Mechanical Properties of Fluids Test

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Mechanical Properties of Fluids Test - 62

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Weekly Quiz Competition

Question 1
1 / -0

In a vessel of water a hole is made at a depth of $$3.5\ m$$ from the free surface. The velocity of efflux will be:

A
$$8.4\ m/s$$

B
$$84\ m/s$$

C
$$8.4\ cm/s$$

D
$$84\ cm/s$$

Solution
Question 2
1 / -0

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

A
$$4Q$$

B
$$\cfrac { Q }{ 2 } $$

C
$$Q$$

D
$$\cfrac { Q }{ 64 } $$

Solution
Question 3
1 / -0

The angle of contact at the interface of water glass is $${0^ \circ }$$, Ethyl-alcohol glass is $${0^ \circ }$$ Mercury glass is $${140^ \circ }$$ and Methyl iodide is $${30^ \circ }$$. A glass capillary is put in a trough containing one of these for liquids it is observed that the meniscus is convex. the liquid in the trough is :

A
Water

B
Ethyl alcohol

C
Mercury

D
Methyl iodide

Solution

Given , angle of contact $$(θ) = 140°$$

Radius of tube $$(r) = 1 mm = 10⁻³ m$$

Surface tension $$(S) = 0.465 N/m$$

Density of mercury$$ (ρ) = 13.6 × 10³ kg/m³$$

Height of liquid rise or fall due to surface tension $$(h)$$

$$ = 2S cos θ/rρg = 2 × 0.465 × cos 140°/1 × 10⁻³ × 13.6 × 10³ × 9.8$$

$$= 2 × 0.465 × (- 0.7660) / 10⁻³ × 13.6 × 10³ × 9.8 $$

$$= - 5.34 mm $$

Hence, the mercury level will depressed by $$5.34 mm.$$
A glass capillary is put in a trough containing one of these for liquids it is observed that the meniscus is convex. the liquid in the trough is Ethyl alcohol.
Question 4
1 / -0

A tank is filled with two immiscible liquids of densities $$2\rho$$ and $$\rho$$ each of height $$h$$. Two holes are made to the side wall at $$\dfrac{h}{2}$$ and $$\dfrac{3h}{2}$$ from upper surface of the liquid, then the ratio of velocity of efflux of the liquids through the holes

A
$$\dfrac{\sqrt2}{3}$$

B
$$\dfrac{\sqrt3}{1}$$

C
$$\dfrac{3}{\sqrt2}$$

D
$$\dfrac{1}{\sqrt2}$$

Solution

Let the velocity at hole is $${ v }_{ 1 }$$
Height is $$\dfrac { h }{ 2 } $$
Therefore velocity is, $${ v }_{ 1 }=\sqrt { 2g\dfrac { h }{ 2 } } \\ $$
Now pressure at hole 2 is
P= $$h\rho g+\dfrac { h }{ 2 } \times 2\rho g$$
Applying Bernoulli's theorem, $${ P }_{ o }+2h\rho g={ P }_{ o }+\dfrac { 1 }{ 2 } (2\rho ){ v }_{ 2 }^{ 2 }$$
where $${ P }_{ o }$$ is the atmospheric pressure
Velocity at hole 2 is $${ v }_{ 2 }=\sqrt { 2g\dfrac { 3h }{ 2 } } =\sqrt { 3gh } $$
Now, $$\dfrac { { v }_{ 2 } }{ { v }_{ 1 } } =\dfrac { \sqrt { 3gh } }{ \sqrt { gh } } $$
$$\dfrac { { v }_{ 2 } }{ { v }_{ 1 } } $$= $$\sqrt { 3 } :1$$
Question 5
1 / -0

A cylindrical vessel has some water in it. A small hole at the bottom is now opened. The ratio of times it takes to become $$75\%$$ empty to completely empty is

A
$$3:4$$

B
$$1:2$$

C
$$1:3$$

D
$$2:3$$

Solution
Question 6
1 / -0

Water is filled upto same height in two identical closed containers $$A$$ and $$B$$. Container $$A$$ has vacuum over the water while container $$B$$ has air over the water. At the same depth of both the containers there is an opening on which identical balloons $$A$$ and $$B$$ are attached as shown in the figure given below. Then

A
Balloon - $$A$$ will bulge more than balloon - $$B$$

B
Balloon - $$B$$ will bulge more than balloon - $$A$$

C
Both the balloons will bulge equally

D
None of the balloons will bulge

Solution

Solution:- (A) Balloon $$A$$ will bulge more than balloon $$B$$.
Since the container $$A$$ has vacuum over the water, thus water will cover the vacuum area first and hence the balloon $$A$$ will bulge more than balloon $$B$$.
Question 7
1 / -0

if the blood vessels in a human being acted as simple pipes what would be the difference in blood pressure between the blood in a $$1.8\ m$$ tall man's feet and in his head when he is standing? Assume the spacific gravity of blood to be $$1.06$$.

