**NCERT Solutions for Class 11 Physics Chapter 10 Mechanical Properties of Fluids**: We all know that the fluids do not have a particular shape.The shape of the fluid is decided by the shape of the container. In the solutions of NCERT class 11 physics chapter 10 mechanical properties of fluids, questions related to properties of fluids (liquid and gas) and certain laws associated with the properties are discussed. Also, questions on all the topics of the chapter are covered in the CBSE NCERT solutions for class 11 physics chapter 10 mechanical properties of fluids and are very important for exam point of view. We all have heard the term pressure; **Pascal's law** is related to pressure and this law states that pressure in a fluid at rest is the same at all points which are at the same height. A change in pressure applied to an enclosed fluid is transmitted to every point of the fluid and the walls of the containing vessel container. One of the applications of this law is a hydraulic lift. Let's try to find a few more examples. The main aim of the NCERT solutions is to check the depth of understanding of the concepts and formulas studied in the chapter. The problems discussed in the NCERT solutions for class 11 physics chapter 10 mechanical properties of fluids are based on the following topics.

10.1 Introduction

10.2 Pressure

10.3 Streamline flow

10.4 Bernoulli’s principle

10.5 Viscosity

10.6 Surface tension

**Q 10.1 (a) **Explain why

The blood pressure in humans is greater at the feet than at the brain

The pressure in a fluid column increases with the height of the column, as the height of the blood column is more than that for the brain the blood pressure in feet is more than the blood pressure in the brain.

**Q 10.1 (b) **Explain why

This is because the air density does not remain the same in the atmosphere. It decreases exponentially as height increases.

**Q 10.1 (c)** Explain why

Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

When a force is applied on fluid the pressure which gets generated gets uniformly transmitted to all directions and therefore has no particular direction and is a scalar quantity. We talk of division of force with area only while considering the magnitudes. The actual vector form of the relation is

**Q 10.2 (a) ** Explain why

(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.

T_{SL} = Surface tension corresponding to the solid-liquid layer

T_{LA} = Surface tension corresponding to liquid-air layer

T_{SA} = Surface tension corresponding to solid-air layer

The angle of contact is

Since the liquid is not flowing over the solid surface the components of T_{SL}, T_{LA }and T_{SA} along the solid surface must cancel out each other.

In case of mercury T_{SA} < T_{SL} and therefore and therefore i.e the angle of contact of mercury with glass is obtuse.

**Q 10.2 (b) **Explain why

Cohesive forces between water molecules is much lesser than adhesive forces between water and glass molecules and that's why water tends to spread out on glass whereas cohesive forces within mercury is comparable to adhesive forces between mercury and glass and that's why mercury tends to form drops.

**Q 10.2 (c) **Explain why

(c) Surface tension of a liquid is independent of the area of the surface

Surface tension is the force acting per unit length at the interface of a liquid and another surface. Since this force itself is independent of area, the surface tension is also independent of area.

**Q 10.2 (d)** Explain why

(d) Water with detergent dissolved in it should have small angles of contact.

As we know detergent with water rises very fast in capillaries of clothes which is only possible when cosine of the angle of contact is the large i.e. angle of contact must be small.

**Q 10.2 (e) ** Explain why

(e) A drop of liquid under no external forces is always spherical in shape

While in a spherical shape the surface area of the drop of liquid will be minimum and thus the surface energy would be minimum. A system always tends to be in a state of minimum energy and that's why in the absence of external forces a drop of liquid is always spherical in shape.

(a) Surface tension of liquids generally ... with temperatures (increases / decreases)

(a) The surface tension of liquids generally __decreases__ with temperatures.

(b) The viscosity of gases __increases__ with temperature, whereas the viscosity of liquids __decreases__ with temperature.

(c) For solids with elastic modulus of rigidity, the shearing force is proportional to __shear strain__, while for fluids it is proportional to the __rate of shear strain__.

(d) For a fluid in a steady flow, the increase in flow speed at a constriction follows from __conservation of mass__ while the decrease of pressure there follows from __Bernoulli’s principle__.

