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Mechanical Engineering Questions and Answers June 12, 2021

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Let w x2 y2 z2 , xintegeral sin(phi)cos(theta), yintegeral sin(phi)sin(theta), zintegeral cos(phi). Find partialWpartial(integeral), partialWpartial(theta)

Find the extreme values of f(x,y) 3x22xyy28y.

Locate all relative extreme and Saddle point of f(x, y) 4xyx4y4

Find the absolute maximum Minimum value of f(x,y) 3xy6x3y7 on the closed triangular region R with vertices (0,0),(3,0),(0,5)

Find the extreme value of f(x,y) x22y2x on the region R, where R is x2 y2

Use Polar coordinates to evaluate the double integral 16x2y2 da, where R is the region is the first quadrant of the circle x2y216.

Find the area is the first quadrant bounded by the Xaxes and the Curves x2 y2 10, y2 9x.

Find the are of the first quadrant of the ellipse x2a2 y2b2 1.

Using double integral, find the area lyng between the parabola y4xx2 the line yx.

Evaluate triple integeral z dv, where v be region is the first octant that is cut from the cylindrical solid y2z2

Evaluate triple integral xyz dxdydz , taken throughout the volume of the sphere x2y2z21 lying in the first octant.

Find the volume of the cylinder x2y24 bounded by the planes Z0 Z3 plane.

Find the volume bounded by the cylinder x2y24 the planes yz0 z0.

Find the volume common to the cylinders x2 y2 a2 and x2 z2 a2.

Find the volume bounded by the co ordinates planes and the plane xa yb zc 1.

Evaluate double integeral (x2y2)dxdy, over the region is the ve quadrant for which xy

Evaluate double integeral x2 dydx, where R is the two dimensional region bounded by the curves yx yx2.

Evaluate double integeral y2 dxdy, where R is region bounded by the parabola y24x, x24y.

A large slab of 100 cm thickness and of thermal conductivity of 2 W/mK is heated from one side and the temperature distribution across the slab as measured by the thermocouples approximates to the following relation: T =100 - 100x + 12x 2 +30x 3 - 20x 4 where T is temperature in C and x in meters considering an area of 10 m 2 , the rate of heat

A piece of lead (sp. Gr. 11.3) is tied to a 130 cc of cork whose specific gravity is 0.25. They float just submerged in water. What is the mass of the cork

A spring system assembly with nodes 1 and 2 are fixed at both ends. Calculate the global stiffness matrix for the given spring system in figure. The spring constants are given, ki 100 Nm and k2500 Nm.

b) A Venturimeter whose throat diameter is 13rd of pipe diameter is fitted in a horizontal pipe of 300 mm diameter carrying water. The pressure in pipeline is 13.8 Ncm (gauge) and,vacuum in throat is 37.5 cm of mercury. Determine the rate of flow through the pipeline. Take (6) Cd0.98.

A submarine moves horizontally in sea and has its axis below the water surface. A pitot tube is placed in front of the submarine along its axis is connected to the two limbs of a Utube containing mercury. The difference in mercury level is found to be 170 mm. Find the speed of submarine in kmhr, knowing that specific gravity of sea water is 1.025.

Find the head loss due to friction in a pipe of diameter 250mm and length 60m, through which water is flowing at a velocity of 3ms, using (i) Darcys formula and (ii) Chezys formula for which C 55 and kinematic viscosity 0.1 stoke.

. A pipe carrying water has a 30 cm x 15 cm venturimeter which is positioned inclined at 30 to the horizontal, the flow being upwards. The converging cone is 45 cm in length and the co efficient of discharge of the meter is 098. A differential U tube manometer with mercury as indicating fluid is connected to the inlet and to the throat and shows a

Determine the total pressure and position of centre of pressure on an isosceles triangular plate of base 5m and altitude 5m when the plate is immersed vertically in an oil of specific (6) gravity 0.8. The base of the plate is 1m below the free surface of oil. motacentric height.

