EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 8220100254963
Author: Palm
Publisher: MCG
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Chapter 7, Problem 7.42P
To determine
The model of the pressure
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An elastic bar of length L = 1m and cross section A = 1cm2 spins with
angular velocity ω about an axis, as shown in the figure below. The
radial acceleration at a generic point x along the bar is a(x) = ω2x,
where ω= 100rad/s is the angular velocity. The bar is pinned on the
rotation axis at x = 0. A mass M = 1kg is attached to the right end of
the bar. Due to the radial acceleration, the bar stretches along x with
displacement function u(x). The displacement u(x) solves the BVP
(strong form) sketched below:
d
dx (σ(x)) + ρa(x) = 0 PDE
σ(x) = E du
dx Hooke’s law
(1)
u(0) =?? essential BC
σ(L) =?? natural BC
where σ(x) is the axial stress in the rod, ρ= 2700kg /m3 is the mass
density, and E = 70GPa is the Young’s modulus
1. Define appropriate BCs for the strong BVP
2. Find the solution of the strong BVP analytically
3. Derive the weak form of the BVP.
Gruebler's formula for the following mechanism?
w/I
- |
العنوان
I need a detailed drawing with explanation
SOLL
эт
4
حكا
The guide vane angle of a reaction turbine (Francis type
make 20° with the tangent. The moving blade angle at entry is
120°. The external diameter of runner is 450 mm and the internal
diameter is 300 mm. Runner width at entry is 62.5mm and at exit
100mm. Calculate the blade angle at exit for radial discharge.
96252
-20125
750 ×2.01
Chapter 7 Solutions
EBK 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
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