Recent content by Appa

Hiah, I've got a question concerning a t-pipe configuration and the corresponding friction coefficient values because there are two different friction coefficients stated in literature. Let's assume we have a simple t-pipe where the main passage is larger than the side branch. The friction...

Hey all, I'd need help with determining the pressure loss over an orifice in a pipe. I have an equation for the friction factor so no problem there, and I know the Reynold's number as well. What confuses me is choosing the suitable velocity for the pressure drop equation; \frac{Δp}{ΔL} =...

I'm having trouble with understanding how to calculate a wall thickness change in a hollow cylinder unde axial loading. The length, outside diameter and initial wall thickness are given as well as the size of the load, Young's modulus and Poisson's ratio. I guess this isn't really a hard...

I'm having trouble working my way through a MATLAB problem. How can I solve a matrix equation for four different variables? Here is my input: (I know all variables except I1 through I4) V = [(R1*I1 -j*(1/(omega*C1))*(I1-I2) +j*omega*L2*(I1-I3)-E1); (-j*(1/(omega*C1))*(I2-I1)...

I'm having a lot of trouble with an adiabatic mixing process. This is what I know: There's an airstream coming from outside and its temperature is T1=5 'C, its relative humidity being \varphi1= 90% at a rate of 20 m3/min. Another airstream is coming from inside and its temperature is T2= 25...

Homework Statement Suppose that the mapping F:Rn\rightarrowRm is continuously differentiable and that there is a fixed mxn matrix A so that DF(x)=A for every x in Rn. Prove that then F is a mapping such that F(x)=Ax+c for some c\inRm Homework Equations DF(x)ij=...

Homework Statement Let A be a subset of Rn and let \vec{w} be a point in Rn. Show that A is open if and only if A + \vec{w} is open. Show that A is closed if and only if A + \vec{w} is closed. Homework Equations The translate of A by \vec{w} is defined by A + \vec{w} := {\vec{w} +...

Homework Statement The sequence fn: [-1,1] -> R, fn(x)= nxe-nx2 converges pointwise to f(x)= 0, x in [-1,1]. Can you verify the following: limn->\infty (\int^{1}_{0}fn(x)dx) = \int^{1}_{0} (limn->\infty fn(x))dx Homework Equations Theorem: If fn is continuous on the interval D for every...

Homework Statement d/dx (\int^{x}_{0} x2t2dt) So the problem is to solve the derivative of the integral \int x2t2dt from 0 to x. Homework Equations d/dx (\int^{x}_{a} f(t)dt) = f(x) The Attempt at a Solution I'm really unsure of how this should be computed but this was my guess...

Now I was able to compute the series \Sigma\stackrel{\infty}{k=1} (\sqrt{k+1} - \sqrt{k})/k to \Sigma\stackrel{\infty}{k=1} 1/k(\sqrt{k+1} + \sqrt{k}). And from there I was able to tell that 1/k(\sqrt{k+1} + \sqrt{k}) < 1/k(2\sqrt{k}) . And because \Sigma\stackrel{\infty}{k=1} 1/k(2\sqrt{k})...

Homework Statement Is the series \Sigma\stackrel{\infty}{k=1} (\sqrt{k+1} - \sqrt{k})/k convergent or divergent? Homework Equations The Comparison Test: 0<=ak<=bk 1.The series \Sigma\stackrel{\infty}{k=1} ak converges if the series \Sigma\stackrel{\infty}{k=1} bk converges. 2. The...

Doesn't that only show that the sequence of terms converges? And that's not a sufficient condition for the series to converge too... To show that the series converges, shouldn't you show that the sequence of partial sums converges, i.e. it is bounded? I'm not sure how to do that in this case...

Yeah, sorry, I got it myself pretty soon after posting this. It feels like the more I study maths, the more I forget..!

Homework Statement I should find this integral: \intb x(1/\Pi)(1/(1+x2)dx -b Homework Equations \int1/(1+x2)dx = arctan(x) The Attempt at a Solution The Only thing I've succeeded in doing is to take the 1/\Pi and put it in front of the integral like this: (1/\Pi)\intb (x/(1+x2)dx...

I gratuated from the Finnish upper secondary last spring and applied to the Tampere University of Technology without a clue of what I wanted to study and ended up as an architect student. During the first couple of weeks I realized that I was in the completely wrong place and I'm definitely...