A community for students.
Here's the question you clicked on:
 0 viewing
across
 2 years ago
Let's do some cool math:
A tank in the form of a rightcircular cylinder standing on end is leaking water through a circular hole in its bottom. Suppose the tank is \(10\) feet in height and has radius \(2\) feet and the circular hole has radius \(1/2\) inch. If the tank is initially full, how long will it take to empty?
Whoever gets this right first gets a cookie.
across
 2 years ago
Let's do some cool math: A tank in the form of a rightcircular cylinder standing on end is leaking water through a circular hole in its bottom. Suppose the tank is \(10\) feet in height and has radius \(2\) feet and the circular hole has radius \(1/2\) inch. If the tank is initially full, how long will it take to empty? Whoever gets this right first gets a cookie.

This Question is Closed

across
 2 years ago
Best ResponseYou've already chosen the best response.0Hint 1: Torricelli's law states that\[v=\sqrt{2gh},\]where \(v\) is the speed of the water leaving at the bottom of a tank of height \(h\). \(g\) stands for the acceleration due to gravity, as usual.

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1I really want to work this out... but, unless I'm missing something, using Bernoulli's, it'd take too long, and I don't think I have the attention span...

across
 2 years ago
Best ResponseYou've already chosen the best response.0@Algebraic!, how did you get that? ;P

across
 2 years ago
Best ResponseYou've already chosen the best response.0That's not a valid explanation! ;O

sara12345
 2 years ago
Best ResponseYou've already chosen the best response.0idk differential equations, but i can try setting up one :p

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, I forgot about Torricelli's law... I had started trying to derive it from Bernoulli's and was like... nope.

sara12345
 2 years ago
Best ResponseYou've already chosen the best response.0flowrate outside = \(\pi (1/2)^2\sqrt{2gh} \) cubic inch per sec

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1using this differential equation : dh/dt = Ah/Aw sqrt (2gh) take g= 32 ft/s^2 Ah=Area of hole , Aw is area of water ,so Aw/Ah = 576 so (h^(1/2))dh = (8/576)dt so 2 (sqrt h) = (8/576) t put h= 10 to get t = 30.36 minutes.

across
 2 years ago
Best ResponseYou've already chosen the best response.0You guys are right. The answer is roughly \(30\) minutes. I guess I'll have to start posting Millennium Prize problems. That way, you guys will take at least five minutes longer to answer correctly. ;P

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1I mean, it's not hard to compute, just a bunch of numbers and converting feet to metres. So, converting everything, we get the very 'elegant' expressions of: \[ f_\text{rate}=(0.0127)^2\pi\sqrt{2\cdot3.048g}\approx0.003918\text{ m}^3/\text{s}\\ vf_\text{rate}\approx30.275\text{ mins.} \]

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1I meant: \[ \frac{v}{f_\text{rate}} \]... oops.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.