PROPERTIES OF BULK MATTER CONCEPTUAL PROBLEMS Q-01 What flows faster than honey. Why? Ans According to poiseuille s formula, the volume V of a liquid flowing per second through a horizontal narrow tube of radius and length under a pressure difference p across the two ends of the tube is given by V = where η is the coeff. of viscosity of the liquid. For the given values of,, and V As η for water is less as compared to honey, therefore V for water is greater than that of honey. On account of this water flows faster than honey. Q-02 From where viscous force come about in moving liquids. Discuss the factors on which viscous drag of liquid depends. Ans When a liquid is in motion, its different layers move with different velocities. Due to force of cohesion between liquid molecules, a fast moving layer will tend to increase the velocity of the adjacent slow moving layer. and a slow moving layer will tend to decreases the velocity of the adjacent fast moving layer. As a result of it, an internal frictional force (called viscous drag) comes into play within the liquid which opposes the relative motion amongst its different layers. A viscous drag (F) acting between the two layers of liquids in motion is related with the following factors. (i) F A (A = Area of each layer) (ii) F / ( / = velocity gradient between the layers) Thus F or F = where η is a constant of proportionality and is called coeff. Of viscosity of liquid. The negative sign shows that the direction of F is opposite to the direction of velocity. Q-03 Explain the difference between solid friction and viscosity. Ans The solid friction and viscosity (i.e. viscous drag) both oppose the relative motion but they differ from each other as discussed below : Solid friction (i) Solid friction bet-ween two solids is independent of the area of solid surfaces in contact. (ii) It is independent of the relative velocity of one body on the surface of another body. (iii) It is directly proportional to the normal reaction between the surface is contact. Viscosity (viscous drag) (i) Viscous drag bet-ween the layers is directly Proportional to the area of liquid layers. (ii) It is directly proportional to the relative Velocity between the two layers of the liquid (iii) It is independent of the normal reaction Between two layers of the liquid. Q-04 Rain drops falling under gravity do not acquire very high velocity. Why? Ans When a rain drop falls under gravity through a viscous medium (say air) a viscous drag acts on it in a direction opposite to that of motion. According to Stoke s law, this viscous drag goes on increasing with the increasing velocity of the drop till a stage comes when the total downward force on the drop is just balanced by the upward viscous drag. At this stage, there is no net force to accelerate rain drop. Hence the rain drop starts moving with uniform velocity. This velocity is called terminal velocity. Q-05 A bigger rain drop falls faster than smaller one. Why? 1
Ans When the rain drops of different sizes fall under gravity, they ultimately move with their terminal velocities due to viscous drag of air. As terminal velocity of a drop varies as the square of its radius, therefore a bigger drop will have greater terminal velocity and hence fall faster than a smaller rain drop. Q-06 Machine parts are jammed in winter. Why? Ans A lubricating oil is generally used between the various parts of a machine to reduce the friction. In winter, since the temperature is low, the viscosity of oil between the machine parts increases considerably, resulting in jamming of the machine parts. Q-07 What is terminal velocity? Discuss the factors on which it depends. Ans Terminal velocity of the body is the maximum constant velocity acquired by the body while falling freely in a viscous medium. Terminal velocity ( ) of a body of radius, density moving through a viscous medium of viscosity η and density σ is given by g. Thus the value of v depends upon r, ρ, ρ and Q-08 Discuss the effect of temperature on the viscosity of liquids. Ans The viscosity of liquid decreases rapidly with rise of temperature.for example, in case of water. The viscosity at 50 0 C is found to be about half of its value at 10 0 C. In case of castor oil, the viscosity at 20 0 C is about 2/5 th of its value at 10 0 C. The velocity of all the gases increases with the rise in temperature. Q-09 Explain viscosity. Give some example. Where is its part being played in nature? Ans Viscosity of a liquid is the property of the liquid by virtue of which it opposes the relative motion amongst its different layers. Consider a liquid layer moving over another layer which is at rest. Due to force of cohesion, the upper layer has tendency to move the lower layer along with it and lower layer tends to stop the motion of the upper layer. As a result, an internal frictional force called viscous drag comes into play, which opposes the relative motion amongst its different layers This internal frictional force in a liquid which opposes the relative motion amongst its different layers is called viscosity. Some of the applications related with the study of