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Re: Hovercraft B/C

Posted: April 15th, 2018, 8:49 am
by photolithoautotroph
Sorry for the wait, had to grind to keep my GPA afloat for the past few days.
What is the optimal angle for a projectile to be launched at to maximize range? height? time?

Re: Hovercraft B/C

Posted: April 15th, 2018, 10:25 am
by Tesel
The range equation is [math]R = \frac{v_0^2}{g}sin(2\Theta)[/math]. Thus, to maximize range, we need to get the maximum value of [math]sin(2\Theta) = 1[/math]. The resulting angle is 45 degrees.
For height and time, the angle should be 90 degrees. Both of these are based on the initial vertical velocity; the maximum vertical velocity occurs when all initial velocity is in the vertical direction.

Re: Hovercraft B/C

Posted: April 15th, 2018, 11:11 am
by photolithoautotroph
Correct, your turn.

Re: Hovercraft B/C

Posted: April 19th, 2018, 7:46 am
by Tesel
Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

Re: Hovercraft B/C

Posted: April 19th, 2018, 12:32 pm
by UTF-8 U+6211 U+662F
Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?

Re: Hovercraft B/C

Posted: April 19th, 2018, 12:39 pm
by photolithoautotroph
Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?
I haven't done enough fluid dynamics to be sure, but I can guess: for an ideal fluid the flow rate would change to 4Q (Q=Av) and for a non-ideal, viscous fluid, the flow rate would change to 16Q (Poiseuille's Law)? Less sure about the second one but either could be wrong. At least I don't actually have to do this for real.

Re: Hovercraft B/C

Posted: April 19th, 2018, 7:52 pm
by Tesel
Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?
I haven't done enough fluid dynamics to be sure, but I can guess: for an ideal fluid the flow rate would change to 4Q (Q=Av) and for a non-ideal, viscous fluid, the flow rate would change to 16Q (Poiseuille's Law)? Less sure about the second one but either could be wrong. At least I don't actually have to do this for real.
I should have clarified the question a lot better.
But yes, you made the right assumptions, and that was the correct use of Poiseuille's Law. Correct!

Re: Hovercraft B/C

Posted: May 1st, 2018, 10:19 am
by CMS AC
Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?
I haven't done enough fluid dynamics to be sure, but I can guess: for an ideal fluid the flow rate would change to 4Q (Q=Av) and for a non-ideal, viscous fluid, the flow rate would change to 16Q (Poiseuille's Law)? Less sure about the second one but either could be wrong. At least I don't actually have to do this for real.
Next question, please.

Re: Hovercraft B/C

Posted: May 3rd, 2018, 4:19 pm
by photolithoautotroph
If nobody posts a question in this long, you can.
Derive a formula for the acceleration of the blocks in a real atwood machine with two masses of mass [math]m1[/math] and [math]m2[/math]and a pulley in the shape of a uniform disk of mass [math]M[/math] and radius [math]r[/math]. The string is massless. Ignore friction.

Re: Hovercraft B/C

Posted: May 3rd, 2018, 4:51 pm
by IvanGe
If nobody posts a question in this long, you can.
Derive a formula for the acceleration of the blocks in a real atwood machine with two masses of mass [math]m1[/math] and [math]m2[/math]and a pulley in the shape of a uniform disk of mass [math]M[/math] and radius [math]r[/math]. The string is massless. Ignore friction.
a = m1g - m2g / m1+ m2