## Hovercraft B/C

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### Re: Hovercraft B/C

What is the difference between turbulent and laminar flow? How does Reynold's number pertain to these concepts? What value (or range of values) distinguishes between turbulent and laminar flow?
In laminar flow, the molecules in the fluid are assumed to not cross over each other's paths, i.e. not have turbulence. Reynold's number relates to the speed at which a fluid is no longer reasonably considered laminar. When Re < 2300, laminar flow occurs, and when Re > 2600, turbulent flow occurs.

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### Re: Hovercraft B/C

What is the difference between turbulent and laminar flow? How does Reynold's number pertain to these concepts? What value (or range of values) distinguishes between turbulent and laminar flow?
In laminar flow, the molecules in the fluid are assumed to not cross over each other's paths, i.e. not have turbulence. Reynold's number relates to the speed at which a fluid is no longer reasonably considered laminar. When Re < 2300, laminar flow occurs, and when Re > 2600, turbulent flow occurs.
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### Re: Hovercraft B/C

What was the original formulation of Newton's Second Law that takes into account changes in mass?

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### Re: Hovercraft B/C

What was the original formulation of Newton's Second Law that takes into account changes in mass?
$F=\frac{d(mv)}{dt}$

Interestingly, Newton was referring to momentum when formulating this law and not force  
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### Re: Hovercraft B/C

What was the original formulation of Newton's Second Law that takes into account changes in mass?
$F=\frac{d(mv)}{dt}$

Interestingly, Newton was referring to momentum when formulating this law and not force  

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### Re: Hovercraft B/C

What was the original formulation of Newton's Second Law that takes into account changes in mass?
$F=\frac{d(mv)}{dt}$

Interestingly, Newton was referring to momentum when formulating this law and not force  
A large cylindrical tank with height 10 meters and radius 2.5 meters is filled up entirely with water. A circular hole with a radius of 10 cm is punctured underneath the tank. Given that the top of the tank is open to the atmosphere, how long will it take for the entire volume of water to flow out of the tank (assuming no change in flow rate due to changing height?
Last edited by Justin72835 on March 12th, 2018, 8:44 pm, edited 1 time in total.
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### Re: Hovercraft B/C

$F=\frac{d(mv)}{dt}$

Interestingly, Newton was referring to momentum when formulating this law and not force  
A large cylindrical tank with height 10 meters and radius 2.5 meters is filled up entirely with water. A circular hole with a radius of 10 cm is punctured underneath the tank. Given that the top of the tank is open to the atmosphere, how long will it take for the entire volume of water to flow out of the tank?
$g(10 m) = \frac{v^2}{2}$
$v = \sqrt{g(5 m)}$
$\frac{V}{t} = \pi (0.1 m)^2 * \sqrt{g(5 m)}$
$\frac{\pi (2.5 m)^2(10 m)}{t} = \pi (0.1 m)^2 * \sqrt{g(5 m)}$
$t = \frac{\pi (2.5 m)^2(10 m)}{\pi (0.1 m)^2 * \sqrt{g(5 m)}} = \textbf{890 s}$

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### Re: Hovercraft B/C

A large cylindrical tank with height 10 meters and radius 2.5 meters is filled up entirely with water. A circular hole with a radius of 10 cm is punctured underneath the tank. Given that the top of the tank is open to the atmosphere, how long will it take for the entire volume of water to flow out of the tank?
$g(10 m) = \frac{v^2}{2}$
$v = \sqrt{g(5 m)}$
$\frac{V}{t} = \pi (0.1 m)^2 * \sqrt{g(5 m)}$
$\frac{\pi (2.5 m)^2(10 m)}{t} = \pi (0.1 m)^2 * \sqrt{g(5 m)}$
$t = \frac{\pi (2.5 m)^2(10 m)}{\pi (0.1 m)^2 * \sqrt{g(5 m)}} = \textbf{890 s}$
I got [b]446 seconds[/b], which is basically half your answer. With that said, I think you made a mistake in your second line. Since you're multiplying both sides by two, the expression underneath the square root is g(20m) instead of g(5m).

All your other work is correct though, so nice job! You can do the next one!
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### Re: Hovercraft B/C

Oh whoops, haha.
Find the final speed of a 100 kg roller coaster car that has dropped 50 m (from rest), gone back up 30 m, dropped 60 m, gone back up 30 m, and then at that level been pushed for 5 seconds with a force of 50 Newtons.

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### Re: Hovercraft B/C

Oh whoops, haha.
Find the final speed of a 100 kg roller coaster car that has dropped 50 m (from rest), gone back up 30 m, dropped 60 m, gone back up 30 m, and then at that level been pushed for 5 seconds with a force of 50 Newtons.
2.5 m/s
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