Tag: pressure exerted by a liquid column

Questions Related to pressure exerted by a liquid column

Two capillaries of same length and radii in the ratio 1: 2 are.connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is 1 m of water, the pressure difference across first capillary is

physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 9.4 m

  2. 4.9 m

  3. 0.49 m

  4. 0.94 m

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Correct Option: D
Explanation:
Here, $l _1 = l _2 = 1m$ and $\displaystyle \frac{r _1}{r _2} = \frac{1}{2}$

As $V = \displaystyle \frac{ \pi P _1 r _1^4 }{8 \eta l} = \frac{ \pi P _2 r _2^4 }{8 \eta l}$ or $\displaystyle \frac{ P _1 }{P _2 } = \left( \frac{ r _2 }{ r _1} \right)^4 = 16$

$\therefore P _1 = 16 P _2$

Since, both tubes are connected in series, hence pressure difference across the combination is
$P = P _1 + P _2$ $\Rightarrow$  $\displaystyle 1 = P _1 + \frac{P _1}{16}$
or $\displaystyle P _1 = \frac{16}{17} = 0.94 m$

A capillary tube of radius $r$ is immersed in water and water rises to a height of $h$. Mass of water in the capillary tube is $5\times 10^{-3}kg$. The same capillary tube is now immersed in a liquid whose surface tension is $\sqrt{2}$ times the surface tension of water. The angle of contact between the capillary tube and this liquid is $45^o$. The mass of liquid which rises into the capillary tube now is (in kg):

physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $5\times 10^{-3}$

  2. $2.5\times 10^{-3}$

  3. $5\sqrt{2}\times 10^{-3}$

  4. $3.5\times 10^{-3}$

Show answer
Correct Option: A
Explanation:

Since the force on liquid is proportional to $Scos(\theta )$, in the latter case, force will be $\sqrt { 2 } cos(\dfrac { \pi  }{ 4 } )=1$ times the force in first case. Hence, since the same force is applied, mass of water rising in the tube will be same.

A liquid is allowed to flow in a tube of truncated cone shape. Identify correct statement from the following.

physics fluid pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. The speed is high at the wider end and low at the narrow end

  2. The speed is low at the wider end and high at the narrow end

  3. The speed is same at both ends in a stream line flow

  4. The liquid flows with uniform velocity in the tube

Show answer
Correct Option: B
Explanation:

For an incompressible liquid equation of continuity $ Av = constant$

or, $ A \propto \cfrac{1}{v}$
Therefore at the wider end speed will be low and at the narrow end speed will be hgih.

If a capillary tube is tilted to $45^{\circ}$ and $60^{\circ}$ from the vertical then the ratio of length $l _{1}$ and $l _{2}$ of liquid columns  in it will be -

physics fluid pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $1: \sqrt{2}$

  2. $\sqrt{2}:1$

  3. 1:2

  4. 2:1

Show answer
Correct Option: A
Explanation:

The expression for the capillary rise in a tube is given by, 


H = $ \dfrac {2T cos \theta}{\rho gr} $


where $ \theta$ is the contact angle and not the angle of tilt.


Thus, for all parameters constant,


at $ 60^o $


$ l _1 = H cos 60^0 $ = H/2


At $ 45^o $


$ l _2 = H cos 45^0 $ = $ H/\sqrt 2 $


Therefore the ratio of the 2 lengths is given by,


$ l _1/l _2 = \dfrac {1}{\sqrt 2} $


A $20$cm long capillary tube is dipped in water. The water rises up to $8$cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be:

physics fluid pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $8$cm

  2. $6$cm

  3. $10$cm

  4. $20$cm

Show answer
Correct Option: D
Explanation:

In a freely falling lift, gravitational pull is zero hence the capillary tube will be filled completely.

Water rises in a vertical capillary tube upto a length of $10cm.$ If the tube is inclined at $45^o$, the length of water risen in the tube will be,

physics fluid pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $10 cm$

  2. $10 \sqrt2 cm$

  3. $\displaystyle \dfrac {10}{\sqrt2}$

  4. none of these

Show answer
Correct Option: B
Explanation:

The vertical rise in the level of liquid is constant.
Hence for an inclined tube, the effective length is $ \displaystyle\dfrac {h}{\cos\theta} $
So, the length of water risen in the tube will be $ 10 \sqrt 2 cm $

Four identical capillary tubes $a, b, c$ and $d$ are dipped in four beakers containing water with tube ‘$a$’ vertically, tube ‘$b$’ at $30^{o}$, tube ‘$c$’ at $45^{o}$ and tube ‘$d$’ at $60^{o}$ inclination with the vertical. Arrange the lengths of water column in the tubes in descending order.

physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $d, c, b, a$

  2. $d, a, b, c$

  3. $a, c, d, b$

  4. $a, b, c, d$

Show answer
Correct Option: A
Explanation:

In capillary tube fluid always rise to the same vertical height as when the tube is perfectly vertical. So, the tube which is making greater angle with vertical will get more water in it.
So, order of lengths of water column will be $d > c > b > a$.

A capillary tube when immersed vertically in a liquid rises to 3 cm. If the tube is held immersed in the liquid at an angle of 60$^{o}$ with the vertical,the length of the liquid column along the tube will be:

physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 2 cm

  2. 4.5 cm

  3. 6 cm

  4. 7.5 cm

Show answer
Correct Option: C
Explanation:


$h = \dfrac {2T cos \theta}{r \rho g}$
$h \alpha cos \theta$
for $\theta = 60^0 cos \theta = \dfrac {1}{2}$
$\therefore$ h is double $\Rightarrow h = 6 cm$.

A capillary tube is dipped in water vertically.Water rises to a height of 10mm. The tube is now tilted and makes an angle 60$^{o}$ with vertical.Now water rises to a height of:

physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 10 mm

  2. 5 mm

  3. 20 mm

  4. 40 mm

Show answer
Correct Option: A
Explanation:

If capillary tube is tilted the vertical height of water in tube remains same but volume of the water increases in the tube. So, height of water column will be 10mm.

Water rises in a capillary upto a height h. If now this capillary is tilted by an angle of $45^{\circ}$, then the length of the water column in the capillary becomes

physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 2h

  2. $\displaystyle \frac{h}{2}$

  3. $\displaystyle \frac{h}{\sqrt{2}}$

  4. $h\sqrt{2}$

Show answer
Correct Option: C
Explanation:

The expression for the capillary rise in a tube is given by, 


H = $ \dfrac {2T cos \theta}{\rho g r} $

for all other parameters kept constant, if I change the angle of inclination to $ 45^o $

$ cos \theta $ will go from 1 to $ \dfrac {1}{\sqrt 2} $

Therefore, the height of capillary tube rise will also change from $ H to \dfrac{H}{\sqrt2} $