PrepFE™

Explanation:

Refer to Fluid Flow Characterization section in the Fluid Mechanics chapter of the FE Reference Handbook.

We know that flow in laminar flow conditions has a triangular distribution where the fluid is moving the fastest at the center of the pipe and moving the slowest near the borders of the pipe. For laminar flow in circular pipe conditions, one can calculate what the fluid velocity is anywhere along the pipe radius via: $$ v(r) = v_{max}\left[1-\left(\frac{r}{R}\right)^2\right] $$ where
$v_{max} = 2\bar{v}=2(2.5\si{m/s})=5\si{m/s}$
$R=\text{radius of the tube}=1\si{m}/2=0.5\si{m}$
$r=\text{distance from the centerline}=0.5\si{m}-(10\si{cm}/100)=0.4\si{m}$ $$ v(0.4\si{m}) = 5\si{m/s}\left[1-\left(\frac{0.4\si{m}}{0.5\si{m}}\right)^2\right] \\ v(0.4\si{m})=1.8\si{m/s} $$ Therefore, the fluid velocity 10 cm off the pipe border is 1.8 m/s

Explanation:

Due to the large liquid to gas expansion that takes place upon evaporation, liquid nitrogen is capable of displacing sufficient oxygen to create an oxygen deficient environment in a small or insufficiently ventilated space, leading to the risk of asphyxiation.

Explanation:

In order to find the roots of an equation, first set $f(x)$ to 0. $$ x^2 -4x - 3 = 0 $$ For simple equations, you can factor them by hand, but this equation does not factor easily. 3 can be factored into 1 and 3. However, one must be negative and one positive for their multiple to be -3. There is no way to sum those to get -4. Not to worry, you can always use the quadratic formula (a.k.a. the quadratic equation) if the equation can't be factored easily or if you are unsure. A quadratic equation is of the form: $$ ax^2+bx+c =0 $$ So we have $a=1$, $b=-4$, and $c=-3$. The quadratic formula is: $$ x = \frac{-b\,±\,\sqrt{b^2-4ac}}{2a} \\ = \frac{-(-4)\,±\,\sqrt{(-4)^2-4(1)(-3)}}{2(1)} \\ = \frac{4\,±\,\sqrt{28}}{2} \\ = \frac{4\,±\,2\sqrt{7}}{2} \\ = 2\,±\,\sqrt{7} $$ The equation is satisfied when $x=2+\sqrt{7}$ or $2-\sqrt{7}$.

Explanation:

The goal of sludge dewatering is to increase the solids concentration. The higher the cake solids, the lower the operating cost for hauling. Most cake is hauled according to a cost per wet ton basis.

Explanation:

Refer to the Polymers section in the Materials Science/Structure of Matter chapter of the FE Reference Handbook.

Plastics (or polymers) are generally organic compounds based upon carbon and hydrogen. They are very large molecular structures. Usually they are low density and are not stable at high temperatures. They can be readily formed into complex shapes. Their strength, stiffness, and melting temperatures are generally much lower than those of metals and ceramics. Their light weight, low cost, and ease of forming make them the preferred material for many engineering applications.