/sci/ - Science & Math

>>11318933
Yes, you are supposed to use Bernoulli. We will take z_1=0 and p_1=101 kPa. From Bernoulli's principle,
[eqn] \frac{p_1}{\rho}+\frac{v_1^2}{2}=\frac{p_c}{\rho}+\frac{v_c^2}{2}+z_cg [/eqn]
Notice that because the container is very large in comparison to the pipe, v_1 is about zero. Also, because both points 1 and c are exposed to the atmosphere, they cancel out. Rearrange to get
[eqn] v_1=\sqrt{-2z_cg}=3.13\text{ m/s} [/eqn]
The next step is important. Realize that because of the implicit assumption that the fluid is incompressible we have it that [math] v_h=v_c [/math]. Also realize that *we cannot have a vacuum* at the apex of the pipe. So [math] p_h>0 [/math]. Apply Bernoulli again:
[eqn] \frac{p_h}{\rho}+\frac{v_h^2}{2}+hg=\frac{p_c}{\rho}+\frac{v_c^2}{2}+z_cg [/eqn]
Cancel the velocity terms and rearrange into an inequality:
[eqn] p_h=p_c+\rho z_cg-\rho hg>0\implies h<\frac{p_c}{\rho g}+z_c=15.1\text{ m} [/eqn]
>Is there any way of doing the 1st one without that assumption i made?
Not unless they give you the dimensions of the tank. And even then, it is very fucky and you will end up with a (non-linear?) differential equation since the pressures and linear head changes with time.

>>10747334
>Why don't scissor jacks implode under the weight of what they are supporting?
Basically because steel is very strong under tension. Suppose we lift a car with weight W and the angle between the top two struts is a. We find that the tensile force on the screw is F=W*tan(a/2). Regular, cold-drawn steel has a yield strength of 53700 psi; with a 1/4" screw, we get the maximum tensile load to be about 2600 lbs. Thus we want F=W*tan(a/2)<2600 lbs. We specify the load we wish to jack, W, and find the angle a that the jack can operate at. But this is only the normal stress in the screw. There is also shear stresses on the threads, which is dependent on geometry like the thread count and pitch, and the a quantity called the tensile stress area (which is an empirical formula).
>It seems like, no matter how much weight this type of jack is supporting, the screw will never turn backwards and fly out of the mechanism?
Because friction holds the screw in place and mechanical advantage. Think of an inclined plane with a very shallow angle to the ground. You push down on the plane and it goes nowhere because of static friction. Now imagine an inclined plane with a large angle. You push down on it, and because of the angle of the surface, your push is broken into a component that is parallel to the ground and is capable of overcoming that friction.

>>10690668
>Sum of all positive integers.......is equal to -1/12
said numberphile, and numberphile is wrong. lrn2 complex analysis. The sum of positive integers is divergence and all proper mathematicians agree on this.
>imaginary numbers
are just as "real" as real numbers. you can have imaginary current, imaginary voltage, imaginary fluid potential flow, etc, and it is all physically meaningful.
>proof by contradiction
Look up "modus tollens". Draw a truth table and prove that it works for yourself.
>infinitesimals
aren't numbers

The answer can be whatever you want it to be because option A. and B. both violate conservation of energy, momentum, violate causality, etc. Neither one makes any more sense than the other, and anyone who strongly feels that one of these is the "best" answer needs to gb2 >>>/v/
>okay so what does the source engine do about this
IIRC, the source engine isn't even consistent if it picks A or B. Portals don't exist on moving surfaces, except in that one part of the second game. The only reason for that is limitations with source, and they had to work around for that part in question so the portals don't even behave how they normally do.
>>10521363
>>10521674
/thread

>>10441605
It's rude to torment the autistic, anon

We already have a thread for this.