A solid cylinder of diameter 5m has a Hight of 4m Find the metacentric height of the cylinder. If the specific gravity of the material of the cylinder is 0.7 and is floating in the water with its axis vertical. State whether the equilibrium is stable or unstable.

b) A triangular plate of base width 2m and height 3m is immersed in water with its plane making an angle of 60 with the free surface of water. Determine the hydrostatic pressure force and the centre of pressure when the apex of the triangle lies 5m below the free water surface

A Utube differential mercury manometer is connected between two pipes X and Y. Pipe X contains a fluid (Sp.gr. 1.59) under a pressure of 103 kNm and pipe Y contains oil (Sp.gr. 0.8) under a pressure of 172 kNm Pipe X is 2.5 m above pipe Y. The mercury level in the limb connected to pipe X is 1.5 m below the centreline of pipe Y. The level of

(4) A vertical rectangular gate of 4m width and 2m depth is hinged at a point 0.25 m below the centre of gravity of the gate. If the top edge of gate is 5 m below free surface of water and total depth of water is 7 m, what horizontal force must be applied at the bottom to keep the gate closed

A rectangular pontoon 10m long 7m broad 2.5m deep weights 686.7KN. It carries on its upper deck an empty boiler of 5m diameter weighing 588.6 KN. The centre of gravity of the boiler and pontoon are at their respective centers along a vertical line. Find metacentric height and check the stability of the body. Weight density of sea water is 10.104

There are two goods. The demand for good 1 is q1 abp1 dp2 and that for good 2 is q2 a bp2 dp1 where a and b are strictly positive and d The production cost of each good is 0. 31) Are the goods differentiated 32) Suppose the goods are produced by the same firm (a monopoly). Calculate optimal prices. Compare the Lerner index and the inverse

Butler trucking company is an independent trucking company in southern California. A major portion of Butlers business involves deliveries throughout its local area. To develop better work schedules, the managers want to estimate the total daily travel time for their drivers. The managers believe that the total daily travel time would be closely

What is the kinetic energy of the electrons in electron volts as they strike the target?

What is the energy of the electrons in joules as they strike the target?

An X-ray tube has a current 2 mA when the accelerating potential is 40kv. Calculate the maximum speed of the electrons as they strike the target

A 200lb block rests on a horizontal plane. Find the magnitude of the force P required to give the block an acceleration of 10 fts to the right. The coefficient of kinetic friction between the block and the plane is meu.i 0.25.

The two blocks shown start from rest. The horizontal plane and the pulley are frictionless, and the pulley is assumed to be of negligible mass. Deter mine the acceleration of each block and the tension in each cord.

Determine the rated speed of a highway curve of radius p 400 ft banked through an angle 18. The rated speed of a banked highway curve is the speed at which a car should travel if no lateral friction force is to be exerted on its wheels.

30 2 m The bob of a 2m pendulum describes an arc of circle in a vertical plane. If the tension in the cord is 2.5 times the weight of the bob for the position shown, find the velocity and the acceleration of the bob in that position.

Using Cylindrical coordwriate evaluate triple integrate z dv where V is the region enclosed by the cylinder x2y24 bounded by the paraboloid zx2y2 and bounded by the xy plane.

Use Spherical coordinates to find the volume of the solid bounded above by the Sphere x2 y2 z216 and below by the Cone zx2 y2

Express the decimal number 5.232323....... as a fraction of two integer.

Find the rational representation of the recurring decimal number 0.412 412 412 using series.

Use Comparison test determine, whether the following Series Converges or diverges. sigma(infinity,n1) 1n 12.

Examine the convergence of 11.3.5 23.5.7 35.7.8 ........

Test the Convergence of the Series sigma(infinity, n1) 1n

Test the Convergence of the following Series sigma(infinity, n1) (nn1)n2.

Prove that the Series 1 12 13 14 15 ..... is convergent

Check whether the series sigma(infinity,K1) (1)k1 KkK is absolutely convergent or not.

Use the alternating series last to show that the series sigma(infinity,n1) (1)n1 n3n(n1) converge.

