch. 11 - Prob. 18CPCh. 11 - In general, how does the drag coefficient vary...Ch. 11 - Fairings are attached to the front and back of a...Ch. 11 - Prob. 21PCh. 11 - The resultant of the pressure and wall shear...Ch. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - To reduce the drag coefficient and thus to improve...Ch. 11 - A circular sign has a diameter of 50 cm and is...Ch. 11 - Prob. 28EPCh. 11 - Prob. 29PCh. 11 - At highway speeds, about half of the power...Ch. 11 - A submarine can be treated as an ellipsoid with a...Ch. 11 - Prob. 32EPCh. 11 - Prob. 33PCh. 11 - A 70-kg bicyclist is riding her 1 5-kg bicycle...Ch. 11 - A wind turbine with two or four hollow...Ch. 11 - Prob. 37EPCh. 11 - During steady motion of a vehicle on a level road,...Ch. 11 - Prob. 40PCh. 11 - Prob. 41PCh. 11 - Prob. 42PCh. 11 - Prob. 43PCh. 11 - The drag coefficient of a vehicle increases when...Ch. 11 - To reduce the drag coefficient and thus to improve...Ch. 11 - How is the average friction coefficient determined...Ch. 11 - What fluid property is responsible for the...Ch. 11 - What does the friction coefficient represent in...Ch. 11 - Prob. 49PCh. 11 - The local atmospheric pressure in Denver, Colorado...Ch. 11 - The top surface of the passenger car of a train...Ch. 11 - The forming section of a plastics plant puts out a...Ch. 11 - Prob. 54EPCh. 11 - Prob. 55EPCh. 11 - Air at 25C and 1 atm is flowing over a long flat...Ch. 11 - Prob. 58PCh. 11 - Prob. 59PCh. 11 - Prob. 60PCh. 11 - Why is flow separation in flow over cylinders...Ch. 11 - Prob. 62CPCh. 11 - Prob. 63CPCh. 11 - Prob. 64PCh. 11 - A 1ong 5-cm-diameter steam pipe passes through...Ch. 11 - Consider 0.8-cm-diameter hail that is falling...Ch. 11 - Prob. 67EPCh. 11 - Prob. 68PCh. 11 - Prob. 69PCh. 11 - Prob. 70PCh. 11 - Prob. 71EPCh. 11 - One of the popular demonstrations in science...Ch. 11 - Prob. 73CPCh. 11 - Air is flowing past a symmetrical airfoil at an...Ch. 11 - What is stall? What causes an airfoil to stall?...Ch. 11 - Prob. 76CPCh. 11 - Air is flowing past a symmetrical airfoil at zero...Ch. 11 - Both the lift and the drag of an airfoil increase...Ch. 11 - Prob. 79CPCh. 11 - Prob. 80CPCh. 11 - Prob. 81CPCh. 11 - Prob. 82CPCh. 11 - Prob. 83CPCh. 11 - How do flaps affect the lift and the drag of...Ch. 11 - A small aircraft has a wing area of 35 m2 a lift...Ch. 11 - Consider an aircraft that takes off at 260 km/h...Ch. 11 - Prob. 87PCh. 11 - Prob. 88EPCh. 11 - Prob. 89PCh. 11 - A tennis ball with a mass of 57 and a diameter of...Ch. 11 - Prob. 92EPCh. 11 - Prob. 93PCh. 11 - Consider a light plane that has a total weight of...Ch. 11 - A small airplane has a total mass of 1800 kg and a...Ch. 11 - Prob. 97PCh. 11 - Prob. 98PCh. 11 - A 2-zn-high, 4-zn-wide rectangular advertisement...Ch. 11 - 11-97 A plastic boat whose bottom surface can be...Ch. 11 - Prob. 102PCh. 11 - Prob. 103EPCh. 11 - A commercial airplane has a total mass of 150.000...Ch. 11 - Prob. 105PCh. 11 - A paratrooper and his 8-m-diameter parachute weigh...Ch. 11 - Prob. 107PCh. 11 - Prob. 108PCh. 11 - Prob. 110PCh. 11 - Prob. 112PCh. 11 - Prob. 113PCh. 11 - Prob. 114PCh. 11 - Prob. 117PCh. 11 - Prob. 118PCh. 11 - Prob. 119PCh. 11 - Prob. 120PCh. 11 - Prob. 121PCh. 11 - The region of flow trailing the body where the...Ch. 11 - Prob. 123PCh. 11 - Prob. 124PCh. 11 - Prob. 125PCh. 11 - Prob. 126PCh. 11 - Prob. 127PCh. 11 - Prob. 128PCh. 11 - An airplane has a total mass of 3.000kg and a wing...Ch. 11 - Prob. 130PCh. 11 - Write a report on the history of the reduction of...Ch. 11 - Write a report oil the flips used at the leading...Ch. 11 - Large commercial airplanes cruise at high...Ch. 11 - Many drivers turn off their air conditioners and...
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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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