Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Chapter 5, Problem 5.70PP
To determine
To Find:
The buoyant force acting on the component and force per meter length.
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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.
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In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0.
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Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
Homework#5
Chapter 5 Solutions
Applied Fluid Mechanics (7th Edition)
Ch. 5 - The instrument package shown in Fig. 5.18 weighs...Ch. 5 - A 1.0 -m-diameter hollow sphere weighing 200 N is...Ch. 5 - A certain standard steel pipe has an outside...Ch. 5 - A cylindrical float has a 10 -in diameter and is...Ch. 5 - A buoy is a solid cylinder 0.3 m in diameter and...Ch. 5 - A float to be used as a level indicator is being...Ch. 5 - A concrete block with a specific weight of...Ch. 5 - Figure 5.19shows a pump partially submerged in oil...Ch. 5 - A steel cube 100mm on a side weighs 80N. We want...Ch. 5 - A cylindrical drum is 2 ft in diameter, 3 ft long,...
Ch. 5 - If the aluminum weights described in Problem 5.10...Ch. 5 - Figure 5.20 shows a cube floating in a fluid....Ch. 5 - A hydrometer is a device for indicating the...Ch. 5 - For the hydrometer designed in Problem 5.13 what...Ch. 5 - For the hydrometer designed in Problem 5.13 , what...Ch. 5 - A buoy is to support a cone-shaped instrument...Ch. 5 - A cube has side dimensions of 18.00 in. It is made...Ch. 5 - A cube has side dimensions of 18.00 in. It is made...Ch. 5 - A ship has a mass of 292 Mg. Compute the volume of...Ch. 5 - An iceberg has a specific weight of 8.72kN/m3....Ch. 5 - A cylindrical log has a diameter of 450 mm and a...Ch. 5 - The cylinder shown in Fig. 5.23 is made from a...Ch. 5 - If the cylinder from Problem 5.22 is placed in...Ch. 5 - A brass weight is to be attached to the bottom of...Ch. 5 - For the cylinder with the added brass (described...Ch. 5 - For the composite cylinder shown in Fig. 5.25 what...Ch. 5 - A vessel for a special experiment has a hollow...Ch. 5 - A light foam cup similar to a disposable coffee...Ch. 5 - A light foam cup similar to a disposable coffee...Ch. 5 - Repeat Problem 5.29, but consider that the steel...Ch. 5 - Figure 5.27 shows a raft made of four hollow drums...Ch. 5 - Figure 5.28 shows the construction of the platform...Ch. 5 - For the raft shown in Fig. 5.27, how much of the...Ch. 5 - For the raft and platform shown in Figs. 5.27 and...Ch. 5 - A float in an ocean harbor is made from a uniform...Ch. 5 - Describe how the situation described in Problem...Ch. 5 - A cube 6.00 in on a side is made from aluminum...Ch. 5 - Prob. 5.38PPCh. 5 - A cylindrical block of wood is 1.00 m in diameter...Ch. 5 - A container for an emergency beacon is a...Ch. 5 - The large platform shown in Fig. 5.29 carries...Ch. 5 - Will the cylindrical float described in Problem...Ch. 5 - Will the buoy described in Problem 5.5 be stable...Ch. 5 - Will the float described in Problem 5.6 be stable...Ch. 5 - A closed, hollow, empty drum has a diameter of...Ch. 5 - Figure 5.30 shows a river scow used to carry bulk...Ch. 5 - Prob. 5.47PPCh. 5 - For the vessel shown in Fig. 5.26and described in...Ch. 5 - For the foam cup described in Problem 5.28, will...Ch. 5 - Referring to Problem 5.29, assume that the steel...Ch. 5 - Referring to Problem 5.30, assume that the steel...Ch. 5 - Prob. 5.52PPCh. 5 - Will the cylinder together with the brass plate...Ch. 5 - A proposed design for a part of a seawall consists...Ch. 5 - A platform is being designed to support some water...Ch. 5 - Prob. 5.56PPCh. 5 - A barge is 60 ft long, 20 ft wide, and 8 ft deep....Ch. 5 - If the barge in Problem 5.57 is loaded with 240000...Ch. 5 - A piece of cork having a specific weight of...Ch. 5 - Figure 5.20 shows a cube floating in a fluid, (a)...Ch. 5 - A boat is shown in Fig. 5.33(a). Its geometry at...Ch. 5 - (a) If the cone shown in Fig. 5.34 is made of pine...Ch. 5 - Refer to Fig. 5.35. The vessel shown is to be used...Ch. 5 - Prob. 5.64PPCh. 5 - Wetsuits are prohibited in some triathlons due to...Ch. 5 - A cylinder that is 500 mm in diameter and 2.0 m...Ch. 5 - The diving bell shown in Fig. 5.2 weighs 72 kN and...Ch. 5 - Prob. 5.68PPCh. 5 - A scuba diver with wet suit, tank, and gear has a...Ch. 5 - Prob. 5.70PPCh. 5 - Does steel float? It has a specific gravity of...Ch. 5 - Prob. 5.72PPCh. 5 - An undersea camera (Figure 5.36 ) is to hang from...Ch. 5 - Work Problem 5.73 again, but this time the camera...Ch. 5 - Write a program for evaluating the stability of a...Ch. 5 - For any cylinder of a uniform density floating in...Ch. 5 - For the results found in Project 2, compute the...Ch. 5 - Write a program for evaluating the stability of a...Ch. 5 - Write a program for determining the stability of a...
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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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