viscosity are : (i) Chemists use this study to determine molecular weights and shape of large organic molecules such as proteins and cellulose. (ii) In industry, the measurement of viscosity and its variation with temperature are useful in judging whether a given lubricant oil is useful for a machine or not. (iii) In railway terminals, the liquids of high viscosity are used as buffers. Q-10 What is an ideal liquid? Ans An ideal liquid has the following qualities ; (i) The liquid is perfectly incompressible. It means the density of the liquid remains constant irrespective of pressure. (ii) The liquid is non viscous i.e. There are no tangential forces between layers of liquid in relative motion. (iii) An ideal liquid can not withstand any shearing stress, howsoever small the stress may be. 2
Q-11 Two stream lines of fluid can not cut each other. Why? Ans If they do so then at the point of intersection the incoming fluid particle could go one way or the other and flow can never be steady or streamline. Q-12 What happens to the pressure of an ideal liquid when it passes through a region where its speed increases? Ans The pressure of an ideal liquid decreases when it passes through a region where its speed increases, according to Bernoulli s theorem. Q-13 Still water runs deep, why? Ans According to equation of continuity = a constant. Where is the area of cross section and is the velocity of liquid flow. In case of still water, is negligible small. Therefore, a becomes extremely large. That is why still water runs deep. Q-14 Why does velocity increase when water flowing in broader pipe enters a narrow pipe? Ans In a stream line flow of a liquid, according to equation of continuity. = a constant. where is the area of cross-section and is the velocity of the liquid flow. When water flowing in a broader pipe enters a narrow pipe, the area of cross-section of the water decreases, therefore the velocity of water increases. Q-15 Distinguish between streamline motion and turbulent motion. Ans Stream line motion of a liquid is an orderly type of motion in which the liquid flows in parallel layers and every particle of the liquid follows the path of its preceding particle with exactly the same velocity in magnitude and direction. In stream line motion, the liquid must flow with a velocity less than the critical velocity of the liquid. Turbulent motion of a liquid is disorderly type of motion in which the liquid flows into eddies and motion of the particles of the liquid becomes irregular at different points. In turbulent flow, the liquid moves with a velocity greater than its critical velocity. Q-16 The shapes of cars and planes are streamlined. Why? Ans When a body moves through a fluid, its motion is opposed by the force of fluid friction, which increases with the speed of the body. When cars and planes, move through air, their motion is opposed by the air friction, which in turn, depend upon the shape of the body. It is due to this reason that the cars or planes are given such shapes (Known as stream-lined shapes) so that air friction is minimum. Rather the movement of air layers on the upper and lower side of streamlined shaped body provides a lift which helps in increasing the speed of the car. Q-17 Two row boats moving parallel to each other and near by, are pulled towards each other. Explain Ans According to Bernoulli s theorem, when velocity of liquid flow increases, the pressure decreases and vice versa. When two boats move in parallel directions close to each other, the stream of water between the boats is set into vigorous motion. As a result, the pressure exerted by water in between the boats becomes less than the pressure of water outside the boats. Due to this difference of pressures, the boats are pulled towards each other. 3
Q-18 A small ball of mass m and density is dropped in a viscous liquid of density σ. After some time the ball falls with a constant velocity. Calculate the viscous force acting on the ball. Ans Volume of the ball, V = / ; mass of the liquid displaced by ball, m = σ. When the ball falls with a constant velocity, then Viscous force = effective weight of the ball. Or F = Q-19 Why is the pressure of water reduced when it comes to narrow pipe from wide pipe while flowing? Ans According to principle of continuity = a constant, or 1/.i.e. as the water flows from wider tube to narrow tube, its velocity increases. According to Bernoulli s principle is large, the pressure is less. where velocity Q-20 According to Bernoulli s theorem the pressure of water should remain uniform in a pipe of uniform radius, But actually it goes on decreasing, why is it so? Ans When water flows through a pipe, work is done against the viscous force. This work done is taken from the pressure energy. As a result of which the pressure of the water falls, with onward movement of water in pipe. It is due to this reason that a house located at a large distance from a water tank receives water at lower pressure than those houses located closer to water tank. Q-21 Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the bottom. If and are the velocity of water and