# Recent content by ganondorf29

Homework Statement [/B] Given the dyad formed by two arbitrary position vector fields, u and v, use indicial notation in Cartesian coordinates to prove: $$\nabla^2 ({\vec u \vec v}) = \vec v \nabla^2 {\vec u} + \vec u \nabla^2 {\vec v} + 2\nabla {\vec u} \cdot {(\nabla \vec v)}^T$$ Homework...
2. ### Stagnation Point flow

Homework Statement The motion described by the Eulerian velocity, v, is given as v = c(x1e1 - x2e2) is called stagnation point flow. How long will it take a particle traveling on a streamline to reach the stagnation point? Homework Equations The Attempt at a Solution I really...
3. ### Fluids Homework Problem

Homework Statement Let R, L, C, K be suitable dimensional constants. In a certain motion of a fluid, the mass density function ρ is given in the Eulerian description by ρ = R*(x1^2+L^2). Is the velocity field v1 = C/(R*(x1^2+L^2)) e1 a possible velocity field? Is v2 = K*exp(-x1/L)...
4. ### Question on Equivalent/Hydraulic Diameter

Homework Statement Hello, I have a question on how to calculate the equivalent/hydraulic diameter for a problem that I'm doing. The problem states that I should use the cross-sectional flow area shown with an equivalent diameter based upon a closed rectangle (entire perimeter)...
5. ### Heat Transfer in 1D

Homework Statement A bare slab fuel element is 0.2 in thick. It has a kf = 10 Btu/(hr*ft*F) and a q''' = 5e7 Btu/(hr*ft^3). At x=0 (left hand face), h_lhs = 400 Btu/(hr*ft^2*F) with a fluid temp of 700F. At x=0.2 in (right hand face) the heat transfer coefficient is h_rhs = 300 Btu/(hr*ft*F)...
6. ### Second Moment of Area

Homework Statement I'm having a problem calculating the I value for this beam. I'm not sure on how to account for the missing circle in the front square and how to account for the beam changing from a 1" x 1" square to a 5" x 0.5" beam Homework Equations Ixx = bh^12/12 The...
7. ### Shaft Problem

Homework Statement I'm supposed to design and analyze a shaft including all features to retain the shaft in the bearings and attach the coupling and sheave and the shaft shouldn't fail in static loading or through fatigue. Homework Equations3 -The flexible coupling attaches your shaft to the...
8. ### Pressurizer Problem

Homework Statement A pressurizer is designed to accommodate an outsurge of 30,800 lbm and an insurge of 20900 lbm. The mass of the water necessary to cover the electric heaters is 4020 lbm. The system's operating pressure is 2250 psia. The hot leg is 600F and and the cold leg is 550F (For the...
9. ### Using Matlab - plotting frequency responses

Does this help at all? http://www.mathworks.com/help/toolbox/signal/freqz.html [Broken]
10. ### Fourier Series

Homework Statement f(t) is given as: from 0 to 0.2s, f(t) = 5 from 0.2s to 0.6s, f(t) = 0 from 0.6s to 0.8s, f(t) = 5, etc Homework Equations for an odd function a0 = 2/p * integral(from -p/2 to p/2) of f(t) dt bn = 4/p * integral(from 0 to p/2) of f(t)*sin(2*pi*n*t/p) dt The Attempt at...
11. ### Convolution Integral

Homework Statement x'' + 2\zeta \omega_{n} x' + \omega_{n}^2 x = u_{s}(t) zeta is underdamped and u_{s}(t) is the unit step function and \omega_n is the natural frequency and there are zero initial conditions. Find the total response via the convolution integral. Homework...
12. ### Linear Algebra - Eigenvectors

For A-5I x1 = x3 x2 = x3 so [1;1;1] is the eigenvector for \lambda = 5 [2,1,2;2,1,2;2,1,2] * [1;1;1] = [5;5;5] But I'm still not sure how to find the eigenvectors for A-0I
13. ### Linear Algebra - Eigenvectors

Homework Statement A = [2,1,2;2,1,2;2,1,2] Find the Eigenvectors of A Homework Equations The Attempt at a Solution First I found the eigenvalues of A det(A - \lambda I) = 0 \lambda = 0,5 __________________________________________ A-5I...
14. ### Material Indices

I'm currently doing a project in my materials class and I wanted to check if these two material indices were right. The objectives are: 1. The material must not fracture 2. The material must be strong (no deformations) Material Index 1 ------------------------ Considering a yield-before-break...
15. ### Convergence of a series

Homework Statement Find the radius of convergence and the interval of convergence for \sum_{n=0}^\infty \frac{x^n}{n3^n} Homework Equations The Attempt at a Solution Ok, so I first applied the ratio test. \lim_{n\rightarrow\infty} | \frac{x^{n+1}}{(n+1)3^(n+1)} / \frac{x^n}{n3^n} |...