Three capillaries of length L, L/2 and L/3 ar | vedclass

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

Question

(A) According to Poiseuille's equation,the rate of flow $Q$ is given by $Q = \frac{\pi P r^4}{8 \eta L}$.Since the capillaries are connected in series

Vedclass · Accepted Answer

The pressure difference across the ends of the second capillary is $8 P$.

Vedclass · Answer

(A) According to Poiseuille's equation,the rate of flow $Q$ is given by $Q = \frac{\pi P r^4}{8 \eta L}$.Since the capillaries are connected in series,the rate of flow $Q$ is the same for all three capillaries.Therefore,the pressure difference $\Delta P$ across a capillary is given by $\Delta P = Q \cdot \frac{8 \eta L}{\pi r^4} \propto \frac{L}{r^4}$.Let $P_1, P_2, P_3$ be the pressure differences across the first,second,and third capillaries respectively.Given $P_1 = P$,$L_1 = L, r_1 = r$.For the second capillary: $L_2 = L/2, r_2 = r/2$.$P_2 = P_1 \cdot \frac{L_2}{L_1} \cdot \left(\frac{r_1}{r_2}\right)^4 = P \cdot \frac{L/2}{L} \cdot \left(\frac{r}{r/2}\right)^4 = P \cdot \frac{1}{2} \cdot (2)^4 = P \cdot \frac{16}{2} = 8P$.For the third capillary: $L_3 = L/3, r_3 = r/3$.$P_3 = P_1 \cdot \frac{L_3}{L_1} \cdot \left(\frac{r_1}{r_3}\right)^4 = P \cdot \frac{L/3}{L} \cdot \left(\frac{r}{r/3}\right)^4 = P \cdot \frac{1}{3} \cdot (3)^4 = P \cdot \frac{81}{3} = 27P$.Thus,the pressure difference across the second capillary is $8P$.

Three capillaries of length $L, L/2$ and $L/3$ are connected in series. Their radii are $r, r/2$ and $r/3$ respectively. If stream-line flow is to be maintained and the pressure difference across the first capillary is $P$,then:

Similar Questions

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 $\%$)

$A$ capillary tube is connected to the bottom of a container. If its radius is increased by $10\%$,what is the percentage change in the rate of flow of the liquid (in $\%$)?

For which of the following Reynolds numbers is a flow considered streamlined (laminar)?

Water flows in a streamline manner through a capillary tube of radius $a$. The pressure difference is $P$ and the rate of flow is $Q$. If the radius is reduced to $\frac{a}{4}$ and the pressure is increased to $4P$,then the rate of flow becomes ................

What are the limitations of the concept of turbulence in fluid dynamics?

Vedclass Test Series

Exam Paper Generator

Online Exam Module