mercury coming out of the holes, find the relation between and. Ans Since velocity of efflux, is independent of density of the liquid, hence Q-22 Two capillary tubes of equal length and inner radii 2 r and 4 r respectively are added in series and a liquid flows through it. If the pressure difference between the ends of the whole system is 8.5 cm of mercury, find the pressure difference between the ends of the first capillary tube. Ans Let P,P 1, P 2 be the pressure at the beginning of a tube, at the joint of two tubes and at the end of second tube. Since the two tubes are in series, so or P P 1 = (P 1 P 2)16 or P = 17P 1 16P 2 i Given, P P 2 = 8.5 or P = P 2 + 8.5 ii From (i) and (ii), we have, P 2 + 8.5 = 17P 1 16 P 2 or P 1 P 2 = 8.5/17 = 0.5 cm of Hg. Pre ure differe e be wee he e d f he fir ube = P P 1 = (P P 2 P 1 P 2) = 8.5 0.5 = 8.0 cm of Hg 4
Q-23 The velocity of a small ball of mass m and density ρ 1 when dropped in a container filled with glycerine becomes constant after sometime. If the density of glycerine is ρ 2, what is the viscous force acting on the ball? Ans Weight of ball = mg ; Volume of ball = m/ρ 1 Buoyancy force on ball = weight of liquid displaced by ball =. Viscous force acting on the ball = net weight of the ball = ρ 2g/ρ 1 = (1 ρ 2/ρ 1). VERY SHORT ANSWERS QUESTIONS Q-01 If water in one flask and caster oil in other are violently shaken and kept on a table, then which one will come to rest earlier. Ans Caster oil will come to rest earlier as its viscosity is higher as compared to that of water. Q-02 What is the acceleration of a body falling through a viscous medium after terminal velocity is reached? Ans Zero, because the body after attaining terminal velocity will continue moving with same velocity through the viscous medium. Q-03 The liquid is flowing steadily through a tube of varying diameter. How are the velocity of liquid flow (V) in any portion and the diameter (D) of the tube in that portion are related? Ans For a steady flow, a constant or Q-04 In a stream-lined flow, what is the velocity of the liquid in contact with the containing vessel. Ans Zero. Q-05 How does the viscosity of gases depend upon temperature? Ans For gases, η T 1/2. Q-06 How is the terminal velocity v of small sized spherical body is related to its radius r while falling vertically in a viscous liquid? Ans Q-07 Out of friction force and viscous force which depends upon velocity. Ans Viscous force depends upon velocity while mechanical friction is independent of velocity. Q-08 The terminal velocity of sphere of radius in a viscous fluid is. What is the terminal velocity of a sphere of radius 2 r and of the same density in a given viscous fluid? Ans So, Q-09 What is the value of Reynold s number, when the flow of liquid in a tube is (i) laminar (ii) turbulent? Ans (i) less than 2000 (ii) greater than 3000. Q-10 An incompressible fluid flows steadily through a cylindrical pipe which has radius 2 R at point A and radius R at point B, along the flow direction. If the velocity of liquid flow at A is, what will be it velocity at point B. 5
Ans From equation of continuity ; or. Q-11 Two liquids of densities ρ 1 and ρ 2 coefficient of viscosity η 1 and η 2 are found to flow through a capillary tube at the same rate. What is the ratio of η 1/η 2? Ans As rate of flow of liquid, V = or is constant. Q-12 Can two streamlines cross each other in a flowing liquid? Explain. Ans No. If they do so it would mean that at the point of intersection of two stream lines two tangents can be drawn, which will give us two directions of liquid flow at that point which is impossible. Q-13 When air is blown in between two balls suspended close to each other, they are attracted towards each other. Why? Ans On blowing air in between the two balls, the air velocity is increased and hence pressure is decreased there. Now the pressure on the outer side of the balls being more will exert the force on the balls so that they move towards each other, resulting a collision between them. Q-14 What is effect on the equilibrium of a physical balance when air is blown below one pan? Ans When air is blown below one pan, there will be increase in air velocity there. Due to which the pressure drops there : Hence the pan goes down. Q-15 Water is coming out of a hole made in the wall of a fresh water tank. If the size of the hole is increased, (i) will the velocity of efflux of water change? (ii) will the volume of the water coming out per second change? Ans (i) Velocity of efflux will remain same as it only depends upon the depth of orifice below the free surface of water. (ii) Volume will change, since volume of the liquid flowing out per second is equal to product of area of hole and velocity of liquid flowing out. Q-16 If, instead of fresh water, sea water is filled in the tank, will the velocity of efflux will change? Ans No, because velocity of efflux is independent of density of liquid Q-17 One flask contains glycerine and other contains water. Both are stirred vigorously and placed on the table. In which flask will the liquid come to rest earlier and why? Ans Since viscosity of