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 7.38P
(a) Determine the capacitance of a spherical tank of radius R, shown in
Figure P7.38.
(b) Obtain a model of the pressure at the bottom of the tank, given the mass flow rate qmi.
Figure P7.38 A spherical tank.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
EXAMPLE 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
50000
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 negligible
5.42 PQ4 If an automobile tire develops a leak, how does the
mass of air and density change inside the tire with time? Assum-
ing the temperature remains constant, how is the change in den-
sity related to the tire pressure?
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
- Q.2 3 A fluid of density 1200 kg/m at 1 atm pressure is compressed to 101 atm pressure isothermally. If the isothermal -5 compression is 4.8x 10 atm, the -1 increase in density in kg/m of fluid isarrow_forwardA graduated cylinder full of water in the lab on a bench that has just been waxed. The cylinder is 1 cm^2 in the inner cross-sectional area, and the water is 10 cm high. The temperature is at room temperature (25 °C) and remains constant. Water-air interface energy (i.e., water surface tension) is approximately 0.072 N/m at 25 °C. All the water spills and forms a puddle that can be approximated as a thin disk. (a) If this disk’s diameter is 14 cm, calculate the work required to create just the air-water interface. (b) Calculate the change in the gravitational potential energy of the water puddle in (b) (g = 9.8 m/s2arrow_forward4.99 For the system shown in Figure P4.99 the aver- age velocity in the pipe is 10 m/s. Up to point A, K = 1.5, from B to C, K = 6.2, and the pump is 80% efficient. If %3D = 200 kPa find and PB Pc PA %3D and the power required by the pump. Water 10 m Device 30 m 100 mm dia. A B ligut ol bai bns Figure P4.99arrow_forward
- A tank of diameter Dis being filled with a fluid of density p at a constant rate of V. The tankhas a hole of diameter d at the bottom. What is the steady-state height, h, of the liquid in the tank?arrow_forwardThe capillary rise h of a fluid is depends on fluid density, ρ, surface tension, σ, diameterof tube, D, contact angle, θ and gravity, g. Obtain an expression for h by Raleigh andBuckingham methods.arrow_forwardA fan delivers 6 meters cubed of air per second at 25 degree Celsius and 1.45bar. assuming molecular weight of air as 28.97mol, calculate the mass of air delivered. Determine also the gas density, specific weight and specific volume.arrow_forward
- Find the size of a wind turbine rotor (diameter in m) that will generate 100kW of electrical power in a steady wind (hub height) of 7.5 m/s. Assume that the air density is 1.225 kg/m3, Cp = 16/27 and n = 1. %3Darrow_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_forwardQ.6 Calculate the capillary effects (in mm) in a glass tube of 4 mm diameter, when immersed in mercury. The temperature of the liquid is 20 °C and the values of surface tension of water and mercury at 20 °C in contact with air are 0.0735 N/m and 0.48 N/m respectively. The contact angle for mercury is 130°.arrow_forward
- When a person ice skates, the surface of the ice actuallymelts beneath the blades, so that he or she skates on a thinsheet of water between the blade and the ice.( a ) Find an expression for total friction force on the bottomof the blade as a function of skater velocity V , bladelength L , water thickness (between the blade and theice) h , water viscosity μ , and blade width W .( b ) Suppose an ice skater of total mass m is skatingalong at a constant speed of V 0 when she suddenlystands stiff with her skates pointed directly forward,allowing herself to coast to a stop. Neglecting frictiondue to air resistance, how far will she travelbefore she comes to a stop? (Remember, she iscoasting on two skate blades.) Give your answer forthe total distance traveled, x , as a function of V 0 , m ,L , h , μ , and W .( c ) Find x for the case where V 0 = 4.0 m/s, m = 100 kg,L = 30 cm, W = 5.0 mm, and h = 0.10 mm. Do youthink our assumption of negligible air resistance is agood one?arrow_forwardBy an inkjet printerthe diameter (d) of the points created, the dynamic of the inkviscosity (µ), density (ρ), surface tension (σ), nozzlediameter (D), the distance of the nozzle from the paper surface (L) andink jet velocity is thought to depend on V.Get an expression to characterize the behavior of the ink jetplease.arrow_forwardThe air bubble formed by explosion inside water perform osillations with time period T which depends onpressure p), density (p) and on energy due to explosion (E). Establish relation between T, p. E and p.arrow_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
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License