Problem statement: A simply supported beam of diameter D, length L, and modulus of elasticity E is subjected to a fluid crossflow of velocity V, density p, and viscosity µ. Its center deflection 8 is assumed to be a function of all these variables. Part A - Rewrite this proposed function in dimensionless form. (Hint: Take L, p, and V as repeating variables.) Part B- Suppose it is known that & is independent of µ, inversely proportional to E, and dependent only upon pV², not p and separately.

Problem statement: A simply supported beam of diameter D, length L, and modulus of elasticity E is subjected to a fluid crossflow of velocity V, density p, and viscosity µ. Its center deflection 8 is assumed to be a function of all these variables. Part A - Rewrite this proposed function in dimensionless form. (Hint: Take L, p, and V as repeating variables.) Part B- Suppose it is known that & is independent of µ, inversely proportional to E, and dependent only upon pV², not p and separately.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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**Problem 1.15 Suppose you wanted to describe an unstable particle, that spon- taneously disintegrates with a "lifetime" t. In that case the total probability of finding the particle somewhere should not be constant, but should decrease at (say) an exponential rate: too P(t) = | V(x,1)1²dx = e=1/*. -0- A crude way of achieving this result is as follows. In Equation 1.24 we tacitly assumed that V (the potential energy) is real. That is certainly reasonable, but it leads to the "conservation of probability" enshrined in Equation 1.27. What if we assign to V an imaginary part: V = Vo – ir, where Vo is the true potential energy and r is a positive real constant? (a) Show that (in place of Equation 1.27) we now get dP 21 = --P. dt (b) Solve for P(1), and find the lifetime of the particle in terms of r.