Chaper Ten MECHANICAL PROPERTIES OF FLUIDS MCQ I 10.1 A all cylinder is filled wih iscous oil. A round pebble is dropped from he op wih zero iniial elociy. From he plo shown in Fig. 10.1, indicae he one ha represens he elociy () of he pebble as a funcion of ime ( ). (a) (b) (c) (d) Fig. 10.1 72
Mechanical Properies of Fluids 10.2 Which of he following diagrams (Fig. 10.2) does no represen a sreamline flow? 10.3 Along a sreamline (a) he elociy of a fluid paricle remains consan. (b) he elociy of all fluid paricles crossing a gien posiion is consan. (c) he elociy of all fluid paricles a a gien insan is consan. (d) he speed of a fluid paricle remains consan. 10.4 An ideal fluid flows hrough a pipe of circular cross-secion made of wo secions wih diameers 2.5 cm and 3.75 cm. The raio of he elociies in he wo pipes is (a) 9:4 (b) 3:2 (c) 3: 2 (d) 2: 3 10.5 The angle of conac a he inerface of waer-glass is 0, Ehylalcohol-glass is 0, Mercury-glass is 140 and Mehyliodideglass is 30. A glass capillary is pu in a rough conaining one of hese four liquids. I is obsered ha he meniscus is conex. The liquid in he rough is MCQ II (a) waer (b) ehylalcohol (c) mercury (d) mehyliodide. 10.6 For a surface molecule (a) he ne force on i is zero. (b) here is a ne downward force. Fig. 10.2 73
Fig. 10.3 (c) he poenial energy is less han ha of a molecule inside. (d) he poenial energy is more han ha of a molecule inside. 10.7 Pressure is a scalar quaniy because (a) i is he raio of force o area and boh force and area are ecors. (b) i is he raio of he magniude of he force o area. (c) i is he raio of he componen of he force normal o he area. (d) i does no depend on he size of he area chosen. 10.8 A wooden block wih a coin placed on is op, floas in waer as shown in Fig.10.3. The disance l and h are shown in he figure. Afer some ime he coin falls ino he waer. Then (a) l decreases. (b) h decreases. (c) l increases. (d) h increase. 10.9 Wih increase in emperaure, he iscosiy of (a) gases decreases. (b) liquids increases. (c) gases increases. (d) liquids decreases. 10.10 Sreamline flow is more likely for liquids wih VSA (a) high densiy. (b) high iscosiy. (c) low densiy. (d) low iscosiy. 10.11 Is iscosiy a ecor? 10.12 Is surface ension a ecor? 10.13 Iceberg floas in waer wih par of i submerged. Wha is he fracion of he olume of iceberg submerged if he densiy of ice is ρ i = 0.917 g cm 3? 10.14 A essel filled wih waer is kep on a weighing pan and he scale adjused o zero. A block of mass M and densiy ρ is suspended by a massless spring of spring consan k. This block is submerged inside ino he waer in he essel. Wha is he reading of he scale? 74
Mechanical Properies of Fluids 10.15 A cubical block of densiy ρ is floaing on he surface of waer. Ou of is heigh L, fracion x is submerged in waer. The essel is in an eleaor acceleraing upward wih acceleraion a. Wha is he fracion immersed? SA 10.16 The sap in rees, which consiss mainly of waer in summer, rises in a sysem of capillaries of radius r = 2.5 10 5 m. The surface ension of sap is T = 7.28 10 2 Nm 1 and he angle of conac is 0. Does surface ension alone accoun for he supply of waer o he op of all rees? 10.17 The free surface of oil in a anker, a res, is horizonal. If he anker sars acceleraing he free surface will be iled by an angle θ. If he acceleraion is a m s 2, wha will be he slope of he free surface?. 10.18 Two mercury droples of radii 0.1 cm. and 0.2 cm. collapse ino one single drop. Wha amoun of energy is released? The surface ension of mercury T= 435.5 10 3 N m 1. 10.19 If a drop of liquid breaks ino smaller droples, i resuls in lowering of emperaure of he droples. Le a drop of radius R, break ino N small droples each of radius r. Esimae he drop in emperaure. 10.20 The sufrace ension and apour pressure of waer a 20 C is 7.28 10 2 Nm 1 and 2.33 10 3 Pa, respeciely. Wha is he radius of he smalles spherical waer drople which can form wihou eaporaing a 20 C? LA 10.21 (a) Pressure decreases as one ascends he amosphere. If he densiy of air is ρ, wha is he change in pressure dp oer a differenial heigh dh? (b) Considering he pressure p o be proporional o he densiy, find he pressure p a a heigh h if he pressure on he surface of he earh is p 0. (c) If p 0 = 1.03 10 5 N m 2, ρ 0 = 1.29 kg m 3 and g = 9.8 m s 2, a wha heigh will he pressure drop o (1/10) he alue a he surface of he earh? (d) This model of he amosphere works for relaiely small disances. Idenify he underlying assumpion ha limis he model. 10.22 Surface ension is exhibied by liquids due o force of aracion beween molecules of he liquid. The surface ension decreases 75
wih increase in emperaure and anishes a boiling poin. Gien ha he laen hea of aporisaion for waer L = 540 k cal kg 1, he mechanical equialen of hea J = 4.2 J cal 1, densiy of waer ρ w = 10 3 kg l 1, Aagadro s No N A = 6.0 10 26 k mole 1 and he molecular weigh of waer M A = 18 kg for 1 k mole. (a) esimae he energy required for one molecule of waer o eaporae. (b) show ha he iner molecular disance for waer is 1/3 M A 1 d = and find is alue. N A ρw (c) 1 g of waer in he apor sae a 1 am occupies 1601cm 3. Esimae he inermolecular disance a boiling poin, in he apour sae. (d) During aporisaion a molecule oercomes a force F, assumed consan, o go from an iner-molecular disance d o d. Esimae he alue of F. (e) Calculae F/d, which is a measure of he surface ension. 10.23 A ho air balloon is a sphere of radius 8 m. The air inside is a a emperaure of 60 C. How large a mass can he balloon lif when he ouside emperaure is 20 C? (Assume air is an ideal gas, R = 8.314 J mole 1 K -1, 1 am. = 1.013 10 5 Pa; he membrane ension is 5 N m 1.) 76