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GATE 2018 : Engineering Sciences [Section B / Fluid Mechanics] (with Final Answer Keys)

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GATE 2018 Fluid Mechanics (XE (B)) Q. 1 Q. 9 carry one mark each & Q. 10 Q. 22 carry two marks each. XE (B): Q.1 Rheological diagram of different types of fluids is shown in figure. Column I represents the nature of the fluid and column II represents the curve showing the variation of shear stress against shear strain rate. Column I Column II (i) Newtonian M (ii) Shear thinning N (iii) Shear thickening O (iv) Bingham plastic P The most appropriate match between columns I and II is, (A) (i) O; (ii) N ; (iii) P; (iv) M (B) (i) O; (ii) P ; (iii) N; (iv) M (C) (i) P; (ii) O ; (iii) M; (iv) N (D) (i) P; (ii) O ; (iii) N; (iv) M Q.2 In a two-dimensional, incompressible and irrotational flow, stream function ( ( x, y) ) and velocity potential ( ( x, y) ) exist. The velocities in x and y directions are non-zero. dy dy and , is The product of dx constant dx constant (A) Q.3 (B) 0 The inviscid flow past a rotating circular cylinder can be generated by the superposition of (A) uniform flow, source and vortex (C) uniform flow, sink and vortex Q.4 = (B) = (C) = (D) The influence of Froude number is most significant in (A) capillary flows (C) free surface flows XE (B) (B) uniform flow, doublet (D) uniform flow, doublet and vortex The velocity field and the surface normal vector are given by, V u i v j wk and n n1 i n2 j n3 k , respectively. If Euler equations are to be solved, the boundary condition that must be satisfied at the wall is, = (A) Q.5 (D) (C) (B) creeping flows (D) compressible flows 1/5 GATE 2018 Q.6 Fluid Mechanics (XE (B)) If the stream function ( ( x, y) ) for a two-dimensional incompressible flow field is given as 2y x 2 y 2 , the corresponding velocity field is (B) V 2 x 3 y i 4 xy j (C) V 2 x y i 4 xy j (D) V 2 x y i 4 xy j (A) V 2 x 2 3 y 2 i 4 xy j 2 2 2 2 Q.7 Water is flowing in two different tubes of diameters D and 2D, with the same velocity. The ratio of laminar friction factors for the larger diameter tube to the smaller diameter tube is (A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0 Q.8 If the velocity field is V xy 2 i 4 xy j m/s, vorticity of the fluid element in the field at (x=1, y=2) in s-1 is ____. Q.9 A pitot-static tube is used to measure air velocity in a duct by neglecting losses. The density of air is 1.2 kg/m3. If the difference between the total and static pressures is 1 kPa, the velocity of air at the measuring location, in m/s, is _______. Q.10 A parallelepiped of (2 m 2 m) square cross-section and 10 m in length, is partially floating in water upto a depth of 1.2 m, with its longest side being horizontal. The specific gravity of the block is (A) 0.8 (B) 0.6 (C) 0.5 (D) 0.4 Q.11 The velocity field in a two-dimensional, unsteady flow is given by V ( x, y, t ) 2 xy 2 i 3xyt j m/s. The magnitude of acceleration of a fluid particle located at x = 1 m, y = 1 m at the time t = 1 s, in m/s2, is (A) 16.0 (B) 18.1 (C) 24.1 (D) 34.1 Q.12 In a two-dimensional, incompressible and irrotational flow, fluid velocity (v) in the ydirection is given by v 2x 5 y . The velocity (u) in the x-direction is (A) u 2x 5 y XE (B) (B) u 2x 5 y (C) u 5x 2 y (D) u 5x 2 y 2/5 GATE 2018 Fluid Mechanics (XE (B)) Q.13 A two-dimensional laminar viscous liquid film of constant thickness (h) steadily flows down an incline as shown in figure. Acceleration due to gravity is g. If the velocity profile in the liquid film is given as, u ky(2h y); v 0 , the value of constant k is g sin 2 (C) g sin (A) g cos 2 (D) g cos (B) Q.14 A water jet of 100 mm diameter issuing