Surface Tension Exercise

SURFACE TENSION Exercise - I UNSOLVED PROBLEMS Q.1 Explain why (a) A balloon filled with helium does not rise in air indefinitely but halts after a certain height (Neglect winds) (b) The force required by a man to raise his limbs immersed in water is smaller than the force for the same movement in air (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel (e) A spinning cricket ball in air does not follow a parabolic trajectory Q.2 Explain why (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute (b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets the glass while mercury does not) (c) Surface tension of a liquid is independent of the area of the surface (d) Detergents should have small angles of contact (e) A drop of liquid under no external forces is always spherical in shape Q.5 A 50 kg girl wearing high heel shoes balances on a single heel. The is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor ? Q.3 Fill in the blanks using the word(s) form the list appended with each statement ; (a) Surface tension of liquid generally................... With temperature (increases/ decreases) (b) Viscosity of gases................ with temperature, whereas viscosity of liquids.................. with temperature ( increases / decreases) (c) For solid with elastic modulus of rigidity, the shearing force is proportional to............ while for fluids it is proportional to ..................(shear strain / rate of shear strain) (d) For a fluid in steady flow, the increase in flow speed at a constriction follows from............ while the decrease of pressure there follows from............(conservation of mass / Bernoulli’s principle) (e) For the model of a plane in a wind tunnel, turbulence occurs at a.......... speed than the critical speed for turbulence for an actual plane (greater / smaller ) Q.4 Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers Q.6 Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density 984 kg m-3. Determine the height of the wine column for normal atmospheric pressure. Q.7 A vertical off-shore structure is built to withstand a maximum stress of 109 Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents. Q.8 A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of crosssection of the piston carrying the load is 425 cm2. What maximum pressure would the smaller piston have to bear ? Q.9 A U-tube contains water and methylated spirit separated by mercury. The mercury column in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit ? Q.10 In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury =13.6) Q.11 Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river ? Explain. Q.12 Does it mater if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain. SURFACE TENSION Q.13 Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 x 10-3 kg s-1, what is the pressure difference between the two ends of the tube ? (Density of glycerine = 1.3 x 103 kg m-3 and viscosity of glycerine = 0.83 Pa s.) [You may also like to check if the assumption of laminar flow in the tube is correct]. Q.14 In a test experiment on a model aeroplane in a wind tunnel, the flow speed on the upper and lower surfaces of the wing are 70 m s -1 and 63 ms -1 respectively. What is the lift on the wing if its area is 2.5 m2 ? Take the density of air to be 1.3 kg m-3. Q.15 Figures (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ? (a) (b) Q.16 The cylindrical tube of a spray pump has a crosssection of 8.0 cm2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min-1, what is the speed of ejection of the liquid through the holes ? Q.17 A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 x 10-2 N (Which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film ? Q.18 Figure (a) shows a thin liquid film supporting a small weight = 4.5 x 10-2 N. What is the weight supported by a film of the same liquid at the same temperature in fig. (b) and (c) ? Explain your answer physically. 40 cm 40 cm (a) (b) 40 cm (c ) Q.19 What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature ? Surface tension of soap solution at the temperature (20 oC) is 4.65 x10-1 N m-1. The atmospheric pressure is 1.01 x 105 Pa. Also give the excess pressure inside the drop. Q.20 What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 oC) is 2.50 x 10-2 N m-1 ? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble ? (1 atmospheric pressure is 1.01 x 105 Pa). Q.21 A tank with a square base of area 1.0 m2 is divided by a vertical, partition in the middle. The bottom of the partition has a small-hinged door of area 20 cm2. The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to a height of 4.0 m. compute the force necessary to keep the door close. Q.22 A manometer reads the pressure of a gas in an enclosure as shown in Fig. (a). When a pump removes some of the gas, the manometer reads as in Fig. (b). The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury. (a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury. (b) How should the levels change incase (b) if 13.6 cm of water (immiscible with mercury) are poured into the right limb of the manometer ? (Ignore the small change in the volume of the gas). (a) (b) Q.23 A spring balance areas 10 kg when a bucket of water is suspended from it. What is the reading on the spring balance when (a) an ice cube of mass 1.5 kg is put into the bucket (b) an iron piece of mass 7,8 kg suspended by another string is immersed with half its volume inside the water inthe bucket ? (Relative density of iron =7.8). SURFACE TENSION Q.24 Two vessels have the same base area but Q.30 Mercury has an angle of contact equal to 140o different shapes. The first vessel takes twice the with soda lime glass. A narrow tube of radius 1.00 mm volume of water that the second vessel requires to fill made of this glass is dipped in a trough containing upto a particular common height. Is the force exerted mercury. By what amount does the mercury dip down by the water on the base of the vessel the same in in the tube relative to the liquid surface outside ? the two cases ? If so, why do the vessels filled with Surface tension of mercury at the temperature of the water to that same height give different readings on experiment is 0.465 N m-1. Density of mercury a weighing scale ? = 13-6 x 103 kg m-3 . Q.25 During blood transfusion the needle is inserted Q.31 Two narrow bores of diameters 3.0 mm and 6.0 in a vein where the gauge pressure is 2000 Pa. At mm are joined together to form a u-tube open at what height must the blood container be placed so both ends. If the U-tube contains water, what is the that blood may just enter the vein ? [Use density of difference in its levels in the two limbs of the tube ? whole blood from Table 10.1]. Surface tension of water at the temperature os the experiment is 7.3 x 10-2 N m-1. Take the angle of contact Q.26 In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change inthe to be zero and density of water to be 1.0 x 10-3 kg m3 (g = 9.8 m s-1). potential and kinetic energy. (a) How does the pressure change as the fluid moves along the tube if Q.32 (a) It is know that density  of air decreases dissipative forces are present ? (b) Do the dissipative with height y (in meters) as forces become more important as the fluid velocity increases ? Discuss qualitatively. Q.27 (a) What is the largest average velocity of blood flow in an artery of radius 2 x 10-3 m if the flow must remain laminar ? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084x10-3 Pa s).   0 e  y / y o where 0 =1.25 kg m-3 is the density at sea level, and yo is a constant. This density variations called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value Q.28 A plane is in level flight at constant speed and of g remains constant. each of its two wings has an area of 25 m2. If the (b) A large he balloon of volume 1425 m3 is used to lift speed of the air is 180 km/h over the lower wing and a payload of 400 kg. Assume that the balloon maintains 234 km/h over the upper wing surface, determine the constat radius as it rises. How high does it rise ? plane’s mass. (Take air density to be 1 km m ). [ Take yo =8000 m and He = 0/18 kg m-3]. -3 Q.29 In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 x 10-5 m and density 1.2 x 10-3 kg m-3. Take the viscosity of air at the temperature of the experiment to be 1.8 x 10-5 Pa s. How much is the viscous force on the drop at that speed ? Neglect buoyancy of the drop to air.