Two capillary tubes of same length each of 50 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to Poiseuille's equation,the resistance to fluid flow $R$ is given by $R = \frac{8 \eta l}{\pi r^4}$,where $\eta$ is the viscosity,$l$ i

Vedclass · Accepted Answer

$\frac{P}{17}$

Vedclass · Answer

(B) According to Poiseuille's equation,the resistance to fluid flow $R$ is given by $R = \frac{8 \eta l}{\pi r^4}$,where $\eta$ is the viscosity,$l$ is the length,and $r$ is the radius of the tube.Since the length $l$ and viscosity $\eta$ are the same for both tubes,we have $R \propto \frac{1}{r^4}$.Let $r_1 = 4 \ mm$ and $r_2 = 2 \ mm$. The ratio of resistances is $\frac{R_1}{R_2} = \left(\frac{r_2}{r_1}ight)^4 = \left(\frac{2}{4}ight)^4 = \left(\frac{1}{2}ight)^4 = \frac{1}{16}$.Thus,$R_2 = 16 R_1$. Let $R_1 = R$,then $R_2 = 16 R$.Since the tubes are connected in series,the same volume flow rate $Q$ passes through both. The pressure difference across each tube is $\Delta P = Q 	imes R$.For the first tube,$\Delta P_1 = Q 	imes R_1 = Q 	imes R$.For the second tube,$\Delta P_2 = Q 	imes R_2 = Q 	imes 16 R$.The total pressure difference is $P = \Delta P_1 + \Delta P_2 = Q R + 16 Q R = 17 Q R$.Therefore,$Q R = \frac{P}{17}$.The pressure difference across the first tube is $\Delta P_1 = Q R = \frac{P}{17}$.

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

Two capillary tubes of same length each of $50 \ cm$ but of different radii $4 \ mm$ and $2 \ mm$ are connected in series. When water flows,the pressure difference between the ends of the arrangement is $P$. Then the pressure difference between the ends of the first tube is

Similar Questions

What is critical speed in the context of fluid flow?

$A$ liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference $P$. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is

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

In Poiseuille's method for the determination of the coefficient of viscosity,the physical quantity that requires the greatest accuracy in measurement is:

Show that the Reynolds number is dimensionless.

Vedclass Test Series

Exam Paper Generator

Online Exam Module