Mechanical Properties of Fluids

Hydrostatics is the scientific study of the mechanical properties of fluids. A fluid is a substance that readily responds to even the slightest applied force. Fluids demonstrate the influence of gravity more effectively than solid objects do, as the strong cohesive force between the particles of solids somewhat counteracts the gravitational effect.

Developing a strong understanding of various concepts explained in Class 11 Physics is crucial not only for Class 12th but also for various international and government exams after 12th Science. From Waves and Oscillations to the Kinetic Theory of Gasses, building a strong foundation is essential for all. In this blog, we have summarised and compiled the essential information related to the Mechanical Properties of Fluids which forms an integral part of the Physics syllabus for class 11! 

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Brief Overview

All the substances in nature and otherwise, that flow, are known as fluids. And the study of the mechanical properties of fluids is known as Fluid Mechanics. However, before proceeding, there are 2 important concepts which you must be aware of:

• The density of fluids is independent of any pressure variation and remains constant. This property is known as incompressibility.
• Two-fluid surfaces in contact do not exert a tangential force on each other. This property is known as non-viscosity.

Now that you have got a brief idea, let us understand the important mechanical properties of fluid in detail. 

Fluid Dynamics

Fluid dynamics incorporate energy into the study of the mechanical properties of fluids. The type of flow in which the velocity of particles crossing a particular point is the same irrespective of time is known as steady flow. The path taken by particles is known as the line of flow.

Surface Tension

Surface tension is defined as the force per unit length in the plane of the liquid surface at right angles to either side of an imaginary line drawn on that surface. Surface energy is the work done over the surface of a liquid to increase its surface area. 

Atmospheric Pressure

Atmospheric pressure is the pressure of the earth’s atmosphere. The value generally taken is 1 bar or 1.013 x 10⁵ Pa. Pressure above atmospheric pressure is termed gauge pressure, while the total pressure is termed absolute pressure. A barometer is used to measure total pressure while a manometer is used to measure the gauge pressure. With its applications rooted across aviation and other sectors, understanding this mechanical property of the fluid is essential.

Fluid Pressure

It is the pressure at any point in the fluid and is defined as the normal force per unit area. The SI unit of pressure is Pascal. The pressure is a scalar quantity and has no direction of its own. It acts perpendicular to any surface in the fluid. The following are the rules governing the determination of pressure with respect to the mechanical properties of fluids:

• The pressure at two points at the same horizontal level in the fluid is the same if it is at rest or moving with a constant velocity.
• If the fluid is accelerating, the pressure difference between two points at different vertical levels is given by the formula:

Where P1 = Pressure at Point 1, P2= Pressure at Point 2, l = distance between two points, and a = acceleration.

Viscosity

The property of a fluid by virtue of which it opposes relative motion between two layers is known as viscosity. Stokes’ Law states that when a solid move through a medium, its motion is opposed by a viscous force depending on the velocity and shape and size of the body. This law is used extensively in studies of the mechanical properties of fluids.

Pascal’s Law

Pascal’s Law is an important axiom in the study of the mechanical properties of fluids. It states that a change in the pressure applied to a closed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. It is used in various industrial applications. Its formula is given as:

F=PA

Where F = Force, P = Pressure, and A = Area

Archimedes’ Principle

This is another important rule in the study of the mechanical properties of fluids. It states that when a body is partially or fully dipped in a fluid, the fluid exerts a contact force on the body which is equal to the weight of the fluid displaced by the body. This force is known as the buoyant force. This force acts vertically against the weight of the body through the centre of gravity of the displaced liquid, known as the centre of buoyancy.

Note The rules of flotation state that a body will float if its average density is less than that of the liquid. The centre of gravity of the body and the centre of buoyancy must be along the same straight line, while the weight of the liquid displaced by the immersed part of the body must be equal to the weight of the body.

Bernoulli’s Theorem

This is an essential theorem in the determination of the mechanical properties of fluids. It states that in the streamlined flow of an ideal fluid, the sum of pressure energy per unit volume, potential energy per unit volume, and kinetic energy per unit volume is always constant at all cross-sections of the liquid.

Here, p = Fluid Pressure, v = Fluid Velocity, ρ = Fluid Density, and h = Container’s Height

Mechanical Properties of Fluids PDF

Mechanical Properties of Fluids Formulas

Here are the important formulas of this chapter-

• The density of a sample at constant density: ρ=mV
  • ρ: density of the fluid
  • m: Mass
  • V: Volume
• Pressure: p=FA
  • p: Pressure
  • F: Force applied
  • A: Area affected
• The pressure at a depth h in a fluid of constant density: p= p0+ρgh
  • p: the pressure at height h
  • p0: the pressure at zero height
  • g: acceleration due to gravity
  • ρ: fluid density
• Volume flow rate: Q= dV/dt
  • Q: flow rate
  • dV: change in volume
  • dt: time period
• Viscosity: η=FL/vA
  • η: fluid viscosity
  • F: Force
  • L: distance between the plates
  • V: constant velocity
  • A: area of the plate

