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(D) According to Poiseuille's law, the volume flow rate $Q$ is given by:$Q = \frac{\pi \Delta P r^4}{8 L \eta}$where $r$ is the radius, $\eta$ is the

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(D) According to Poiseuille's law, the volume flow rate $Q$ is given by:$Q = \frac{\pi \Delta P r^4}{8 L \eta}$where $r$ is the radius, $\eta$ is the viscosity, and $\Delta P$ is the pressure difference.Since the flow rate $Q$ does not depend on the density of blood, the change in density does not affect the flow rate.Taking the logarithmic differentiation of the formula:$\frac{\Delta Q}{Q} = 4 \frac{\Delta r}{r} - \frac{\Delta \eta}{\eta}$Given that the radius $r$ increases by $1 \%$ $(\frac{\Delta r}{r} = 0.01)$ and the viscosity $\eta$ increases by $1 \%$ $(\frac{\Delta \eta}{\eta} = 0.01)$:$\frac{\Delta Q}{Q} = 4(0.01) - 0.01 = 0.04 - 0.01 = 0.03$Therefore, the percentage change in the flow rate is $0.03 	imes 100 = 3 \%$.

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

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 $\%$)

Similar Questions

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

The rate of flow of liquid in a tube of radius $r$ and length $l$,whose ends are maintained at a pressure difference $P$,is given by $V = \frac{\pi Q P r^4}{\eta l}$,where $\eta$ is the coefficient of viscosity. What is the value of $Q$?

The rate of flow of water in a capillary tube of length $\ell$ and radius $r$ is $V.$ The rate of flow in another capillary tube of length $2 \ell$ and radius $2 r$ for the same pressure difference would be $....V$

If $R_e > 2000$,then which type of flow exists? Explain.

If $R_e > 1000$,then which type of flow exists? Explain.

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