out of a nozzle at a speed of 50 m/s strikes a vane and flows along it as shown in figure. The vane is attached to a cart which is moving at a constant speed of 20 m/s on a frictionless track. The jet is deflected at an angle of 30o. Take the density of water as 1000 kg/m3. Neglecting the friction between the vane and the fluid, the magnitude of the force exerted by water on the cart in the x-direction, in N, is ______. Q.15 Capillary waves are generated in the sea. The speed of propagation (C) of these waves is known to be a function of density ( ), wave length ( ), and surface tension ( ). Assume, and to be constant. If the surface tension is doubled, in the functional form of the relevant non-dimensional group, the percentage increase in propagation speed (C) is _______ . XE (B) 3/5 GATE 2018 Fluid Mechanics (XE (B)) Q.16 Consider a fully developed, two-dimensional and steady flow of a viscous fluid between two fixed parallel plates separated by a distance of 30 mm. The dynamic viscosity of the fluid is 0.01 kg/m-s and the pressure drop per unit length is 300 Pa/m. The fluid velocity at a distance of 10 mm from the bottom plate, in m/s, is ________. Q.17 A 2.6 gram smooth table-tennis (ping-pong) ball has a diameter of 38 mm. Density ( ) of air is 1.2 kg/m3. Neglect the effect of gravity. Take coefficient of drag as 0.5. If the ball is struck with an initial velocity of 30 m/s, the initial deceleration, in m/s2, is _________. Q.18 On a flat plate, transition from laminar to turbulent boundary layer occurred at a critical Reynolds number (Recr). The empirical relations for the laminar and turbulent boundary layer thickness are given by la m 5.48Re x0.5 and turb 0.37 Re x0.2 , respectively. The x x ratio of laminar to turbulent boundary layer thickness, at the location of transition, is 0.3. The value of Recr is _______. Q.19 In a capillary tube of radius R = 0.25 mm, a fully developed laminar velocity profile is R 2 dp r 2 dp defined as, u 1 MPa/m, is the dynamic 1 2 . In this expression, 4 dx R dx viscosity of the fluid, and r is the radial position from the centerline of the tube. If the flow rate through the tube is 1000 mm3/s, the viscosity of the fluid, in Pa-s, is ______________. Q.20 The skin friction coefficient for a turbulent pipe flow is defined as, C f w , where 1 2 V 2 w is the wall shear stress and V is the average flow velocity. The value of C f is 0.25 empirically given by the relation: C f = 0.065 2 Re , where Re is the Reynolds number. If the average flow velocity is 10 m/s, diameter of the pipe is 250 mm, kinematic viscosity of the fluid is 0.25 10 6 m2/s, and density of the fluid is 700 kg/m3, the skin friction drag induced by the flow over 1 m length of the pipe, in N, is ___________. XE (B) 4/5 GATE 2018 Fluid Mechanics (XE (B)) Q.21 A (150 mm 150 mm) square pillar is located in a river with water flowing at a velocity of 2 m/s, as shown in figure. The height of the pillar in water is 8 m. Take density of water as 1000 kg/m3 and kinematic viscosity as 1 10 6 m/s2. The coefficient of drag of the pillar is 2.0. The drag force exerted by water on the pillar in N is _______. Q.22 An orifice plate is used to measure flow rate of air (density = 1.23 kg/m3) in a duct of 250 mm diameter as shown in figure. The volume flow rate is 1 m3/s. Flow at sections 1 and 3 is uniform and section 2 is located at vena contracta. The diameter ratio, Dt/D1, is 0.66. The flow area at vena contracta, A2 = 0.65At, where At is area of the orifice. The pressure difference between locations 2 and 3 in N/m2 is ____________. END OF THE QUESTION PAPER XE (B) 5/5 Q.No. Type Section Key/Range Marks 1 MCQ GA A 1 2 MCQ GA C 1 3 MCQ GA B 1 4 MCQ GA B 1 5 MCQ GA B 1 6 MCQ GA A 2 7 MCQ GA D 2 8 MCQ GA D 2 9 MCQ GA B 2 10 MCQ GA C 2 1 MCQ XE A D 1 2 MCQ XE A A 1 3 NAT XE A 0.01 to 0.01 1 4 NAT XE A 5 to 5 1 5 NAT XE A 0.29 to 0.32 1 6 NAT XE A 250 to 250 1 7 NAT XE A 108 to 108 1 8 MCQ XE A B 2 9 MCQ XE A C 2 10 NAT XE A 3 to 3 2 11 NAT XE A 0.04 to 0.04 2 1 MCQ XE B B 1 2 MCQ XE B A 1 Q.No. Type Section Key/Range Marks 3 MCQ XE B D 1 4 MCQ XE B A 1 5 MCQ XE B C 1 6 MCQ XE B B 1 7 MCQ XE B A 1 8 NAT XE B 4 to 4 1 9 NAT XE B 39 to 42 1 10 MCQ XE B B 2 11 MCQ XE B C 2 12 MCQ XE B C 2 13 MCQ XE B A 2 14 NAT XE B 900 to 990 2 15 NAT XE B 40 to 42 2 16 NAT XE B 2.9 to 3.1 2 17 NAT XE B 107 to 127 2 18 NAT XE B 440000 to 442000 2 19 NAT XE B 0.001 to 0.002 2 20 NAT XE B 30 to 45 2 21 NAT XE B 4800 to 4800 2 22 NAT XE B 1200 to 1350 2 1 MCQ XE C C 1 2 MCQ XE C A 1 3 MCQ XE C B 1 Q.No. Type Section Key/Range Marks 4 MCQ XE C C 1 5 MCQ XE C A 1 6 MCQ XE C D 1 7 MCQ XE C C 1 8 NAT XE C 2 to 2 1 9 NAT XE C 6 to 6 1 10 MCQ XE C B 2 11 MCQ XE C A 2 12 MCQ XE C B 2 13 NAT XE C 430 to 500 2 14 NAT XE C 124 to 124 2 15 NAT XE C 2.60 to 2.70 2 16 NAT XE C 59.00 to 60.00 2 17 NAT XE C 1.85 to 2.00 2 18 NAT XE C 132 to 132 2 19 NAT XE C 5.01 to 5.17 2 20 NAT XE C 5 to 5 2 21 NAT XE C 15.5 to 18.5 2 22 NAT XE C 1420 to 1480 2 1 MCQ XE D D 1 2 MCQ XE D A 1 3 MCQ XE D D 1 4 MCQ XE D B 1 Q.No. Type Section Key/Range Marks 5 MCQ XE D B 1 6 NAT XE D 52.50 to 53.50 1 7 NAT XE D 27.00 to 28.00 1 8 NAT XE D 80 to 80 1 9 NAT XE D 220.00 to 222.00 1 10 MCQ XE D B 2 11 MCQ XE D B 2 12 MCQ XE D D 2 13 MCQ XE D C 2 14 MCQ XE D C 2 15 MCQ XE D A 2 16 MCQ XE D D 2 17 NAT XE D 195.00 to 197.00 2 18 NAT XE D 0.01 to 0.02 2 19 NAT XE D 14.5 to 15.5 2 20 NAT XE D 26.00 to 27.00 2 21 NAT XE D 3.10 to 3.20 2 22 NAT XE D 13.5 to 14.5 2 1 MCQ XE E B 1 2 MCQ XE E A 1 3 MCQ XE E C 1 4 MCQ XE E A 1 5 MCQ XE E C 1 Q.No. Type Section Key/Range Marks 6 MCQ XE E D 1 7 NAT XE E 160.0 to 161.0 1 8 NAT XE E 14.5 to 15.0 1 9 NAT XE E 0.30 to 0.32 1 10 MCQ XE E C 2 11 MCQ XE E C 2 12 MCQ XE E D 2 13 MCQ XE E B 2 14 MCQ XE E A 2 15 MCQ XE E D 2 16 NAT XE E 332.5 to 336.5 2 17 NAT XE E 3.01 to 3.07 2 18 NAT XE E 838.0 to 844.0 2 19 NAT XE E 961.0 to 962.0 2 20 NAT XE E 5.7 to 6.1 2 21 NAT XE E 12950.0 to 13000.0 2 22 NAT XE E 513.0 to 517.0 2 1 MCQ XE F C 1 2 MCQ XE F A 1 3 MCQ XE F D 1 4 MCQ XE F B 1 5 MCQ XE F D 1 6 MCQ XE F B 1 Q.No. Type Section Key/Range Marks 7 MCQ XE F A 1 8 NAT XE F 1500.00 to 1500.00 1 9 NAT XE F 48.52 to 48.72 1 10 MCQ XE F D 2 11 MCQ XE F A 2 12 MCQ XE F B 2 13 MCQ XE F D 2 14 MCQ XE F B 2 15 MCQ XE F D 2 16 MCQ XE F C 2 17 MCQ XE F C 2 18 NAT XE F 25.00 to 24.50 2 19 NAT XE F 98.80 to 99.10 2 20 NAT XE F 0.90 to 0.93 2 21 NAT XE F 17.91 to 18.00 2 22 NAT XE F 2600 to 2600 2 1 MCQ XE G B 1 2 MCQ XE G A 1 3 MCQ XE G C 1 4 MCQ XE G D 1 5 MCQ XE G D 1 6 NAT XE G 1.55 to 1.65 1 7 NAT XE G 103.0 to 103.2 1 Q.No. Type Section Key/Range Marks 8 NAT XE G 54 to 56 1 9 NAT XE G 0 to 0 1 10 MCQ XE G B 2 11 MCQ XE G C 2 12 MCQ XE G C 2 13 MCQ XE G A 2 14 MCQ XE G D 2 15 MCQ XE G A 2 16 MCQ XE G C 2 17 MCQ XE G B 2 18 NAT XE G 9.8 to 10.2 2 19 NAT XE G 1.1 to 1.8 2 20 NAT XE G 14.5 to 15.5 2 21 NAT XE G 6.0 to 6.4 2 22 NAT XE G 10 to 10 2 1 MCQ XE H B 1 2 MCQ XE H C 1 3 MCQ XE H A 1 4 MCQ XE H B 1 5 MCQ XE H B 1 6 MCQ XE H C 1 7 MCQ XE H D 1 8 MCQ XE H D 1 Q.No. Type Section Key/Range Marks 9 MCQ XE H B 1 10 MCQ XE H A 2 11 MCQ XE H B 2 12 MCQ XE H A 2 13 MCQ XE H B 2 14 NAT XE H 1254 to 1256 2 15 NAT XE H 19.42 to 19.44 2 16 NAT XE H 734.8 to 735.0 2 17 NAT XE H 9.16 to 9.18 2 18 NAT XE H 12.8 to 13.2 2 19 NAT XE H 92.4 to 92.8 2 20 NAT XE H 1.3 to 1.4 2 21 NAT XE H 0.11 to 0.12 2 22 NAT XE H 9.99 to 10.01 2

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