
A venturi meter is connected to two points in the mains where its radii are $20\,cm$ and $10\,cm$ . And the levels of the water column in the tubes differ by $10\,cm$. How much water flows through the pipe per minute?
Answer
408.6k+ views
Hint: In fluid mechanics, Venturimeter is a mechanical device which measures how much of fluid is flowing through a given time or we can say the rate of flow of a fluid through a pipe is measured by venturi meter and basically it measures in units of $litre{\min ^{ - 1}}$.
Complete step by step answer:
Let us suppose the area of first radii section which is $20\,cm$ is denoted by ${A_1} = \pi {(20)^2}\,c{m^2}$ and let the area of second radii section is denoted by ${A_2} = \pi {(10)^2}\,c{m^2}$
So now we have,
${A_1} = \pi {(20)^2}\,c{m^2}$
$\Rightarrow {A_2} = \pi {(10)^2}\,c{m^2}$
Acceleration due to gravity is $g = 980\,cm{\sec ^{ - 2}}$
And it’s given that the height up to which the water rises is $h = 10cm$
Volume flowing per second through the venturi meter is given by
$V = {A_1}{A_2}\sqrt {\dfrac{{2gh}}{{{A_1}^2 - {A_2}^2}}} $
In order to convert this flow of water in second to minutes and the cubic centimetres to litre,
Just multiply by $60$ we get,
$V = {A_1}{A_2}\sqrt {\dfrac{{2gh}}{{{A_1}^2 - {A_2}^2}}} \times 60\,litre\,{\min ^{ - 1}}$
Putting the values of all known parameters we will get:
$V = {(\dfrac{{22}}{7})^2}{(20)^2}{(10)^2}\sqrt {\dfrac{{2 \times 980 \times 10}}{{300(3.14)}}} \times 60litre{\min ^{ - 1}}$
$\Rightarrow V = {(\dfrac{{22}}{7})^2}2400000\sqrt {\dfrac{{19600}}{{942}}} litre{\min ^{ - 1}}$
$\therefore V = 2726.58\,litre\,{\min ^{ - 1}}$
Hence, the rate of flow of water measured by venturi meter in litres per minute is $V = 2726.58\,litre{\min ^{ - 1}}$.
Note: It should be remembered that, the basic units of conversions like: acceleration due to gravity is $g = 9.8m{\sec ^{ - 2}}$ into $g = 980cm{\sec ^{ - 2}}$ and litre is the most standard unit of volume which is used while measure large amount of fluids and its relation with cubic centimetre is given as $1litre = 1000c{m^3}$.
Complete step by step answer:
Let us suppose the area of first radii section which is $20\,cm$ is denoted by ${A_1} = \pi {(20)^2}\,c{m^2}$ and let the area of second radii section is denoted by ${A_2} = \pi {(10)^2}\,c{m^2}$
So now we have,
${A_1} = \pi {(20)^2}\,c{m^2}$
$\Rightarrow {A_2} = \pi {(10)^2}\,c{m^2}$
Acceleration due to gravity is $g = 980\,cm{\sec ^{ - 2}}$
And it’s given that the height up to which the water rises is $h = 10cm$
Volume flowing per second through the venturi meter is given by
$V = {A_1}{A_2}\sqrt {\dfrac{{2gh}}{{{A_1}^2 - {A_2}^2}}} $
In order to convert this flow of water in second to minutes and the cubic centimetres to litre,
Just multiply by $60$ we get,
$V = {A_1}{A_2}\sqrt {\dfrac{{2gh}}{{{A_1}^2 - {A_2}^2}}} \times 60\,litre\,{\min ^{ - 1}}$
Putting the values of all known parameters we will get:
$V = {(\dfrac{{22}}{7})^2}{(20)^2}{(10)^2}\sqrt {\dfrac{{2 \times 980 \times 10}}{{300(3.14)}}} \times 60litre{\min ^{ - 1}}$
$\Rightarrow V = {(\dfrac{{22}}{7})^2}2400000\sqrt {\dfrac{{19600}}{{942}}} litre{\min ^{ - 1}}$
$\therefore V = 2726.58\,litre\,{\min ^{ - 1}}$
Hence, the rate of flow of water measured by venturi meter in litres per minute is $V = 2726.58\,litre{\min ^{ - 1}}$.
Note: It should be remembered that, the basic units of conversions like: acceleration due to gravity is $g = 9.8m{\sec ^{ - 2}}$ into $g = 980cm{\sec ^{ - 2}}$ and litre is the most standard unit of volume which is used while measure large amount of fluids and its relation with cubic centimetre is given as $1litre = 1000c{m^3}$.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
10 examples of friction in our daily life

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Define least count of vernier callipers How do you class 11 physics CBSE

The combining capacity of an element is known as i class 11 chemistry CBSE
