Title 11. Fluid Mecha Hard.pdf ✅

(1.) A vessel with water is placed on a weighing pan and reads 600 g. Now a ball of 40 g and density 0.80 g/cc is sunk into the water with a pin as shown in fig. keeping it sunk. The weighing pan will show a reading (a.) 600 g (b.) 550 g (c.) 650 g (d.) 632 g (2.) In which one of the following cases will the liquid flow in a pipe be most streamlined (a.) Liquid of high viscosity and high density flowing through a pipe of small radius (b.) Liquid of high viscosity and low density flowing through a pipe of small radius (c.) Liquid of low viscosity and low density flowing through a pipe of large radius (d.) Liquid of low viscosity and high density flowing through a pipe of large radius (3.) An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is (a.) 3.0 m/s (b.) 1.5 m/s (c.) 1.0 m/s (d.) 2.25 m/s (4.) Water enters through end A with speed 1 v and leaves through end B with speed 2 v of a cylindrical tube AB. The tube is always completely filled with water. In case I tube is horizontal and in case II it is vertical with end A upwards and in case III it is vertical with end B upwards. We have 1 2 v v = for (a.) Case I (b.) Case II (c.) Case III (d.) Each case (5.) Water is moving with a speed of 5.18 ms–1 through a pipe with a cross-sectional area of 4.20 cm2 . The water gradually descends 9.66 m as the pipe increase in area to 7.60 cm2 . The speed of flow at the lower level is (a.) 3.0 ms–1 (b.) 5.7 ms–1 (c.) 3.82 ms–1 (d.) 2.86 ms–1 (6.) The velocity of kerosene oil in a horizontal pipe is 5 m/s. If 2 g m s =10 / then the velocity head of oil will be (a.) 1.25 m (b.) 12.5 m (c.) 0.125 m (d.) 125m (7.) In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and Care connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that th (a.) Height of the liquid in the tube A is maximum (b.) Height of the liquid in the tubes A and B is the same (c.) Height of the liquid in all the three tubes is the same (d.) Height of the liquid in the tubes A and C is the same (8.) A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is  , then the difference in the heights of the liquid at the centre of the vessel and the edge is (a.) 2 r g  C B A
(b.) 2 2 2 r g  (c.) 2gr (d.) 2 2 2gr  (9.) A manometer connected to a closed tap reads 3.5 × 105N/m2 . When the valve is opened, the reading of manometer falls to 3.0 × 105N/m2 , then velocity of flow of water is (a.) 100 m/s (b.) 10 m/s (c.) 1 m/s (d.) 10 10 m/s (10.) A large tank filled with water to a height ‘h’ is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from h to 2 h and from 2 h to zero is (a.) 2 (b.) 1 2 (c.) 2 1− (d.) 1 2 1− (11.) A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s) through a small hole on the side wall of the cylinder near its bottom is (a.) 10 (b.) 20 (c.) 25.5 (d.) 5 (12.) There is a hole of area A at the bottom of cylindrical vessel. Water is filled up to a height h and water flows out in tsecond. If water is filled to a height 4h, it will flow out in time equal to (a.) t (b.) 4t (c.) 2 t (d.) t/4 (13.) A cylinder containing water up to a height of 25 cm has a hole of cross-section 1 2 4 cm in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out (a.) Increase of 12.5 gm-wt (b.) Increase of 6.25 gm-wt (c.) Decrease of 12.5 gm-wt (d.) Decrease of 6.25 gm-wt (14.) A cylindrical tank has a hole of 1 cm2 in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 70 cm3 /sec. then the maximum height up to which water can rise in the tank is (a.) 2.5 cm (b.) 5 cm (c.) 10 cm (d.) 0.25 cm (15.) A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise, distance between the plates in m is (a.) 0.1 (b.) 0.05 (c.) 0.005 (d.) 0.0005 (16.) The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like 25 cm
(a.) (b.) (c.) (d.) (17.) Spherical balls of radius 'r' are falling in a viscous fluid of viscosity '' with a velocity 'v'. The retarding viscous force acting on the spherical ball is (a.) Inversely proportional to 'r' but directly proportional to velocity 'v' (b.) Directly proportional to both radius 'r' and velocity 'v' (c.) Inversely proportional to both radius 'r' and velocity 'v' (d.) Directly proportional to 'r' but inversely proportional to 'v' (18.) 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 continues to fall at that speed. The work done by air friction against the sphere during the first 100 m of fall is (a.) Greater than the work done by air friction in the second 100 m (b.) Less than the work done by air friction in the second 100 m (c.) Equal to 100 mg (d.) Greater than 100 mg (d.) Greater than 100 mg (19.) Two drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be (a.) 10 cm per sec (b.) 2.5 cm per sec (c.) 1/3 5 (4)  m persec (d.) 5 2  cm per sec (20.) A ball of radius r and density  falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is , the value of h is given b (a.) 2 1 2 9 r g     −     (b.) 2 1 2 81 r g     −     X V X V X V X V
(c.) 2 2 1 4 81 r g     −     (d) 2 2 1 4 9 r g     −     (21.) The rate of steady volume flow of water through a capillary tube of length 'l' and radius 'r' under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P) (a.) 16 V (b.) 17 V (c.) 16 17 V (d.) 17 16 V (22.) A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference P. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is (a.) P (b.) 3 4 P (c.) 2 P (d.) 4 P (23.) Two capillary tubes of same radius r but of lengths l1 and l2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the length of a single tube that can replace the two tubes so that the rate of flow is same as before (a.) 1 2 l l + (b.) 1 2 1 1 l l + (c.) 1 2 1 2 ll l l + (d.) 1 2 1 l l + (24.) We have two (narrow) capillary tubes T1 and T2. Their lengths are l1 and l2 and radii of cross-section are r1 and r2 respectively. The rate of flow of water under a pressure difference P through tube T1 is 8cm3 /sec. If l1 = 2l2 and r1 =r2, what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before (= P) (a.) 4 cm3 /sec (b.) (16/3) cm3 /sec (c.) (8/17) cm3 /sec (d.) None of these (25.) A capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by 10% then the rate of flow of liquid will change nearly by (a.) + 10% (b.) + 46% (c.) – 10% (d.) – 40% (26.) An open pan filled with water (density w) is placed on a vertical rod, maintaining equilibrium. A block of density  is placed on one side of the pan as shown. Water depth is more than height of the block. (a.) Equilibrium will be maintained only if <W