(B) According to Poiseuille's law,the volume flow rate $V$ is given by $V = \frac{P}{R}$,where $R$ is the fluid resistance.Resistance $R$ is given by

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(B) According to Poiseuille's law,the volume flow rate $V$ is given by $V = \frac{P}{R}$,where $R$ is the fluid resistance.Resistance $R$ is given by $R = \frac{8\eta l}{\pi r^4}$.For the first tube,$R = \frac{8\eta l}{\pi r^4}$.For the second tube with radius $r' = \frac{r}{2}$,the resistance $R'$ is:$R' = \frac{8\eta l}{\pi (r/2)^4} = \frac{8\eta l}{\pi r^4} \times 16 = 16R$.When connected in series,the total resistance $R_{total} = R + R' = R + 16R = 17R$.The new volume flow rate $V_{new}$ is:$V_{new} = \frac{P}{R_{total}} = \frac{P}{17R} = \frac{V}{17}$.

Class 11 Physics Fluid Mechanics and Surface Tension Reynold's Number and Poiseuille's Equation

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$A$ capillary tube of length $l$ and radius $r$ is connected to the bottom of a container. When the pressure difference across it is $P$,the volume of water flowing out per second is $V$. If another capillary tube of the same length but half the radius is connected in series with the first one,what will be the new volume of liquid flowing out per second? (The total pressure difference across the system is $P$.)

A
$\frac{V}{16}$
B
$\frac{V}{17}$
C
$\frac{16V}{17}$
D
$\frac{17V}{16}$

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Class 11

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Chapter

Fluid Mechanics and Surface Tension

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Reynold's Number and Poiseuille's Equation

$A$ capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by $10\%$,then the rate of flow of liquid will change nearly by ......... $\%$

Medium

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Range of Reynolds number are given in Column - $I$ and types of flow are given in Column - $II$. Match them appropriately.

Column - $I$ Column - $II$

$(a)$ $R_e > 2000$ $(i)$ Streamline

$(b)$ $1000 < R_e < 2000$ $(ii)$ Turbulent

$(iii)$ Unsteady

Column - $I$	Column - $II$
$(a)$ $R_e > 2000$	$(i)$ Streamline
$(b)$ $1000 < R_e < 2000$	$(ii)$ Turbulent
	$(iii)$ Unsteady

Easy

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What is the value of Reynolds number for streamline flow?

Medium

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Consider an increase of $1 \%$ in each of the radius of the artery,the viscosity of blood,and the density of blood,respectively. The percentage change in the flow rate of blood in the artery is (in $\%$)

MediumTS EAMCET 2022

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$A$ horizontal pipeline carrying gasoline has a cross-sectional diameter of $5 \,mm$. If the viscosity and density of the gasoline are $6 \times 10^{-3} \,Poise$ and $720 \,kg/m^3$ respectively,the velocity after which the flow becomes turbulent is:

MediumTS EAMCET 2017

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$A$ capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by $10\%$,then the rate of flow of liquid will change nearly by ......... $\%$

Range of Reynolds number are given in Column - $I$ and types of flow are given in Column - $II$. Match them appropriately. Column - $I$ Column - $II$ $(a)$ $R_e > 2000$ $(i)$ Streamline $(b)$ $1000 < R_e < 2000$ $(ii)$ Turbulent $(iii)$ Unsteady

What is the value of Reynolds number for streamline flow?

Consider an increase of $1 \%$ in each of the radius of the artery,the viscosity of blood,and the density of blood,respectively. The percentage change in the flow rate of blood in the artery is (in $\%$)

$A$ horizontal pipeline carrying gasoline has a cross-sectional diameter of $5 \,mm$. If the viscosity and density of the gasoline are $6 \times 10^{-3} \,Poise$ and $720 \,kg/m^3$ respectively,the velocity after which the flow becomes turbulent is:

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Range of Reynolds number are given in Column - $I$ and types of flow are given in Column - $II$. Match them appropriately.

Column - $I$ Column - $II$

$(a)$ $R_e > 2000$ $(i)$ Streamline

$(b)$ $1000 < R_e < 2000$ $(ii)$ Turbulent

$(iii)$ Unsteady