A
$$16.239kPa$$

B
$$18.7kPa$$

C
$$17.3kPa$$

D
$$15.5kPa$$

Solution
Question 8
1 / -0

If $$A$$ denotes the area of free surface of a liquid and $$h$$ the depth of an orifice of area of cross-section $$a$$, below the liquid surface, then the velocity $$v$$ of flow through the orifice is given by:

A
$$v = \sqrt {\left( {2gh} \right)} $$

B
$$v = \sqrt {\left( {2gh} \right)} \sqrt {\left( {\frac{{{A^2}}}{{{A^2} - {a^2}}}} \right)} $$

C
$$v = \sqrt {\left( {2gh} \right)} \sqrt {\left( {\frac{A}{{A - a}}} \right)} $$

D
$$v = \sqrt {\left( {2gh} \right)} \sqrt {\left( {\frac{{{A^2} - {a^2}}}{{{A^2}}}} \right)} $$

Solution

$$v_{1}=$$ velocity of surface of liquid

$$v_{2}=$$ velocity of liquid far om orifice

Acc. to continuity theorem.

$$A v_{1}=a v_{2} \Rightarrow \dfrac{A v_{1}}{a}=v_{2}$$

$$\Rightarrow \dfrac{a v_{2}}{A}=v_{1}$$

Acc. to Bernoulli's Theorem

$$P_{0}+\rho g h+\dfrac{1}{2} \rho v_{1}^{2}=P_{0}+\rho g(0)+\dfrac{1}{2} \rho v_{L}^{2}$$

$$\rho g h+\dfrac{1}{2} \rho\left[\dfrac{a^{2} v_{1}^{2}}{A^{2}}-v_{1}^{2}\right]=0$$

$$\dfrac{v_{1}^{2}}{2}\left[\dfrac{A^{2}-a^{2}}{A^{2}}\right]=g h$$

$$v_{1}=\sqrt{2 g h} \sqrt{\dfrac{A^{2}}{A^{2}-a^{2}}}$$

Answer: $$ \sqrt{2 g h} \sqrt{ \dfrac{A^{2}}{A^{2}-a^{2}}}$$
Question 9
1 / -0

The angle of contact at the interface of water-glass is $$0^\circ $$. Ethyl alcohol-glass is $$0^\circ $$. Mercury-glass is $$140^\circ $$ and Methyl iodide-glass is $$30^\circ $$. A glass capillary is put in trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is:

A
water

B
ethylalcohol

C
mercury

D
methyliodide

Solution

Given ,
Angle of contact $$(\theta)=140^o$$
Radius of tube $$(r)= 1 mm =10^{-3}m$$
Surface tension $$(S) = 0.465N/m$$
Density of mercury$$ (ρ) = 13.6 \times 10^{3} kg/m^3$$
Height of liquid rise or fall due to surface tension (h)
$$=\dfrac{2Scos{\theta}}{rρg} $$

$$=\dfrac{2 \times 0.465 \times cos140^o }{1×10^{-3} \times 13.6 \times 10^{3} \times 9.8}$$

$$=2 \times 0.465 \times (−0.7660)/10^{-3} \times 13.6 \times 10^{3} \times 9.8$$

$$=−5.34\,mm $$

Hence, the mercury level will depressed by $$5.34$$ mm.
The meniscus of liquid in a capillary tube will be convex upward if angle of contact is obtuse. It is so when one end of glass capillary tube is immersed in a though of mercury.
Question 10
1 / -0

A balloon of volume $$1500{m}^{3}$$ and weighing $$1650 kg$$ with all its equipment is filled with helium (density $$0.2 kg/{m}^{3}$$). if the density of air is $$1.3 kg/{m}^{3}$$, the pull on the rope tied to the ballon will be

A
$$300 kg$$

B
$$16500 kg$$

C
$$1950 kg$$

D
$$zero$$

Solution