Other important formulas of this chapter are-

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Mechanical Properties of Fluids Neet Notes

During NEET exam preparation, aspirants must know these important pointers:

• The floating body is in stable equilibrium when the metacentre is above the centre of gravity (the centre of gravity is below the centre of buoyancy).
• The floating body is in an unstable equilibrium when the metacentre lies below the centre of gravity (the centre of gravity is above the centre of buoyancy).
• The floating body is in the neutral equilibrium when the centre of gravity coincides with the metacentre (the centre of gravity coincides with the centre of buoyancy).
• The wooden rod cannot float vertically in a pond of water because the centre of gravity lies above the metacentre
• The ST is a molecular phenomenon as ST is due to ‘cohesion’ between the molecules of a liquid.
• The force of attraction between the molecules of the same substance is called a cohesive force and that between molecules of a different substance is called an adhesive force.
• The molecular range is the maximum distance (10–9 m) up to which the molecules attract each other.
• In general, the ST of liquids decreases with an increase in temperature but the ST of molten Cadmium and Copper increases with an increase in temperature.
• If the impurity is completely soluble then by mixing it in the liquid, its surface tension increases. For example on dissolving ionic salts in small quantities in a liquid, its surface tension increases. On dissolving salt in water, its surface tension increases.
• For all those liquids which neither rise nor get depressed in a capillary tube, the angle of contact is a right angle (θ = 90°), e.g. silver and water.
• The angle of contact depends on impurities, waterproofing agent, surface in contact and temperature. The angle of contact θ_C ∝ T where T is the temperature.

Also Read: Best Books for NEET

NEET Questions 

Some of the NEET questions related to the mechanical properties of fluids are as follows:

• An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by an additional 46 cm. What will be the length of the air column above the mercury in the tube now?
• Two capillary tubes are of the same diameter. One is dipped in a liquid of relative density 0.8 while the other is in a liquid of relative density 0.6. If the surface tensions of these liquids are 60 and 50 milli N / m liquids in the capillary tubes. , respectively, and the angles of the contact are equal, compare the rise.
• A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube then rotated in a horizontal plane about one of its ends with a uniform angular velocity w. The force exerted by liquid at the other end is?
• The radius of a soap bubble is increased from R to 2 R. Work done in this process is?
• The flow rate from a tap of diameter 1.25 cm is 3lit / m * i * n The coefficient of viscosity of water is 10 ^ – 3 Pas. The nature of flow is?
• The cylindrical tube of a spray pump has a radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v,-the speed of the ejection of the liquid through the holes?
• Water flowing from a hose pipe fills a 15-litre container in one minute. The speed of water from the free opening radius 1 cm is (in ms^ -1 ) : 25 pi/2.5?
• A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t)

Also Read: NEET Entrance Exam 2023 – Complete Guide

Mechanical Properties of Fluids Important Questions

Enlisted below are the important question of this chapter-

1. The free surface of the oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle 8. If the acceleration is ms? What will be the slope of the free surface?.
2. The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius r = 2.5×10-5 m. The surface tension of sap is T = 7.28 * 10-2 Nm– and the angle of contact is 0°. Does surface tension alone account for the supply of water to the top of all trees?
3.  If a drop of liquid breaks into smaller droplets, it results in a lowering of the temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop in temperature. Two mercury droplets of radii 0.1 cm. and 0.2 cm. collapse into one single drop. What amount of energy is released? The surface tension of mercury T= 435.5 x 10-3 Nm-4
4.  A hot air balloon is a sphere of radius 8 m. The air inside is at a temperature of 60°C. How large a mass can the balloon lift when the outside temperature is 20°C? (Assume air is an ideal gas, R = 8.314 ) mole-1K-2, 1 atm. = 1.013 * 105 Pa; the membrane tension is 5 Nm-1.)
5. Pressure decreases as one ascends the atmosphere. If the density of air is p, what is the change in pressure dp over a differential height dh?
6. Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is po.
7. (C) If p. = 1.03 x 105 N m2, P. = 1.29 kg m-3 and g = 9.8 m 52, at what height will the pressure drop to (1/10) the value at the surface of the earth?
8.  What are the values of systolic and diastolic blood pressure of a healthy human being?
9. What are the values of the Reynolds number (Ng) for different types of flows?
10. A cylinder is filled with non-viscous liquid of density p, height h, and a hole is made at height h2 from the bottom of the cylinder. What is the velocity of the liquid coming out of the hole?

Mechanical Properties of Fluids: NCERT Solutions

Here is the PDF for NCERT Solutions of this chapter

FAQs

The class 11 Physics syllabus has been very meticulously curated to give the students the current knowledge of the core chapters of Physics in an easy and comprehensible manner. The concepts, including that of the mechanical properties of fluids, are used to frame questions for competitive exams like SAT, JEE Advanced, etc, and hence becomes important to develop a stronghold over it. Join Leverage Edu’s live online classes for SAT where you will get access to scores of sample questions and your doubts will be cleared through one-on-one interaction!