Two tubes of radii r_1 and r_2,and lengths l_ | vedclass

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Question

(D) For a liquid flowing through tubes in series under streamline conditions,the rate of flow of liquid $(V)$ remains constant through both tubes.Acco

Vedclass · Accepted Answer

$\frac{r_1}{2}$

Vedclass · Answer

(D) For a liquid flowing through tubes in series under streamline conditions,the rate of flow of liquid $(V)$ remains constant through both tubes.According to Poiseuille's equation,the rate of flow is given by $V = \frac{\pi P r^4}{8 \eta l}$.Since $V_1 = V_2$,we have:$\frac{\pi P_1 r_1^4}{8 \eta l_1} = \frac{\pi P_2 r_2^4}{8 \eta l_2}$Simplifying the expression,we get:$\frac{P_1 r_1^4}{l_1} = \frac{P_2 r_2^4}{l_2}$Given that $P_2 = 4P_1$ and $l_2 = \frac{l_1}{4}$,substitute these values into the equation:$\frac{P_1 r_1^4}{l_1} = \frac{(4P_1) r_2^4}{l_1 / 4}$$\frac{P_1 r_1^4}{l_1} = \frac{16 P_1 r_2^4}{l_1}$$r_1^4 = 16 r_2^4$Taking the fourth root on both sides:$r_1 = 2 r_2$Therefore,$r_2 = \frac{r_1}{2}$.

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

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

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

What will be the nature of flow of water from a circular tap,when its flow rate increases from $0.18\, L/min$ to $0.48\, L/min$? The radius of the tap is $0.5\, cm$ and the viscosity of water is $10^{-3}\, Pa\cdot s$. (Density of water: $10^{3}\, kg/m^{3}$)

$Assertion :$ For Reynolds number $Re > 2000$, the flow of fluid is turbulent.
$Reason :$ Inertial forces are dominant compared to the viscous forces at such high Reynolds numbers.

What is the value of the Reynolds number $(R_e)$ for unsteady flow?

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