Determine the x, y, z components of the angular momentum Hp of the particle having a mass of m 4.4 kg about point P using scalar notation. (Figure 1) Express your answers using three significant figures separated by commas. (HP) (HP) (Hp), Submit 1 vec Request Answer wwwww. Review kg. ms

It is planned to insulate the shell of a heat exchanger. The outside diameter of the shell is 30cm, its outer surface temperature is at 280C and it may be assumed to be remains constant even after applying insulation on the shell. 32. If the outside surface heat transfer coefficient is 2, what is the maximum thermal conductivity of insulating

An insulated steam pipe of 160 mm inner diameter and 180 mm outer diameter is covered with insulation of 40 mm thickness and carries steam at 200C. K(pipe) 29 WmC, K(insulation) 0.23 WmC h (steam) 11.6 Wm C, h(air) 23.2 Wm C, If the temp of the air surrounding the pipe is 25C, the the rate of heat loss to the surroundings from the pipe of 5 m

Choose the correct option for the free convection. (a) Heat transfer coefficient depends on the characteristic length in case of laminar flow but it does not depend on characteristic length in case of turbulent flow (b) Heat transfer coefficient depends on characteristic length for both laminar and turbulent flows (c) Heat transfer coefficient

Water at 20C flows with a velocity of 10ms over a flat plate which is maintained at 80C. Find the thermal boundary layer thickness at 1.5m from the leading edge. Viscosity and thermal conductivity of water 4.510 Pas Pas and and 0.65 WmK are respectively. (a) 0.91 mm (c) 17.4 mm (b) 12.5 mm (d) 1.85 mm

Air is flowing at a velocity of 3ms perpendicular to a long pipe as shown in the figure. The outer diameter of the pipe is 6cm and the temperature at the outside surface of the pipe is maintained at 100C. The temperature of the air far from the tube is 30C.,Surface temperature100C Data for air Nu Kinematic Viscosity (v) 18x10 ms Thermal

Calculate superheat. Rrefrigerant SPsuction pressure SLT suction line temperature SHsuperheat 1. R 22 2. R 22 3. R 22 4. R 134a 5. R 134a 5. R 134a SP 74 PSIG SLT 54 F SP 68 PSIG SLT 48 F SP 20 PSIG SLT OF SP 40 PSIG SLT 55 F SP 44 PSIG SLT 56 F SP 22 PSIG SLT 33 F SP 5PSIG SLT 13F 8. R 410 SP 130 PSIG SLT 49F 9. R 410 SP 110 PSIG SLT 41F 10. R

Identify the cutting speed end mill. Table 42. Recommended Cutting Speeds and Feeds Turning Workpiece Material Aluminum Brass Copper Iron, cast (medium) Magnesium Steel Cold rolled Low carbon (annealed) Stainless (316) Note 1. Feeds same for all materials Dril diameter (n.) Feed (IPR) Table 4.3 Material Steel 300 300 Cemented Carbide Speed Feed
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In a refrigerator, the power rating impressed on the compressor is 1.2 kW. The circulating wire in the evaporator is 5 kW and the cooling water took away 10 kW from the condenser coil. The operating temperatures range is 18C and 0C and their corresponding latent heats are 170 kJ/kg and 230 kJ/kg and the difference between the liquid energy is 35

A water cooler using R12 refrigerant works between 30C to 9C. Assuming the volumetric and mechanical efficiency of the compressor to be 80 and 90 respectively, and the mechanical efficiency of motor to be 90, and 20 of useful cooling is lost into water cooler, find 1) The power requirement of the motor 2) Volumetric displacement of the compressor

If the pressure in the air shown in Figure P2.4 is increased by 10 kPa, what will be the magnitude of H will be nearest (initially H 16 cm) 4 m Air Water Fig. P2.4 H Hg

The idealized stress strain diagram of mild steel specimen is shown below. The modulus of resilience of the material is given by (MPa units) O 0.002 (a) 1.25 (c) 0.5 Oy250 MPa 1 0.004 E (b) 1 (d) 0.25

Find the strain energy stored due to bending of a steel prismatic bar of crosssection 22241 100 mm x 150 mm deep and 2 meters long acting as a cantilever supporting a load of 20 kN at the free end. ke E 200 kNmm. (a) 85.41 kNmm (c) 94.81 kNmm (b) 89.83 kNmm (d) 98.85 kNmm

The ratio of stresses developed in two steel bars, one of square (side 100 mm) cross section to the circular (D 100 mm) cross section bar whose strain energy is same when axially loaded of same length and same material is

A cantilever beam is subjected to following three different loading conditions (1) a concentrated load P at its free end (Fig. a) (II) a couple Mo at its free end (Fig. b) (III) both loads acting simultaneously (Fig. c) L energy is L energy is L (c) The flexural rigidity of the beam may be assumed as EI. The strain energy due to bending when both

