System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 7, Problem 7.30P
Figure P7.3O shows an example of a hydraulic accumulator, which is a device for reducing pressure fluctuations in a hydraulic line or pipe. The fluid density is p, the plate mass is am, and the plate area is A. Develop a dynamic model of the pressure p with the pressures p\ and p^ as the given inputs. Assume that mx of the plate is small, and that the hydrostatic pressure pgh is small.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
4. For the following system
a. Give differential equations to model the fluid heights in each container.
b. Write the state-variable equations in matrix form (there should be 2 variables).
c. Suppose that qmi = 0, h1 = 4, h2 = 5, A1 = 10, and A2 = 4. Does fluid flow from container 1 to 2
or from container 2 to 1?
Imi
h2
A27
Air is compressed by a compressor in steady-state operation, i.e. the inlet mass flow rate q is constant in time. The compressor is airtight. The area of
the inlet and outlet cross-section is A/N and AOUT, respectively. The outlet-to-inlet density ratio is POUT/PIN, the outlet-to-inlet mass flow rate ratio is
9m-OUT/9m-IN. What is the outlet-to-inlet volume flow rate ratio? qv-out/9V-IN = ?
Select one:
○ a.
9v-OUT/9V-IN = 9m-OUT/9m-IN
O b. 9v-OUT/9V-IN = PIN/POUT
O c. qv-OUT/QV-IN = (AOUT/AIN)-(POUT/PIN)
O d. qv-OUT/QV-IN-AOUT/AW
A cylinder with a diameter D, floats upright in a liquid as shown in Figure Q4. When the
cylinder is displaced slightly along its vertical axis, it will oscillate about its equilibrium
position with a frequency, o. Assume that this frequency is a function of the diameter, D,
the mass of the cylinder, m, and the specific weight, y, of the liquid. With the aid of
dimensional analysis, answer the following questions in sequence.
(a) List all the variables that are involved in the problem.
(b) Express each of the variables in term of basic dimensions using the FLT system.
(c) Determine the required number of pi terms.
(d)
Form the pi term(s) by inspection using the FLT system.
(e) Check the resulting pi term(s) using the MLT system.
(f) How is the frequency related to these variables?
(g)
If the mass of the cylinder is increased, would the frequency increase or decrease?
D
Figure Q4
Cylinder
diameter D
Chapter 7 Solutions
System Dynamics
Ch. 7 - Prob. 7.1PCh. 7 - Refer to the water storage and supply system shown...Ch. 7 - Prob. 7.3PCh. 7 - In Figure P7.4 the piston of area A is connected...Ch. 7 - Refer to Figure 7.1.4a. and suppose that p\ — p2=...Ch. 7 - Pure water flows into a mixing tank of volume V =...Ch. 7 - Consider the mixing tank treated in Problem 7.6....Ch. 7 - Derive the expression for the fluid capacitance of...Ch. 7 - Prob. 7.9PCh. 7 - Prob. 7.10P
Ch. 7 - 7.11 Derive the expression for the capacitance of...Ch. 7 - Air flows in a certain cylindrical pipe 1 m long...Ch. 7 - Derive the expression for the linearized...Ch. 7 - Consider the cylindrical container treated in...Ch. 7 - A certain tank has a bottom area A = 20 m2. The...Ch. 7 - A certain tank has a circular bottom area A = 20...Ch. 7 - The water inflow rate to a certain tank was kept...Ch. 7 - Prob. 7.18PCh. 7 - Prob. 7.19PCh. 7 - In the liquid level system shown in Figure P7.20,...Ch. 7 - The water height in a certain tank was measured at...Ch. 7 - Derive the model for the system shown in Figure...Ch. 7 - (a) Develop a model of the two liquid heights in...Ch. 7 - Prob. 7.24PCh. 7 - Design a piston-type damper using an oil with a...Ch. 7 - Prob. 7.26PCh. 7 - 7.27 An electric motor is sometimes used to move...Ch. 7 - Prob. 7.28PCh. 7 - Prob. 7.29PCh. 7 - Figure P7.3O shows an example of a hydraulic...Ch. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - (a) Determine the capacitance of a spherical tank...Ch. 7 - Obtain the dynamic model of the liquid height It...Ch. 7 - Prob. 7.40PCh. 7 - Prob. 7.41PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - The copper shaft shown in Figure P7.46 consists of...Ch. 7 - A certain radiator wall is made of copper with a...Ch. 7 - A particular house wall consists of three layers...Ch. 7 - A certain wall section is composed of a 12 in. by...Ch. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - A steel tank filled with water has a volume of...Ch. 7 - Prob. 7.53PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.55P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- For the piping system shown below, water is flowing from left to right at steady-state and constant temperature. You may assume the flow is frictionless. The pipe diameter is larger in section A than section B. The diameters of sections A and C are the same. If gravitation and frictional effects are negligible, which of the following relationships is true about the static pressure in sections A and B? Pc Ps Flow section A section B section C OPA Pg because pressure decreases as velocity increases at steady-state OPA = Pg because friction is assumed to be negligiblearrow_forwardA mass weighting 24 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 21 lbs when the mass has a velocity of 6 ft/sec. Suppose the object is displaced an additional 6 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) =arrow_forwardAssume that the wall shear stress, Tw, created when a fluid flows through a pipe (see Figure a) depends on the pipe diameter, D, the flowrate, Q, the fluid density, p, and the kinematic viscosity, v. Some model tests run in a laboratory using water in a 0.2-ft-diameter pipe yield the Tw vs. Q data shown in Figure b. Perform a dimensional analysis and use model data to predict the wall shear stress in a 0.3-ft- diameter pipe through which water flows at the rate of 1.5 ft3/s. 0.7 Diameter = D 0.6 2 0.5 0.4 Model data (a) 0.3 0.2 0.1 0.5 1.5 Flowrate, Q, ft/s (b) Tw Ib/ft2 Wall shear stress, T,, Ib/ft? n * m N -arrow_forward
