An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are <math> <mn>6.4</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> and <math> <mn>4.8</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

Using equation of continuity A 1 V 1 = A 2 V 2 V 1 V 2 = A 2 A 1 = d 2 d 1 2 = 4.8 6.4 2 = 9 16 <!- [endif]-><!- [endif]->

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are <math> <mn>6.4</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> and <math> <mn>4.8</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Physics Class 11th Physics Mechanical Properties of Fluids

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4 c m$ and $4.8 c m$ , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

Option 1 -

$\frac{3}{4}$

Option 2 -

$\frac{81}{256}$

Option 3 -

$\frac{\sqrt[]{3}}{2}$

Option 4 -

$\frac{9}{16}$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

Using equation of continuity

$\begin{array}{r} A_{1} V_{1} = A_{2} V_{2} \\ \frac{V_{1}}{V_{2}} = \frac{A_{2}}{A_{1}} = {(\frac{d_{2}}{d_{1}})}^{2} = {(\frac{4.8}{6.4})}^{2} = \frac{9}{16} \end{array}$

Using equation of continuity <math> <mtable columnalign="right"> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <msub> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <msup> <mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>4.8</mn> </mrow> </mrow> <mrow> <mrow> <mn>6.4</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>9</mn> </mrow> </mrow> <mrow> <mrow> <mn>16</mn> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </math> <!- [endif]-><!- [endif]->

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An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4 c m$ and $4.8 c m$ , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

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An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 c m and 4.8 c m , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

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An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4 c m$ and $4.8 c m$ , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is