Taking into account only the effect of normal stresses, the strain energy of the prismatic beam AB for the loading as shown in the figure below is (a) (c) P A a D 3 Pa 6EI Pa(a L) 6EI L (b) (d) B PaL 2EI Pa(a L) 2EI

A 25 kN load drops from a height h over a vertical wooden pole 350 mm in diameter and 5 m long. If the permissible compressive stress in wood is 20 Nmm. Find the permissible maximum height h. (Ewood 1.1 x 10Nmm) (a) 340.76 mm (esimo (b) 349.85 mm (c) 352.52 mm (d) 380.89 mm

A shaft can carry a torque of 5 kNm and a bending load of 5 kN.m with a factor of safety based on maximum shear stress theory as 2. If the shaft is subjected to a torque of 8.5 kNm and a bending load of 1.5 kNm, the corresponding factor of safety is (a) 2 (b) 1.8 (c) 1.6 (d) 1.4

A cantilever beam of span L subjected to a point load P, with flexural rigidity El. The strain energy due to bending is. PL (a) 3EI (c) PL 4EI (b) (d) PL 6EI PL 48EI

(c) Tmax,a Tmax,b (d) Tmax,a Tmax,b Tmax,c Tmax,d Tmax,c Tmax,d ,Which of the following options shows correct relation for maximum shear stress developed in the shaft carrying bending moment M and torque T a. M5 T 5 b. M 4 c. M 6 d. M 7 T 6 T4 T 3 (a) Tmax,a Tmax,b Tmax,c Tmax,d (b) Tmax,a Tmax,b Tmax,c Tmax,d

A steel rod 60 mm in diameter is 4 m long. A pull of 80 kN is suddenly applied to it. besprotoveh 200 GPa. Find the instantaneous Shia) 218002 Take E elongation. (a) 0.98 mm (c) 1.23 mm es (b) 1.13 mm que gober (d) 1.52 mm

and CAD In helical spring the slope of helix may be assumed small, is required to transmit a maximum pull of 0.5 kN and to extend 10 mm for 100 N load. G 80 GPa and f 100 MPa. The mean diameter of the coil is to be 80 mm. The diameter of wire is 12 mm. Calculate the no. of coils required (a) 21 (c) 12 (b) 41 (d) 14

A shaft is subjected to bending moment of 100 Nm and turning moment of 50 Nm. If the yield strength of material is 200 MPa. then the minimum allowable design diameter of shaft in mm according to maximum distortion energy theory is (mm). da

The twist at the free end of the shaft shown in figure is A 12 (a) (T 2T) l GJ B T2 12 (J Polar movement of Inertia of the shaft and G Modulus of Rigidity) (b) (c)(2TT) (d) GJ l C 2GJ T (T 2T) (2TT) l 2GJ

A weight of 20 N falls from a height of 200 mm on a rigid massless bar supported by two identical springs as shown in the figure below. K ww 20 N 1200 mm K L L If the maximum deflection of the spring is 10 mm, then the stiffness (K) of spring is Nmm.

A hollow shaft with 30 mm outside diameter, is required to transmit 1 kW at 60 rpm. The working stress is 50 MPa. The inside diameter of the shaft is (a) 24 mm (c) 30 mm (b) 28 mm (d) 35 mm

A wagon weighing 25 kN and moving at 4 kmhour is to be stopped at the bufferstop. Compute the number of closecoiled springs that would be required in the buffer stop to absorb the energy of motion during a compression of 250 mm. Each spring has 20 coils, made of 20 mm wire, the mean diameter of the coils being 200 mm. Take G0.84 10Nmm. X (a) 5 (c)

A solid and hollow shafts are transmitting the same power at a constant speed and subjected to the same maximum shear stress. The inside diameter of the hollow shaft is 23 of the outside diameter. The ratio of their weights is (a) 1.15 (b) 1.25 (c) 1.37 (d) 1.55

In a closely coiled helical spring having 100 mm mean diameter and made of 20 turns of 10 mm diameter steel wire. The spring carries an axial load of 100 N, modulus of rigidity 84 GPa. The shearing stress developed in the spring is MPa is 20 160 (b) (a) (c) 120 100 TU P (d) TU 80 T

