Tag: pressure in fluids and atmospheric pressure

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Questions Related to pressure in fluids and atmospheric pressure

Multiple choice physics pressure in fluids and atmospheric pressure common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

 If the the height $(h)$ at which the atmospheric pressure is reduced to half. Find the value $\displaystyle h$.

  1. $\displaystyle h=\dfrac{0.693RT}{Mg}$.
  2. $\displaystyle h=\dfrac{6.93RT}{Mg}$.
  3. $\displaystyle h=\dfrac{693RT}{Mg}$.

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle P=P _{0}e^{-Mgh/RT} $
But $\displaystyle P=0.5P _{0}$
Hence, $\displaystyle 0.5P _{0}=P _{0}e^{-Mgh/RT} $
$\displaystyle 0.5=e^{-Mgh/RT} $


Take natural logarithm on both sides.
$\displaystyle \ln0.5=e^{-Mgh/RT} $
$\displaystyle -0.693 =  {-Mgh/RT}$
Hence, $\displaystyle \displaystyle h=\dfrac{0.693RT}{Mg} $

Multiple choice physics pressure in fluids and atmospheric pressure common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

A fully loaded Boeing aircraft has a mass of $33\times 10^{5}$ kg. Its total wing area is $500 m^2$. It is in level flight with a speed of $960 km/h$. (a) Estimate the pressure difference between the lower and upper surfaces of the wings. (b) Estimate the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface. The density of air is $\rho = 1.2 kg m^{-3}$ and $g = 9.81 m^{-2}$.

  1. $0.067$
  2. $0.075$
  3. $0.98$
  4. $0.88$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using Bernoulli's principle and the lift force equation (F = delta(P) * A), the pressure difference is calculated. Then, using the lift equation, the fractional speed increase is derived.

Multiple choice 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

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

  1. 9.4 m

  2. 4.9 m

  3. 0.49 m

  4. 0.94 m
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $\displaystyle P _1 = \frac{16}{17} = 0.94 m$
Multiple choice 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

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):

  1. $5\times 10^{-3}$
  2. $2.5\times 10^{-3}$
  3. $5\sqrt{2}\times 10^{-3}$
  4. $3.5\times 10^{-3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice 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

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.

  1. $d, c, b, a$
  2. $d, a, b, c$
  3. $a, c, d, b$
  4. $a, b, c, d$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $d > c > b > a$.

Multiple choice 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

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:

  1. 2 cm

  2. 4.5 cm

  3. 6 cm

  4. 7.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $\Rightarrow h = 6 cm$.

Multiple choice 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

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:

  1. 10 mm

  2. 5 mm

  3. 20 mm

  4. 40 mm
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice 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

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

  1. 2h
  2. $\displaystyle \frac{h}{2}$
  3. $\displaystyle \frac{h}{\sqrt{2}}$
  4. $h\sqrt{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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} $

Multiple choice 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

Two parallel glass plates are dipped partly in a liquid of density $'d'$ keeping them vertical. If the distance between the plates is $'x'$ Surface tension for liquid is $T$ & angle of contact is $\displaystyle \theta $ then rise of liquid between the plates due to capillary will be

  1. $\displaystyle \dfrac{T\cos \theta }{xd}$
  2. $\displaystyle \dfrac{2T\cos \theta }{xdg}$
  3. $\displaystyle \dfrac{2T}{xdg\cos \theta}$
  4. $\displaystyle \dfrac{T\cos \theta }{xdg}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

weight of liquid of height 'h' = (area of tube x h) x g x d= (3.14/4)hdg${x}^2$

vertical component of surface tension force=(1/2)x(Txcircumference)x cosθ=3.14Txcosθ
therefore, (3.14/4)hgd${x}^2$=(1/2)Tx3.14xcosθ
h=(2Tcosθ)/(gdx)
θ
θθs=Tx3.14x

Multiple choice 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

Two capillary tubes of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube is filled with water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is $7.3 \times 10^{-2} N/m$. Take the angle of contact to be zero and density of water to be $10^3 kg/m^3(g = 9.8 m/s^2)$

  1. 5 mm

  2. 10 mm

  3. 15 mm

  4. 20 mm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\varrho gh=\dfrac { 2T }{ R } $

${ h } _{ 1 }=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times 1.5\times { 10 }^{ 3 } } $
${ h } _{ 2 }=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times 3\times { 10 }^{ -3 } } $
So $\triangle h={ h } _{ 1 }-{ h } _{ 2 }$
             $=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times { 10 }^{ -3 } } \left( \dfrac { 2 }{ 3 } -\dfrac { 1 }{ 3 }  \right) $      
             $=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times 3\times { 10 }^{ -3 } } $
             $\boxed { \triangle h=5mm } $