glycerine is large than water, therefore glycerine will destroy the relative motion between its layers quickly than that of water. That is why glycerine will come to rest earlier than water. Q-18 The diameter of ball A is twice of that of B. What will be the ratio of their terminal velocities in water. Ans As terminal velocity (radius of ball) 2, therefore ratio of terminal velocities of A and B will be 4 : 1. Q-19 What is the terminal velocity of a body in a freely falling system? Ans The terminal velocity of a body in a freely falling system is zero, because g = 0 for this system and. Q-20 Define one unit of coefficient of viscosity in cgs system. Ans The coefficient of viscosity of a liquid is said to be 1 dyne cm -2 s if 1 dyne tangential force is required to maintain a velocity gradient of 1 cm s 1 /cm between two parallel layers each of area 1 cm 2. 6
Q-21 When water flows through a pipe in the form of coaxial layers, which layer moves fastest? Ans The axial layer moves fastest. Q-22 The hotter liquid flows faster than the cold ones. Explain, why. Ans The coefficient of viscosity of liquid decreases with rise in temperature. As a result of which, the hotter liquid flows faster than the cold one, under the given tangential force. Q-23 What is meant by critical velocity of a liquid? Ans It is that maximum velocity above which the flow of liquid becomes turbulent and below which the flow of liquid is streamline. Q-24 What is pressure head? Ans The pressure head at a location = P/ρg. Q-25 What is the velocity head? Ans The velocity head at a location in a liquid flow =. Q-26 What are the properties of a liquid satisfying the Bernoulli s Theorem? Ans The liquid must be ideal one i.e. non viscous, incompressible and the liquid flow should be streamline. Q-27 What are the S.I. unit and cgs unit of viscosity. Give the relation between them. Ans S.I. unit of viscosity is Pa-s and cgs unit of viscosity is dyne cm 2 s, where 1 Pa-s = 10 dyne cm 2 s. Q-28 A rain drop of radius r falls in air with a terminal velocity. What is the terminal velocity of a rain drop of radius 2 r? Ans Terminal velocity i.e. SHORT ANSWERS QUESTIONS Q-01 Explain the effect of (i) density (ii) temperature and (iii) pressure on the viscosity of liquids and gases. Ans (i) In case of liquids, viscosity increases with increase in density and for gases, it decreases with increase in density. (ii) with the rise in temperature, the viscosity of liquid decreases while that of gases increases. (iii) With the increases in pressure, the viscosity of liquids (except water) increases while that of gases is practically independent of pressure. The viscosity of water decreases with the increases in pressure. Q-02 Two equal drops of water falling through air with a steady velocity. If the drops coalesced, what will be the new steady velocity? Ans The terminal velocity of a drop of radius, density while falling through a viscous medium of viscosity η and density σ is (i) 7
If R is the radius of the new drop formed when two drop coalesced, then or R =. New terminal velocity of drop of raidus R is [from (i)] Q-03 The velocity of water in a river is less on the bank and large in the middle ; why? Ans In the river water flows in the form of streams. The forces of adhesion is less on the streams in the middle of river than those near the bank. Due to which the velocity of streams near the bank is least and is maximum in the middle of river. Q-04 Establish equation of continuity of liquid flow. Ans Refer to Art.7(c).13. Q-05 Deep water runs slow. Explain. Ans According to equation of continually, = a constant i.e. 1/. In a case of deep water, area of crosssection a is large, so velocity is small i.e. deep water runs slow. Q-06 Flags flutter in breeze. Why? Ans When air is breezing, the air layers are moving with unequal velocity on the two faces of cotton flag. Due to which there will be unequal pressure on the two faces of the flag according to Bernoulli s Theorem, which results fluttering of flag. Q-07 How will the weight of a body be affected, when it falls with its terminal velocity through a viscous medium? Ans When a body falls through a viscous medium with its terminal velocity, it is moving with a constant velocity. It means no resultant force is acting on the body, since the gravity pull has been balanced by viscous drag and buoyancy of medium. Therefore, the effective weight of body becomes zero. Q-08 Explain the limitations of Bernoulli s Theorem. Ans Refer to Art 7(c). 15. Q-09 It is advised not to stand near a running train. Why? Ans When fast moving train passes on a rail, then the velocity of air streams in between the rail and the person standing near rail will be very large as compared to the velocity of air streams on the other side of person away from the rail. According to Bernoulli s Theorem, the pressure of air will becomes low in between person and rail and is high on the other side of person. As a result of this pressure difference a thrust acts on the person which may push the person towards rail side and the person may met with an accident. Q-10 The velocity of fall of a man jumping with a parachute first increases and then becomes constant. Explain. Ans As a mass jumps out from a height in air with a parachute its velocity increases first, because the gravity pull dominates the viscous drag and buoyancy of air which oppose the motion. As the velocity increases, the viscous drag of air also increases and soon a stage is reached where viscous drag and buoyancy of air balances the gravity pull. Then the man with a parachute falls with a constant velocity, called terminal velocity. 8