(e) For the model of a plane in a wind tunnel, turbulence occurs at a __greater__ speed for turbulence for an actual plane.

**Q 10.4 (a) **Explain why

(a) To keep a piece of paper horizontal, you should blow over, not under, it

As per Bernoulli's principle when we blow over a piece of paper the pressure there decreases while the pressure under the piece of the paper remains the same and that's why it remains horizontal.

**Q 10.4 (b)** Explain why

This is because when we cover the tap there are very small gaps remaining for the water to escape and it comes out at very high velocity in accordance with the equation of continuity.

Because of the extremely small size of the opening of a needle, its size can control the flow with more precision than the thumbs of a doctor.

According to the equation of continuity area * velocity= constant. if the area is very small the velocity must be large. Thus if the area is small flow becomes smooth

**Q 10.4 (d) **Explain why

(d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel

Through a small area, velocity will be large. A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel in accordance with the law of conservation of linear momentum.

(e) A spinning cricket ball in air does not follow a parabolic trajectory

The ball while travelling rotates about its axis as well causing a difference in air velocities at different points around it thus creating pressure difference which results in external forces. In the absence of air, a ball would have travelled along the expected parabolic path.

Mass of the girl m = 50 kg.

Gravitational acceleration g = 9.8 m s^{-2}

Weight of the girl (W) , mg = 490 N

Atmospheric pressure is

The density of French wine

Height of the wine column h_{w} would be

The density of water is

Depth of the ocean is 3 km

The pressure at the bottom of the ocean would be

The above value is much lesser than the maximum stress the structure can withstand and therefore it is suitable for putting up on top of an oil well in the ocean.

Maximum Pressure which the piston would have to bear is

Since the mercury columns in the two arms are equal the pressure exerted by the water and the spirit column must be the same.

Therefore the specific gravity of spirit is 0.8.

Let the difference in the levels of mercury in the two arms be h_{Hg}

**Q 10.11** Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river? Explain.

No. Bernoulli's equation can be used only to describe streamline flow and the flow of water in a river is turbulent.

No, unless the atmospheric pressures at the two points where Bernoulli’s equation is applied are significantly different.

The volumetric flow rate of glycerine flow would be given by

The viscosity of glycerine is

Assuming Laminar flow for a tube of radius r, length l, having pressure difference P across its ends a fluid with viscosity would flow through it with a volumetric rate of

Reynolds number is given by

Since Reynolds Number is coming out to be 0.3 our Assumption of laminar flow was correct.

The speed of air above and below the wings are given to be v_{1} = 70 m s^{-1} and v_{2} = 63 m s^{-1} respectively.

Let the pressure above and below the wings be p_{1} and p_{2} and let the model aeroplane be flying at a height h from the ground.

Applying Bernoulli's Principle on two points above and below the wings we get

The pressure difference between the regions below and above the wing is 605.15 Pa

The lift on the wing is F

By the continuity equation, the velocity of the non-viscous liquid will be large at the kink than at the rest of the tube and therefore pressure would be lesser here by Bernoulli's principle and the air column above it, therefore, should be of lesser height. Figure (a) is therefore incorrect.

Cross-sectional area of cylindrical tube is a_{1} = 8.0 cm^{2}

The total area of the 40 fine holes is a_{2}

Speed of liquid inside the tube is v_{1} = 1.5 m min^{-1}

Let the speed of ejection of fluid through the holes be v_{2}

Using the continuity equation

Total weight supported by the film

Since a soap film has two surfaces, the total length of the liquid film is 60 cm.

Surface Tension is T

As the liquid and the temperature is the same in all three the surface tension will also be the same. Since the length is also given to be equal (40 cm) in all three cases the weight being supported is also the same and equal to .

