Unformatted text preview: h t + ( uh ) x = 0 u t + uu x = g sin θ-fu 2 /h where f is an empirical constant of bed friction and g is the gravitational con-stant. Determine the characteristics. 3. The following equation describes the time evolution of the momentum distribu-tion function, W ( p,t ), in the theory of Brownian motion: W t = ( pW ) p + W pp Consider an initial value problem, where W ( p, 0) = f ( p ) is a prescribed initial velocity distribution function for-∞ < p < ∞ . Adopting the boundary con-ditions at inﬁnity W, W p → 0 for p → ±∞ , solve this equation by ﬁrst Fourier transforming over p to reduce the order of the PDE, then applying the method of characteristics, and ﬁnally back-transforming. 4. Prepare solutions to the following problems in your RHB text: 18.8, 18.9, 18.10....
View Full Document
- Fall '10
- Chemical Engineering, Boundary value problem, Department of Chemical Engineering, Glenn Fredrickson, constant reference values