Two capillary of length $L $ and $2L$ and of radius $R$ and $2R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X = \pi P{R^4}/8\eta L)$
Diffcult
Download our app for free and get started
(a)Fluid resistance is given by $R = \frac{{8\eta l}}{{\pi {r^4}}}.$
When two capillary tubes of same size are joined in parallel, then equivalent fluid resistance is
${R_e} = {R_1} + {R_2} = \frac{{8\eta L}}{{\pi {r^4}}} + \frac{{8\eta \times 2L}}{{\pi {{(2R)}^4}}} = \left( {\frac{{8\eta L}}{{\pi {r^4}}}} \right) \times \frac{9}{8}$
Equivalent resistance becomes $\frac{9}{8}$times so rate of flow will be $\frac{8}{9}X$
When two capillary tubes of same size are joined in parallel, then equivalent fluid resistance is
${R_e} = {R_1} + {R_2} = \frac{{8\eta L}}{{\pi {r^4}}} + \frac{{8\eta \times 2L}}{{\pi {{(2R)}^4}}} = \left( {\frac{{8\eta L}}{{\pi {r^4}}}} \right) \times \frac{9}{8}$
Equivalent resistance becomes $\frac{9}{8}$times so rate of flow will be $\frac{8}{9}X$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A spring balance reads $200 \,gF$ when carrying a lump of lead in air. If the lead is now immersed with half of its volume in brine solution, what will be the new reading of the spring balance? specific gravity of lead and brine are $11.4$ and $1.1$ respectively ........... $gF$View Solution
- 2An inverted bell lying at the bottom of a lake $ 47.6 m$ deep has $50$ $cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be ......... $cm^3$ (atmospheric pressure $ = 70\,cm$ of $Hg$ and density of $Hg = 13.6$ $cm^3$)View Solution
- 3The density of the atmosphere at sea level is $1.29 \;kg / m ^{3} .$ Assume that it does not change with altitude. Then how high (in $km$) would the atmosphere extend?View Solution
- 4Water is flowing on a horizontal fixed surface, such that its flow velocity varies with $y$ (vertical direction) as $v=k\left(\frac{2 y^2}{a^2}-\frac{y^3}{a^3}\right)$. If coefficient of viscosity for water is $\eta$, what will be shear stress between layers of water at $y=a$.View Solution
- 5View SolutionA vessel containing water is given a constant acceleration a towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid
- 6A cube of external dimension $10\ cm$ has an inner cubical portion of side $5\ cm$ whose density is twice that of the outer portion. If this cube is just floating in a liquid of density $2\ g/cm^3$, find the density of the inner portionView Solution
- 7A air bubble rises from bottom of a lake to surface. If its radius increases by $200 \%$ and atmospheric pressure is equal to water coloumn of height $H$. then depth of lake is ..... $H$View Solution
- 8View SolutionWater containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross-section. In this region, the bubbles
- 9For the situation shown in the figure, water flows on the surface of a fixed plate. TheView Solution
velocity of water as a function of distance $'y'$ is given as : $u = \alpha \left[ {\frac{y}{h} - 2{{\left( {\frac{y}{h}} \right)}^2}} \right]$ . Determine the magnitude of the shear stress that the water applies at the base of the plate. Coefficient of viscosity is $\eta$
- 10A small wooden ball of density $ \rho$ is immersed in water of density $\sigma $ to depth $h $ and then released. The height $H$ above the surface of water up to which the ball will jump out of water isView Solution