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 $\Delta P_1 = Q R = \frac{P}{17}$.

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

Water is conveyed through a uniform tube of $8 \text{ cm}$ in diameter and $3140 \text{ m}$ in length at the rate of $2 \times 10^{-3} \text{ m}^3/\text{s}$. The pressure required to maintain the flow is (Viscosity of water $= 10^{-3} \text{ SI units}$):

What is critical velocity? Write its equation.

In the case of a liquid, if the Reynolds number '$R_n$' is $1450$, then the flow of the liquid will

$A$ 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 ......... $\%$

Which of the following quantities has the dimensions of $\frac{\pi P r^4}{8 Q l}$? (Where $P =$ pressure,$r =$ radius,$Q =$ volume flow rate in $m^3/s$,and $l =$ length.)

Vedclass Test Series

Exam Paper Generator

Online Exam Module