(A) (1) (C) (2) (3) I K LIL 22 L (1) (2) (3) alo LK L LL 22 (B) (D) (1) L L (2) LIL 2 2 (3) (1) (2) (3) LIL 2 2 L L,There are three slabs placed side by side as shown in figure. Heat generation takes place in slab (2) only and thermal conductivity of slab (1) is greater than that of slab (3). Which one of the following profiles of heat flux is

A solid shaft is transmitting power with stress acting on it as shown in figure below. REBO T 100 MPa, d 10 mm Shear stress (T) is varying along the radius as 10 MPamm. If the shaft can transmit a maximum torque of 50 Nm, the factor of safety according to Trescas theory is (a) 1.80 (b) 3.6 (c) 2 (d) 7.2

In the four bar mechanism shown in figure, BC is parallel with AD. AB is vertical. DC makes an angle of 1350 with AD and has an instantaneous angular velocity of one radsec. The angular velocity of the couple BC is 90 (a) 1 radsec 60 cm (c) 13 radsec 135 ads UR 20 cm D (b) zero 1 (0) 18 CON radsec

In the mechanism shown in figure, a, b, c, d are link lengths and they satisfy the equation a b c d, b c a d, b d 2a. Member c is neither smaller nor longer. The mechanism is of the type b C a d (a) Crank Crank (b) Crank Rocker (c) Rocker Crank (d) Rocker Rocker

Heat is generated uniformly in a 4 cm 2.4 diameter, 12cm long solid bar (k WmK). The temperature at the center and at the surface of the bar are measured to be 210C and 45C respectively. The rate of thermal energy generation within the bar is Watt.

In a parallelogram type fourbar mechanism. the motion of the coupler is (a) pure rotational (b) pure translational (c) both a and b (d) neither a nor b

A brick wall of 20cm thickness has thermal conductivity of 0.7 WmK. An insulation of thermal conductivity 0.2 WmK is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75. The same temperature difference is maintained across the wall before and after applying the insulation. The required thickness (in

In the mechanism shown in figure, AB and DC are vertical, BC is horizontal. AB 30 cm, BC 40 cm and the velocity ratio is 2 The length of the fixed link, is

The bottom face of a horizontal slab of thickness 6mm is maintained at 300C. The top face is exposed to a flowing gas at 30C. The thermal conductivity of the slab is 1.5 WmK and the convective heat transfer coefficient is 30 WmK. At steady state, the temperature (in C) of the top face is

The degrees of freedom for the planar linkage shown in figure below is aloit fi (a) 1 (b) 2 (c) 3 (d) 0

The lining of box type furnace is made up of a refractory layer and steel plate as shown in the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the outer steel surface is 473 K. If the steady state heat flux through the refractory steel plate composite is 1600 Wm, and heat flow is along xdirection only, the

A wall of thickness 5 mm is heated by a hot gas flowing along the wall. The gas is at a temperature of 3000 K, and the convective heat transfer coefficient is 160 WmK. The wall thermal conductivity is 40 WmK. If the colder side of the wall is held at 500 K, the temperature of the side exposed to the 62 hot gas is (a) 549.02C (c) 276.02 K (b)

Heat conduction through spherical wall is given by QkAm (TT) ( 1) where Am is SE the a) Arithmetic mean area (b) Geometric mean area (c) Logarithmic mean area (d) Harmonic mean area

The configuration of a mechanism is shown in the figure, where the link AB is collinear with link AD and both are horizontal. The link DC is vertical. The link AB has an instantaneous angular velocity of 3 radsec in CCW direction. AB 10 cm, BC 50 cm, CD 30 cm, AD 50 cm. The angular velocity of link DC is A B (a) 34 radsec CCW (b) 43 radsec CW

A masonary wall (k 0.75 WmK) transfers 80 of the heat loss through another wall (k 0.25 WmK, x 100 mm). If the temperature difference across both the walls is same, the thickness of masonary wall would be (a) 150 mm (c) 300 mm (b) 240 mm (d) 375 mm

A circular disc cam with an oscillating follower is shown in figure. If the cam rotates at a constant speed of 1000 rpm counter clockwise, the angular velocity of follower is (rads).

The heat generated in a solid sphere of radius R is q (Wm). The constant heat flux (q) from surface of sphere is 2q qR qR 2 R 3 (a) (b) ligus (c) 3q (d) R