- Find the equation of pressure, P exerted by a fluid as a function of density, r, gravity, g and height of the fluid, h.arrow_forwardEXAMPLE Leaking Tank. Outflow of Water Through a Hole (Torricelli's Law) This is another prototype engineering problem that leads to an ODE. It concerns the outflow of water from a cylindrical tank with a hole at the bottom. You are asked to find the height of the water in the tank at any time if the tank has diameter 2 m, the hole has diameter 1 cm, and the initial height of the water when the hole is opened is 2.25 m. When will the tank be empty? 2.20 M Water level asime Outiine walls 200 200 30t .00- 50- D 10000 30000 tebe Revelion 50000arrow_forwardIn this question, assume the "additional displacement" is in the positive u direction. A mass weighing 16 lbs stretches a spring 8 inches. The mass is in a medium that exerts a viscous resistance of 1 lbs when the mass has a velocity of 2 ft/sec. Suppose the object is displaced an additional 5 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) =arrow_forward
- In figure below, fluid A is water (PH20=62.1 lbm/ft^3), fluid B is mercury (PHg=0.488 lbm/in^3). Local acceleration of gravity is standard, z=4.5 ft. What is the pressure difference?arrow_forwardThe left field wall at a baseball park is 320 feet down the third base line from home plate; the wall itself is 37 feet high. A batted ball must clear the wall to be a home run. Suppose a ball leaves the bat, 3 feet off the ground, at an angle of 45°. Use g = 32 ft/sec as the acceleration due to gravity and ignore any air resistance. Complete parts (a) through (d). (a) Find parametric equations that model the position of the ball as a function of time. Choose the correct answer below. x= (Vo cos 45) t, y = - 16t + (Vo sin 45) t+3 x= (Vo sin 45) t, y = 16t - (Vo cos 45) t+ 3 x= (Vo cos 45) t, y = - 32t + (Vo sin 45)t+3 x= (Vo sin 45) t, y = 32t - (vo cos 45)t+3 (b) What is the maximum height of the ball if it leaves the bat with a speed of 75 miles per hour? Give your answer in feet. The maximum height of the ball is feet. (Type an integer or decimal rounded to two decimal places as needed.) (c) What is the ball's horizontal distance from home plate at its maximum height? Give your…arrow_forward(a) Find the pressure at the bottom of the container in the figure below. Ра h: liquid level (m) A: tank cross sectional area (m²) p: density of the fluid Pa: atmospheric pressure Ра R Ps Point 1 Point 2 Point 3 Point 1: Point 2: Point 3: (b) Derive the differential equation representing the hydraulic system above. (c) Determine the stability of the system assuming Ps=0. Explain why. (d) What is the volume flow rate coming out through the hole of the container shown below? m PE = mgh, KE = 0 T h PE = 0, KE = marrow_forward
- You are doing a problem that requires Reynold's Transport Theorem with Conservation of Mass. You carefully write the equation and then on the second line you write: 0 = v3 A3 - Svị dA1 + f vzdA2 What statements in the question or assumptions you make would lead you to this simplification? Mark all that apply. The flow is steady. Newtonian Fluid Incompressible fluid. Inviscid fluid. Inlets have uniform flow. Exits have uniform flow. Velocity is only in the x-direction.arrow_forwardCakulate the time rate of change of air density during expiration Assume that the lung (Fig. 3.11) has a total volume of 6000 ml, the diameter of the trachea is 18 mm, the airflow velocity out of the trachea is 20 cm/s, and the density of air is 1.225 kg/m. Also assume that lung volume is decreasing at a rate of 100 mL/s. Hello sir, I want the same solution, but in a detailed way and mention his data, a question, and a solution in detailing mathematics without words. Solution We will start from Eq. (3.24) because we are asked for the time rate of change of density. We are asked to find the time rate of change of air density; this suggests that Example 3.5 condis tions are representing a nonsteady flow scenario. In addition, we were told what the rate of change in the lung volume is during this procedure, further supporting the use of Eq. (3.24). pdV+ (3.24 ams Assume that at the instant in time that we are measuring the system, density is uniform within the volume of interest. This…arrow_forwardAir is compressed by a compressor in steady-state operation, i.e. the inlet mass flow rate qm is constant in time. The compressor is airtight. The area of the inlet and outlet cross-section is A and AOUT, respectively. The outlet-to-inlet density ratio is PouT PIN the outlet-to-inlet mass flow rate ratio is 9m-OUT/9m-IN- What is the outlet-to-inlet volume flow rate ratio? 9V-OUT/av-IN =? Select one: a. 9V-OUT/av-IN = (A OUT'A IN) (POUT PIN b. 9V-OUT/av-IN = PIN/POUT C. 9V-OUT/av-IN = 9m-OUT/ 9m-IN d. 9V-OUT/av-IN=AOUTAINarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY