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1 Gate Mock Test-I I with Solution Mechanical By: Mr. Arvind Rai GM your success our pride i-gate Mentor

2 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 1 Q.1 Q.5 Carry One Mark Each 1. The viscosity of a fluid varies with (A) Temperature (B)temperature & pressure (C) pressure (D)Density. An ideal flow of any fluid must fulfill the following (A) Newton s law of viscosity (C) Boundary layer theory (B) Newton s law of motion (D) Continuity equation 3. Normal stress is same in all directions at a point in fluid (A) Regardless of motion of one fluid layer relative to an adjacent layer. (B) When there is no fluid motion of one layer relative to adjacent layer (C) Only when the fluid is frictionless (D) Only when the fluid is frictionless & incompressible 4. Mercury is suitable for manometer because (A)It has high density (C)It does not stick to tube walls (B)It can easily seen in tube (D)It is generally not used in manometer 5. Match the following 1. Stream fine (i) Locus of all particles that has passed a fixed point at a particular time.. Path line (ii) Line drawn on the tangent of the velocity of fluid particles at any time 3. Streak line (iii)orthogonal to stream line 4. Equipotential line (iv)path followed by same fluid particle (A) 1-ii, -iv, 3-i, 4-iii, (B) i-ii, -iii, 3-iv, 4-I (C) 1-i, -iii, 3-ii, 4-iv (D) 1-iv, -i, 3-ii, 4-iii 6. The shear stress at a point in a glycerin mass in motion if the velocity gradient is 0.5m/s per meter will be ( ρ =19.3kg/m 3 ; ν = m /sec) (A) kg / m (B) kg / m (C) kg / m (D) None of these 7. The resultant hydrostatic force acts through a point known as (A) Centre of gravity (C) Centre of buoyancy (B) Centre of pressure (D) None of these 8. The vertical distance of the center of pressure below the centroid of the inclined plane area is (A) IC sin θ Ah c (B) IC cos θ Ah c (C) IC Asin θ h c (D) IC Acos θ h c 9. Flow of fluid in a pipe takes place from (A)higher level to lower level (B)small end to large end i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

3 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) (C)Higher pressure to lower pressure 10. Existence of velocity potential implies that fluid is (D)Higher energy to lower energy (A)Ideal (B) Incompressible (C) Irrotational (D) None of these 11. Boundary layer separation is caused by (A) reduction of pressure gradient to zero (B) on adverse pressure gradient (C) release of bubbles from the fluid when the pressure goes below the vapour pressure (D) Sudden entrapping of air 1. At the point of boundary layer separation, (A) shear stress is maximum (C) velocity is negative (B) shear stress is zero (D) Density variation is maximum 13. The surface tension of water air interface is 0.06 N/m, the gauge pressure inside a rain-drop of 1mm diameter is (A) 60Pa (B) 10 Pa (C) 180 Pa (D) 40 Pa 14. An 85% efficient turbine accepts 0.8m 3 /s of water of under pressure of 600 kpa. What is maximum power output in kw, (A) 8 (B) 560 (C) 640 (D) For sudden expansion in pipe flow, what is the diameter of the pipe after expansion for maximum pressure rise, diameter of pipe before expansion is 1cm. (A)18.05 cm (B)16.97 cm (C)17.5 cm (D)15.8cm 16. One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is [GATE - 010] (A) equal to entropy change of the reservoir (C) equal to zero (B) equal to entropy change of water (D) always positive 17. A mono-atomic ideal gas (γ = 1.67, molecular weight = 40) is compressed adiabatically form 0.1 MPa 300 K to 0. MPa. The universal gas constant is KJ kmol -1 K -1 The work of compression of the gas (in KJ kg -1 ) is [GATE- 010] (A) 9.7 (B) 19.9 (C) 13.3 (D) If a closed system is undergoing an irreversible process, the entropy of the system [GATE- 009] (A) Must increase (C) Must decrease (B) Always remains constant (D) Can increase decrease or remain constraint i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

4 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) A frictionless piston cylinder device contains a gas initially at 0.8 MPa and m 3. It expands quasi statically at constant temperature to a final volume of m 3 The work output (in KJ) during this process will be [GATE - 009] (A) 8.3 (B) 1.00 (C) (D) moles of oxygen are mixed adiabatically with another moles of oxygen in mixing chamber so that the final total pressure and temperature of the mixture become same as those of the individual constituents at their initial states. The universal gas constant is given as R. The change in entropy due to mixing per mole of oxygen is given by [GATE- 008] (A) R ln (B) 0 (C) R ln (D) R ln Evaluate: lim x x (A) (B) 0 (C) - (D) None of the above. Which of the following statements is true? (A) Both cos x and sin x are differentiable at x = 0 (B) Only cos x but not sin x is differentiable at x = 0 (C) Only sin x but not cos x is differentiable at x = 0 (D) Neither cos x nor sin x is differentiable at x = 0 3. Which of the following is true? (A) Every continuous function has derivative at every point. (B) Every differentiable function may not be continuous everywhere. (C) Every differentiable function is automatically continuous. (D) A function is continuous off it is differentiable. 4. Which of the following doesn t correspond to infinite discontinuity? (A) neither forward nor backward derivative exist at point of discontinuity. (B) infinite increase of differential quotient at point of discontinuity (C) existence of vertical tangent at the point of discontinuity (D) existence of horizontal tangent at the point of discontinuity. i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

5 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 4 5. Which of the following is false? (A) The derivative of a function at a point tells us about the characteristic of that function at different other points. (B) The derivative of a function reflects a local property of the function (C) The difference quotient tells us the values of a function for distinct values of x. (D) The difference quotient reflects properties of the function in-the-large. Q.6 Q.55 Carry One Mark Each y A = x Which of the following relation between x and y makes the matrix A singular? (A) 3 y = x 1 (B) 3 y = 1 x (C) 3 y = x + 1 (D) None of the above. 7. Which of the following are eigen vectors of the real matrix A = (A) 1 1 c, d 1 i 1+ i (B) 1 1 c, d 1+ i 1 i (C) 1 1 c, d i 1 i+ 1 (D) none of the above 8. The domain of definition of the function f ( x) = log x is: x 5x + 6 (A) R {, 3} (B) (, 0) ( 0, 3) (C) ( 0,) ( 3, ) (D) (,0) ( 0,) (, ) 9. Solve the equation f ( x) = g ( x ) where ( ) ( ) f x = x + 15 and g x = 8x (A) 3, 5 (B) -3, -5 (C) ±3, ±5 (D) ±3, -5 i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

6 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) π sin x converges only if with the options p x 0 (A) p > (B) p < (C) p = (D) Always diverges 31. Two kg of water at 80 0 C are mixed adiabatically with 3 kg of water at 30 0 C in a constant pressure process of 1 atmosphere. Find the increase in the entropy of the total mass of water due to the mixing process in KJ/K(C p of water = 4.187KJ/kg K) (A) (B) (C) (D) Each of three identical bodies satisfied the equation U=CT, where C is the heat capacity of each of the bodies. Their initial temperatures are 00 K, 50 K, and 540 K. If C=8.4 KJ/K, what is the maximum amount of work that can be extracted in a process in which these bodies are brought to a final common temperature? (A) 315KJ (B) 465KJ (C) 57KJ (D) 756KJ 33. A 50 ohm resistor carrying a constant current of 1 A is kept at a constant temperature of 7 0 C by a steam of cooling water. In a time interval of 1s. what is the change of entropy of the resistor? (A) 0 (B) J/K (C) J/K (D) Data insufficient 34. In a steam generator, water is evaporate at 60 0 C, while the combustion gas (C p = 1.08 KJ/kg K) is cooled from C to 30 0 C. The surroundings are at 30 0 C. Determine the loss in available energy due to the above heat transfer per kg of water evaporated. (Latent heat of vaporization of water at 60 0 C = KJ/kg) (A) KJ (B) 543.6kj (C) KJ (A) KJ 35. Eighty kg of water at C are mixed with 50 kg of water at 60 0 C, while the temperature of the surroundings is 15 0 C. Determine the decrease in available energy due to mixing. (A) KJ (B) 36kJ (C) 443 KJ (A) 343 KJ 36. In the figure, what will be the head loss between A and B for water flowing from A to B. Given D A = 400mm V A = 30m/s P A = 30 N/cm D B = 400mm P B = 3 N/cm A 30m B 3m (A) 8m (B) 4m (C) 5m (D) 0 i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

7 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) The water is flowing through a pipe having diameter cm and cm at entry and exit π π respectively. If entry is 6m above datum and exit is 4m above datum, with entry pressure as 40N/cm, the exit pressure for flow rate of 40 lit/s is (A) 30N / cm (B) 5N / cm (C) 1N / cm (D) 0N / cm 38. A pitot static tube is used to measure the velocity of water in a pipe. The stagnation pressure head is 10m and static pressure head is 8m. The velocity of flow assuming the co-efficient of tube equal to 0.98 (taking g= 98 m/s ) will be (A) 6.4 m/s (B) 3.8 m/s (C) 4.34 m/s (D). m/s 39. For the flow in pipes as shown in figure, V C is 5cm / s, 4cm 6cm / s,5cm 4cm / s,10cm V,cm c (A) cm/s (B) 5 cm/s (C) 3 cm/s (D) 15 cm/s 40. A horizontal venturimeter with inlet and throat diameter 30cm and 15cm respectively is used to measure the velocity of water. If the pressure difference between the pipe and throat section is found to be 10kPa, the flow velocity is (A) m/s (B) 16m/s (C) 4m/s (D) 8m/s 41. The head loss when a pipe of diameter 00mm is suddenly enlarged to a diameter of 400mm will be (take rate of flow of water through the pipe as 50 lit/s) (A) 1.m (B) m (C) 8m (D) 1.8m 4. For a flow in circular pipe, the ratio of average velocity to maximum velocity is (A) 1.5 (B) 0.5 (C) 0.61 (D) The pressure drop in a 100mm radius horizontal pipe is 0kPa over a length of 10m. The shear stress of the pipe wall is (A) 0.1kPa (B) 0.05kPa (C) 0.kPa (D) kpa i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

8 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) The shear stress at the two horizontal parallel plates for the laminar flow of oil with a maximum velocity of 1m/s between two horizontal parallel fixed plates which are 00mm apart is (take μ =.5Ns/m ) (A) 100N / m (B) 50N / m (C) 00N / m (D) 1000N / m 45. A laminar flow changes to turbulent flow when (A) diameter of a pipe is decreased (B) velocity of flow in a pipe is decreased (C) viscosity of fluid flowing in a pipe is decreased (D) all of the above 46. Consider the following parameters in a fluid flow 1) Boundary layer thickness )Momentum thickness 3) Displacement thickness The correct ascending order of the magnitude of the above parameters is (A) 1<<3 (B) 3<1< (C) <3<1 (D)<1<3 47. The displacement thickness for the velocity distribution in the boundary layer given by ( δ ) ( ) δ u y y is U = (A) δ (B) δ (C) 3 δ (D) 3 7δ Common data for Questions 48 and 49: The stream function of a flow is ψ = x -y The velocity field of this flow is (A) ^ y i +x j (B) ^ ^ -y i +x j (C) ^ ^ ^ y i -x j (D) ^ ^ -y i -x j 49. Pressure change between the points (1,1)and(,) is (A) 1kN/m (B) 3kN/m (C) 18kN/m (D) 4kN/m Common data for Questions 50 and 51: consider the pipe and manometer system as shown in Figure. The pipe contains water. i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

9 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 8 _ 50. Value of manometer reading h, if there is no flow (a) 0 (b) 10mm (c) 15 mm (d) 0 mm 51. If there is a flow from A towards B and pressuree difference p A - p B (a).53 kpa (b) 3.53 kpa Link answer question 5 & 53 the manometer reading is h = 60 mm, then the static (c) 4.53 kpa (d) 5.53 kpa A rectangular gate 6m x 3m is hinged at its base and inclined at 60 0 to the horizontal as shown in the figure. To keep the gate in a stable position a counter weight of 60kN is attached at the upper end of the gate. 5. What will be the depth of water at which the gate begins to fall. Assume the gate as weight lesss and hinge and pulley are frictionless. 60kN w B m (A) 3.8m (B).m A (C) 4.5m ( D) 1.5m 53. Total force F exerted by the water on gate is _ i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

10 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 9 (A) 45.35kN (B) 8.8kN (C) 344kN (D) 38.3kN Link answer question 54 & 55 A pipe diameter 0 cm and length 000 m connects two reservoirs, having difference of water levels as 0m. Take co-efficient of friction, f=0.015 and neglect minor losses. 54. The discharge through pipe is (A) m 3 /sec (B) m 3 /sec (C) m 3 /sec (D) m 55. If an additional pipe of diameter 0 cm and length 100 m is attached to the last 100 m length of the existing pipe, what is the increase in discharge? (A) 0% (B) 35% (C) 50% (D) 65% Q. No Carry One Mark Each 56. If the denominator is increases by 0% and the numerator is diminished by 10%, the value of the fraction is 1/6. The original fraction is? (A) 5/4 (B) 7/4 (C) 4/7 (D) 14/3 57. If the side of a square is increased by 0%, its area is increased by? (A) 4% (B) 0 % (C) 44 % (D) 40 % Common data for Questions 58 and 59: From the given options, choose the pair of words which has a Relationship similar to that expressed in the question pair. 58. LYING: PERJURY (A) statement: testimony (B) seeing : observing (C) taking: stealing (D)eating : dining 59. PREHTSTORIC: MEDIEVAL (A) Akbar: British (B) present: future (C) Shakespeare: Tennyson (D)colossus: elephant 60. Find the next number of series, 8, 4, 1, 48, 144, 7, 88, 864, (A) 43 (B) 178 (C) 48 (D) 174 Q. No Carry Two Marks Each Common data for Questions 63 and 65: Rang Barsey Paint Company (RBPC) is in the business of manufacturing paints. RBPC buys RED, YELLOW, WHITE, ORANGE, and PINK paints. ORANGE paint can be also produced by mixing RED and YELLOW paints in equal proportions. Similarly, PINK paint can also be produced by mixing i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

11 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 10 equal amounts of RED and WHITE paints. Among other paints, RBPC sells CREAM paint, (formed by mixing WHITE and YELLOW in the ratio 70:30) AVOCADO paint (formed by mixing equal amounts of ORANGE and PINK paint) and WASHEDORANGE paint (formed by mixing equal amounts of ORANGE and WHITE paint). The following table provides the price at which RBPC buys paints. 61. The cheapest way to manufacture AVOCADO paint would cost (A) Rs per litre (B) Rs per litre (C) Rs.0.00 per litre (D) Rs.0.5 per litre 6. WASHEDORANGE can be manufactured by mixing (A) CREAM and RED in the ratio 14:10 (B) CREAM and RED in the ratio 3:1 (C) YELLOW and PINK in the ratio 1:1 (D) RED, YELLOW, and WHITE in the ratio 1:1: 63. Assume that AVOCADO, CREAM, and WASHEDORANGE each sells for the same price. Which of the three is the most profitable to manufacture? (A) AVOCADO. (B) CREAM. (C) WASHEDORANGE. (D) Sufficient data is not available. 64. The distance between two stations A and B is 600 km. One train leaves station A towards station B at the average speed of 54 kmph. After an hour another train left station B towards station A at the average speed of 66 km per hour. The distance from station A where the two trains meet is? (A) 7.7 km (B) 99.7 km (C) km (D) km 65. If log 3, log 3 (x 5), log 3 (x 7/) are in arithmetic progression, then the value of x is equal to (A) 5 (B) 4 (C) (D) 3 i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

12 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 11 Answer Key 1 A 11 B 1 D 31 A 41 D 51 B 61 B D 1 B B 3 D 4 B 5 A 6 D 3 B 13 D 3 C 33 A 43 A 53 A 63 B 4 A 14 D 4 D 34 C 44 B 54 B 64 B 5 A 15 B 5 A 35 B 45 C 55 B 65 B 6 D 16 D 6 A 36 C 46 C 56 D 7 B 17 A 7 A 37 A 47 B 57 C 8 A 18 D 8 C 38 A 48 D 58 A 9 D 19 A 9 C 39 B 49 A 59 B 10 C 0 C 30 B 40 C 50 A 60 A 7. According to Newton s law of viscosity, du du = μ = dy = dy 0.5 = kg / m 9. r0 1 m v = Umax (1 r/ r0 ) π rdr A 1. 0 r0 = 1 m Umax (1 r/ r0 ) π rdr π r = U x max 1 ( m+ )( m+ ) 1 1 lim = Letf ( x) = x 0+ 0x x 1 lim = x x since lim f x f x ( x) ( ) lim ( ) x 0+ 0 x 0 0 lim f doesn't exist. taking 1 r = z r Since, the derivative at a point tells us nothing about the function at any other point y x 1 1 = ( ) or, 3 + y x or, y = x 1 7. Characteristic equation: 3 λ = λ i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

13 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 1 ( )( ) or, 3 λ 1 λ + 8 = 0 or, λ λ + 5 = 0 ± 4 0 ± i 16 ± i 4 λ = = = = 1 ± i λ= 1+ i Associated eigen vector: AX= ( 1+i) X or, i x y = 0 4x + i y = 0 ( ) ( ) ( ) i ( ) 4 + i = 0 the two equations are identical ( 1-i) x y = 0 Put x = c y = ( 1 i) c x 1 X = = c y 1 i 1 Eigen vector corresponding to λ=1-i is d 1 + i where c, d are arbitrary numbers. 8. f ( x) is defined if x > 0 and x x ( x ) ( x ) 9. ie.. x 3 > 0 x >, x > 3 or, x > 0 x 3 < 0 x <, x < 3 x < 0 Domain: (0,) (3, ). x + 15 = 8 x when x > 0 ( x 3)( x 5) = 0 x = 3,5 x + 15 = 8 x when x < 0 x + 3 x + 5 = 0 x = 3, 5 ( )( ) 30 0: the point of discontinuity sin x 1 sin x = p p x x 1 x sin x 1 p p x x 1 π dx Also, converges only if p - 1 < 1, p x 1 0 (A) > 0 3 > 0 i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

14 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) Bernoulli s equation at section A and B p v p v A + A B B Z + = + A Z + + B hl ρg g ρg g ( 30) ( 30) = h hl = = 5m 37. Bernoulli s equation V1 Pexit V = A1V1 = 0.04 v1 = 4;A V = 0.04 V = 16 P = 30N/cm exit 38 d ( ) 39. ( ρ Av) = ( ρ Av) V = C gh = = 6.4m / s i i in i i out = v v = 5m/s 40. AV 1 1 = AV 4V1 = V P1 V1 P V Bernoulli's equation, ρg + g = ρg + g 15V ( P P ) 1 1 = 1 = = g 1000g ( V V ) ( ) c V 16 4m/s 1 hc = = = 1.816m g 9.8 Q Q V1 = = 7.96m / s V = = 1.99m / s π π d1 d p U 1 p avg 1 uavg = R umax = R = 8μ x 4μ x u 43. Shear stress at the pipe wall is given by: 1dp dp 8μu dx dx t max 44. τ= t; = τ= 50N / m 45. VD R e =ρ as R e increases μ turbulance increases c max L p r τ= =. = 0.1kPa x 10 i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

i-gatementor Test Series for GATE 013- Mock Test (Mechanical) 14 47. δ δ 3 x u y y δ δ = 1 dy y U = + = 3 0 δ 3δ 0 48. ψ ψ ^ ^ u = = y, v= = x v= yi x j y y 49.

15 i-gatementor Test Series for GATE 013- Mock Test (Mechanical) δ δ 3 x u y y δ δ = 1 dy y U = + = 3 0 δ 3δ ψ ψ ^ ^ u = = y, v= = x v= yi x j y y 49. at point (1,1), V (1,1) = m/ s, at point (,), V (,) = 4 ms; change in pressure (4 ) ( ) = = 1000 N / m & 53 Let h be the height of water over the gate. AE = h AE h AD = = 0 sin 60 3 h Area of gate immersed in water 3 3hm = = 3 Depth of C.G. of the immersed area = Total force F = h =ρ g 3h = ρ 3 gh N h h = = 0.5h 0. IG sin θ Centre of pressure of immersed area h = + h Ah h E F A 0 60 C 6m D B h h ( ) IG = M.O.I. = b AD = 3 = h sin 60 h h h h h* = CH = + = = 3 3 3h h 6 3 CH h 4h = = =, Now, CD sin h 4h h AC = AD CD = = taking moments about A h 3 h W 6=F = ρ g 3 h 3 3, 3 3, Total force F= 3 gh ρ = 56. Let the fraction be y x 45.35kN h = 3.8m The numerator i.e. x is reduced by 10 % so it becomes 10 x x = 0. 9x 100 i-gatementor,a-13, Street 7, Smriti nagar, Bhilai , Contact ,Mobile

16 igate Mechanical Mock Test II With Solution By Mr Arvind Rai Publisher : igate Author : Type the URL : Get this ebook

UNIT I FLUID PROPERTIES AND STATICS

UNIT I FLUID PROPERTIES AND STATICS SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: II-B.Tech & I-Sem Course & Branch: