Getting the rate of drain from a tank [closed]

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A tank with a top radius of 1m, a bottom radius of 0.5m and a height of 2m is initially filled with water. Water drains through a square hole of side 3cm in the bottom.

How do I get the rate of drain,
begin{equation}
frac{partial V}{partial t}
end{equation}
of the tank?

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

closed as off-topic by Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz Nov 25 at 9:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz

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up vote
0
down vote

favorite

A tank with a top radius of 1m, a bottom radius of 0.5m and a height of 2m is initially filled with water. Water drains through a square hole of side 3cm in the bottom.

How do I get the rate of drain,
begin{equation}
frac{partial V}{partial t}
end{equation}
of the tank?

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

closed as off-topic by Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz Nov 25 at 9:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

up vote
0
down vote

favorite

A tank with a top radius of 1m, a bottom radius of 0.5m and a height of 2m is initially filled with water. Water drains through a square hole of side 3cm in the bottom.

How do I get the rate of drain,
begin{equation}
frac{partial V}{partial t}
end{equation}
of the tank?

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

A tank with a top radius of 1m, a bottom radius of 0.5m and a height of 2m is initially filled with water. Water drains through a square hole of side 3cm in the bottom.

How do I get the rate of drain,
begin{equation}
frac{partial V}{partial t}
end{equation}
of the tank?

calculus

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

asked Nov 25 at 6:24

Gabriel Henry J. Lopez

closed as off-topic by Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz Nov 25 at 9:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz Nov 25 at 9:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Jyrki Lahtonen, Leucippus, José Carlos Santos, Mostafa Ayaz

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment |

1 Answer
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0
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Conservation of mass and constant density tells us change in volume in the tank equals change in volume out of tank.

Thinking area times velocity gives you rate of volume change out of tank, by dimensional analysis.

Bernouli s principle says

$frac{1}{2}v^2=gh$

$v=sqrt{2gh}$

Area=side length of square hole squared.

Keep in mind h varies with time.

Volume in tank:
$V=frac{pi}{3}(h+2)(r_1+frac{h(r_2-r_1)}{2})^2-frac{pi}{3}2r_1^2$

So :

$Asqrt{2gh}=frac{dV}{dt}$

Will give you a differential equation in h as function of t.

Insert back into expression for V to get it as function of t. Differentiate to find alternative expression for derivative.

edited Nov 25 at 7:31

answered Nov 25 at 6:53

TurlocTheRed

798211

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

up vote
0
down vote

accepted

Conservation of mass and constant density tells us change in volume in the tank equals change in volume out of tank.

Thinking area times velocity gives you rate of volume change out of tank, by dimensional analysis.

Bernouli s principle says

$frac{1}{2}v^2=gh$

$v=sqrt{2gh}$

Area=side length of square hole squared.

Keep in mind h varies with time.

Volume in tank:
$V=frac{pi}{3}(h+2)(r_1+frac{h(r_2-r_1)}{2})^2-frac{pi}{3}2r_1^2$

So :

$Asqrt{2gh}=frac{dV}{dt}$

Will give you a differential equation in h as function of t.

Insert back into expression for V to get it as function of t. Differentiate to find alternative expression for derivative.

edited Nov 25 at 7:31

answered Nov 25 at 6:53

TurlocTheRed

798211

add a comment |

up vote
0
down vote

accepted

Conservation of mass and constant density tells us change in volume in the tank equals change in volume out of tank.

Thinking area times velocity gives you rate of volume change out of tank, by dimensional analysis.

Bernouli s principle says

$frac{1}{2}v^2=gh$

$v=sqrt{2gh}$

Area=side length of square hole squared.

Keep in mind h varies with time.

Volume in tank:
$V=frac{pi}{3}(h+2)(r_1+frac{h(r_2-r_1)}{2})^2-frac{pi}{3}2r_1^2$

So :

$Asqrt{2gh}=frac{dV}{dt}$

Will give you a differential equation in h as function of t.

Insert back into expression for V to get it as function of t. Differentiate to find alternative expression for derivative.

edited Nov 25 at 7:31

answered Nov 25 at 6:53

TurlocTheRed

798211

add a comment |

up vote
0
down vote

accepted

Conservation of mass and constant density tells us change in volume in the tank equals change in volume out of tank.

Thinking area times velocity gives you rate of volume change out of tank, by dimensional analysis.

Bernouli s principle says

$frac{1}{2}v^2=gh$

$v=sqrt{2gh}$

Area=side length of square hole squared.

Keep in mind h varies with time.

Volume in tank:
$V=frac{pi}{3}(h+2)(r_1+frac{h(r_2-r_1)}{2})^2-frac{pi}{3}2r_1^2$

So :

$Asqrt{2gh}=frac{dV}{dt}$

Will give you a differential equation in h as function of t.

Insert back into expression for V to get it as function of t. Differentiate to find alternative expression for derivative.

edited Nov 25 at 7:31

answered Nov 25 at 6:53

TurlocTheRed

798211

Conservation of mass and constant density tells us change in volume in the tank equals change in volume out of tank.

Thinking area times velocity gives you rate of volume change out of tank, by dimensional analysis.

Bernouli s principle says

$frac{1}{2}v^2=gh$

$v=sqrt{2gh}$

Area=side length of square hole squared.

Keep in mind h varies with time.

Volume in tank:
$V=frac{pi}{3}(h+2)(r_1+frac{h(r_2-r_1)}{2})^2-frac{pi}{3}2r_1^2$

So :

$Asqrt{2gh}=frac{dV}{dt}$

Will give you a differential equation in h as function of t.

Insert back into expression for V to get it as function of t. Differentiate to find alternative expression for derivative.

edited Nov 25 at 7:31

answered Nov 25 at 6:53

TurlocTheRed

798211

edited Nov 25 at 7:31

answered Nov 25 at 6:53

TurlocTheRed

798211

answered Nov 25 at 6:53

TurlocTheRed

798211

answered Nov 25 at 6:53

TurlocTheRed

798211

add a comment |

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