Surface Tension of Mercury is

The radius of the drop of Mercury is r = 3.00 mm

Excess pressure inside the Mercury drop is given by

Atmospheric Pressure is

Total Pressure inside the Mercury drop is given by

Excess pressure inside a bubble is given by

(It's double the usual value because of the presence of 2 layers in case of soap bubble)

where T is surface tension and r is the radius of the bubble

Atmospheric Pressure is

The density of soap solution is

The pressure at a depth of 40 cm (h) in the soap solution is

Total Pressure inside an air bubble at that depth

Pressure in the waterside at the bottom is

Pressure in the acid side at the bottom is

The pressure difference across the door is

Area of the door, a = 20 cm^{2}

The force necessary to keep the door closed is

Note: The dimensions of the door are small enough to neglect pressure variations near it.

In figure (a)

Gauge Pressure = 20 cm of Mercury

Absolute Pressure = Atmospheric Pressure + Gauge Pressure

Absolute Pressure = 76 + 20= 96 cm of Mercury

In figure (b)

Gauge Pressure = -18 cm of Mercury

Absolute Pressure = Atmospheric Pressure + Gauge Pressure

Absolute Pressure = 76 + (-18)= 58 cm of Mercury

As we know Specific Gravity of Mercury is 13.6 therefore 13.6 cm of water column would be equal to 1 cm of Mercury column.

The pressure at the Mercury Water interface in the right column = Atmospheric Pressure + 1 cm of Mercury = 77 cm of Mercury

The difference in Pressure due to the level of the Mercury column = Pressure at the Mercury Water interface - Absolute Pressure of the Glass enclosure

= 77 - 58 = 19 cm of Mercury.

The difference in the two limbs would, therefore, become 19 cm.

Since the height of the water level in the vessels is the same the Pressure at the bottom would be equal. As the area of the bottom is also the same the Force exerted by the water on the bottom would be the same.

The difference in the reading arises due to the fact that the weight depends on the volume of the water inside the container which is more in the first vessel. The vertical component of the force exerted by the fluid on the sidewalls would be more in the first vessel and the difference in this vertical component is equal to the difference in the readings on a weighing scale.

The density of whole blood

Gauge Pressure

Height at which the blood container must be placed so that blood may just enter the vein

The diameter of the artery is

The viscosity of blood is

The density of blood is

The average velocity is given by

Taking the Maximum value of Reynold's Number ( N_{Re} = 2000) at which Laminar Flow takes place we have

As the fluid velocity increases the dissipative forces become important as turbulence rises due to which drag due to friction forces increases.

The diameter of the artery is d

The viscosity of blood is

The density of blood is

The average velocity is given by

Taking the Maximum value of Reynold's Number ( N_{Re} = 2000) at which Laminar Flow takes place we have

Volumetric flow rate is given as

Speed of the wind above the upper wing surface is v_{1} = 234 km h^{-1}

Speed of the wind over the lower wing is v_{2} = 180 km h^{-1}

Let the pressure over the upper and lower wing be P_{1} and P_{2}

Let the plane be flying at a height of h

The density of air is

Applying Bernoulli's Principle at two points over the upper and lower wing we get

Area of each wing is a = 25 m^{2}

The net upward force on the plane is F

This upward force is equal to the weight m of the plane.

The mass of the plane is about 4400 kg

Neglecting buoyancy due to air the terminal velocity is

Viscous Force F_{v} at this speed is

Since the angle of contact is obtuse the Pressure will be more on the Mercury side.

This pressure difference is given as

The dip of mercury inside the narrow tube would be equal to this pressure difference

The mercury dips down in the tube relative to the liquid surface outside by an amount of 5.34 mm.

For the angle of contact , radius of the tube r, surface tension t, the density of fluid the rise in the column is given by

The radii of the two limbs r_{1} and r_{2} are 3.0 mm and 1.5 mm respectively

The level in the limb of diameter 6.0 mm is

The level in the limb of diameter 3.0 mm is

The difference in the heights is h_{2} - h_{1} = 4.96 mm

- If we are familiar with the CBSE NCERT solutions for class 11 physics chapter 10 mechanical properties of fluids then it is very easy to solve problems from other reference books too.
- The solutions of NCERT class 11 physics chapter 10 mechanical properties of fluids will help to score well in class 11 final exam and in competitive exams like JEE Main and NEET also.

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