Under a pressure head,the rate of orderly vol | vedclass

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

Question

(A) According to Poiseuille's law,the rate of volume flow $Q$ is given by $Q = \frac{\pi P r^4}{8 \eta \ell}$,where $P$ is the pressure difference,$r$

Vedclass · Accepted Answer

$\frac{Q}{32}$

Vedclass · Answer

(A) According to Poiseuille's law,the rate of volume flow $Q$ is given by $Q = \frac{\pi P r^4}{8 \eta \ell}$,where $P$ is the pressure difference,$r$ is the radius,$\eta$ is the viscosity,and $\ell$ is the length of the tube.From this formula,$Q \propto \frac{r^4}{\ell}$.Let the initial length be $\ell_1 = \ell$ and the initial radius be $r_1 = r$. The new length is $\ell_2 = 2\ell$ and the new diameter is halved,so the new radius is $r_2 = \frac{r}{2}$.The new rate of flow $Q^{\prime}$ is given by:$Q^{\prime} = Q 	imes \left(\frac{r_2}{r_1}ight)^4 	imes \left(\frac{\ell_1}{\ell_2}ight)$$Q^{\prime} = Q 	imes \left(\frac{r/2}{r}ight)^4 	imes \left(\frac{\ell}{2\ell}ight)$$Q^{\prime} = Q 	imes \left(\frac{1}{2}ight)^4 	imes \left(\frac{1}{2}ight)$$Q^{\prime} = Q 	imes \frac{1}{16} 	imes \frac{1}{2} = \frac{Q}{32}$.

Under a pressure head,the rate of orderly volume flow of a liquid through a capillary tube is $Q$. If the length of the capillary tube is doubled and the diameter of the tube is halved,the rate of flow would become:

Similar Questions

Under a constant pressure head,the rate of flow of liquid through a capillary tube is $V$. If the length of the capillary is doubled and the diameter of the bore is halved,the rate of flow would become

What is Reynolds number?

When a liquid flows through a tube,the Reynolds number is $900$. The flow of the liquid is:

Two capillary tubes of the same radius but lengths $l_1$ and $l_2$ are connected in parallel at the bottom of a vessel. What should be the length of a single capillary tube of the same radius that replaces both,such that the flow rate remains the same?

$A$ 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 $\%$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module