Q-11 Two capillaries of same length and radius in the ratio of 1 : 2 are connected in series and a liquid flows through this system under streamline conditions. If the pressure across the two extreme ends of combination is 1 of water, what is the pressure difference across the (i) first capillary (ii) second capillary? Ans V = or P 1 = 16p 2 But So or and Q-12 16 cm 3 of water flows per second through a capillary tube of radius cm and of length cm. When connected to a pressure head of cm of water. If a tube of the same length and radius /2 is connected to the same pressure head, what is the volume of water flowing per second through the tube. Ans As V = so V ; Therefore or V 1 = V cm 3. Q-13 Under a constant pressure head, the rate of streamlined volume flow of a liquid through a capillary tube is V. If the length of the capillary tube is doubled and diameter of the bore is halved, find the rate of flow of the liquid through the capillary tube. Ans V = or V Q-14 If the velocity head of a stream of water is equal to 10 0 cm, find its speed of flow. Ans Velocity head, or cm/s. Q-15 A small sphere of mass m is dropped from a great height. After it has fallen 100 m, it has attained its terminal velocity and continue to fall at that speed. The work done by air friction against the sphere during 100 m falls is W 1 and during next 100 m fall is W 2, then compare W 1 and W 2. Ans Since the viscous force F = 6 π η F so the viscous force in the first 100 m will be smaller than the next 100 m fall. Hence work done W 1 will be less than that of W 2. Q-16 The water level on a tank is 5 m high. There is a hole of 1 cm 2 cross-section at the bottom of the tank. Find the initial rate with which water will leak through the hole. (g = 10 ms 2 ). Ans Rate of leakage of water, V = Q-17 The cylindrical tube of a spray pump has a radius R, one end of which has fine holes, each of radius r. If the speed of the liquid in the tube is V, find the speed of the ejection of the liquid through the holes. Ans Area of cross section of tube, A = π R 2 ; Area of cross section of each hole = π r 2 Let be the speed of ejection of the liquid through each hole. Using equation of continuity, we have π R 2 V = (π r 2 ) or Q-18 In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the lower and upper surfaces Ans of the wing are and respectively. If the density of air is ρ and the surface area of the wing is A, what is the dynamic lift on the wing of aeroplane. Let P 1 and P 2 be the air pressures on the upper and lower surface of the wing. Using Bernoulli s theorem, 9
We have The force of dynamic lift = Q-19 The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. Explain how? Ans As the stream falls, its speed will increase and hence its area of cross-section will decrease, according to equation of continuity i.e. A = a constant. That is why the stream will become narrow. When the stream will go up, its speed will decrease, hence its area of cross section will increase i.e. it will become broader and spreads out like a fountain. Q-20 There are two holes, each of cross-sectional area, on the opposite sides of a wide rectangular tank containing a liquid of density ρ. When the liquid flows out of the holes, find the net force on the tank. Given, h is the vertical distance between two holes. Ans When liquid flows out of the hole from the tank of area of cross-section a with velocity then force on the tank is equal to rate of change of linear momentum i.e. F = Net force on tank = = = 2 a g. Q-21 Explain viscosity of a liquid. Discuss its cause. Q-22 Explain coefficient of viscosity ; its units and give its dimensional formula. Q-23 Explain Poiseuille s formula and derive it by using the method of dimensions. Q-24 State and Establish Stoke s law Q-25 What do you understand by terminal velocity. Find the relation for it? Q-26 Mention some practical uses of the knowledge of viscosity. Q-27 What do you understand by critical velocity? Establish a relation for it by using method of dimensions. Q-28 What do you understand by Reynold number? Give its physical significance Q-29 Write a note on venturimeter. Q-30 State and explain Torricelli s Theorem. 10
Q-31 What do you understand by blood flow and heart attack. LONG ANSWERS QUESTIONS Q-01 Explain streamline flow, laminar flow and turbulent flow. Q-02 What are the various forms of energies of a liquid in motion? Write their relations in terms of unit mass. Q-03 State and prove Bernoulli s theorem. Q-04 Write a note on (i) Atomiser (ii) Lift on an aeroplane (iii) Curved motion of a spinning ball (iv) Blowing off the roofs during storms. 11