Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Chapter 10, Problem 10.53PP
To determine
Find the pressure drop across the value by using given information.
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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 10 Solutions
Applied Fluid Mechanics (7th Edition)
Ch. 10 - Determine the energy loss due to a sudden...Ch. 10 - Determine the energy loss due to a sudden...Ch. 10 - Determine the energy loss due to a sudden...Ch. 10 - Determine the pressure difference between two...Ch. 10 - Determine the pressure difference for the...Ch. 10 - Determine the energy loss due to a gradual...Ch. 10 - Determine the energy loss for the conditions in...Ch. 10 - Compute the energy loss for gradual enlargements...Ch. 10 - Plot a graph of energy loss versus cone angle for...Ch. 10 - For the data in Problem 10.8, compute the length...
Ch. 10 - Add the energy loss due to friction from Problem...Ch. 10 - Another term for an enlargement is a diffuser. A...Ch. 10 - Compute the resulting pressure after a "real"...Ch. 10 - Compute the resulting pressure after a "real"...Ch. 10 - Determine the energy loss when 0.04m3/s of water...Ch. 10 - Determine the energy loss when 1.50ft3/s of water...Ch. 10 - Determine the energy loss when oil with a specific...Ch. 10 - For the conditions in Problem 10.17, if the...Ch. 10 - True or false: For a sudden contraction with a...Ch. 10 - Determine the energy loss for a sudden contraction...Ch. 10 - Determine the energy loss for a gradual...Ch. 10 - Determine the energy lass for a sudden contraction...Ch. 10 - Determine the energy loss for a gradual...Ch. 10 - For the data in Problem 10.22, compute the energy...Ch. 10 - For each contraction described in Problems 10.22...Ch. 10 - Note in Figs. 10.10 and 10.11 that the minimum...Ch. 10 - If the contraction from a 6-in to a 3-in ductile...Ch. 10 - Compute the energy loss that would occur as 50...Ch. 10 - Determine the energy loss that will occur if water...Ch. 10 - Determine the equivalent length in meters of pipe...Ch. 10 - Repeat Problem 10.30 for a fully open gate valve.Ch. 10 - Calculate the resistance coefficient K for a...Ch. 10 - Calculate the pressure difference across a fully...Ch. 10 - Determine the pressure drop across a 90 C standard...Ch. 10 - Prob. 10.35PPCh. 10 - Repeat Problem 10.34 for a long radius elbow....Ch. 10 - A simple heat exchanger is made by installing a...Ch. 10 - A proposed alternate form for the heat exchanger...Ch. 10 - A piping system for a pump contains a tee, as...Ch. 10 - A piping system for supplying heavy fuel oil at 25...Ch. 10 - A 25 mm ODx2.0 mm wall copper tube supplies hot...Ch. 10 - Specify the radius in mm to the centerline of a 90...Ch. 10 - The inlet and the outlet shown in Fig. 10.36 are...Ch. 10 - Compare the energy losses for the two proposals...Ch. 10 - Determine the energy loss that occurs as 40 L/min...Ch. 10 - Figure 10.38 shows a test setup for determining...Ch. 10 - Compute the energy loss in a 90 bend in a steel...Ch. 10 - Compute the energy loss in a 90 bend in a steel...Ch. 10 - For the data in Problem 10.47, compute the...Ch. 10 - For the data in Problem 10.48, compute the...Ch. 10 - A tube similar to that in Problem 10.47 is being...Ch. 10 - Prob. 10.52PPCh. 10 - Prob. 10.53PPCh. 10 - Prob. 10.54PPCh. 10 - Prob. 10.55PPCh. 10 - Repeat Problem 10.55 for flow rates of 7.5 gal/min...Ch. 10 - Prob. 10.57PPCh. 10 - Prob. 10.58PPCh. 10 - Prob. 10.59PPCh. 10 - Prob. 10.60PPCh. 10 - A 34 plastic ball valve carries 15 gal/min of...Ch. 10 - A 114 plastic butterfly valve carries 60 gal/min...Ch. 10 - A 3 -in plastic butterfly valve carries 300...Ch. 10 - A 10-in plastic butterfly valve carries 5000...Ch. 10 - A 1 12 plastic diaphragm valve carries 60 gal/min...Ch. 10 - Prob. 10.66PPCh. 10 - Prob. 10.67PPCh. 10 - Prob. 10.68PPCh. 10 - Prob. 10.69PPCh. 10 - An 8 -in plastic swing check valve carries 3500...Ch. 10 - Use PIPE-FLO software to determine the pressure...Ch. 10 - Use PIPE-FLO to calculate the head loss 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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