List of top Questions asked in GATE ME

Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right. Pressure at location B is observed to be higher than that at an upstream location A. Which among the following options can be the reason?

Which of the following non-dimensional terms is an estimate of Nusselt number?

A polynomial \[ \varphi(s) = a_n s^n + a_{n-1} s^{n-1} + \cdots + a_1 s + a_0 \] of degree $n>3$ with constant real coefficients has triple roots at $ s = -\sigma $. Which one of the following conditions must be satisfied?

Which one of the following is the definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen?

A massive uniform rigid circular disc is mounted on a frictionless bearing at the end E of a massive uniform rigid shaft AE which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings AB and CD as shown, where G is the center of mass of the shaft-disc assembly and g is the acceleration due to gravity. The disc is then given a rapid spin $\omega$ about its axis in the positive x-axis direction as shown, while the shaft remains at rest. The direction of rotation is defined using the right-hand thumb rule. If the string AB is suddenly cut, assuming negligible energy dissipation, the shaft AE will

A structural member under loading has a uniform state of plane stress which in usual notations is given by $\sigma_x = 3P$, $\sigma_y = -2P$ and $\tau_{xy} = \sqrt{2}\,P$, where $P>0$. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of $P$ at which yielding starts (according to the maximum distortion energy theory) is

Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components A and B is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, including the solidus and liquidus lines, are straight lines. If this binary alloy with 15 weight % of B is poured into a mould at a pouring temperature of 800\,$^\circ$C, then the solidification range is ________________.

A shaft of diameter $25^{-0.04}_{-0.07}$ mm is assembled in a hole of diameter $25^{+0.02}_{+0.00}$ mm. Match the allowance and limit parameter in Column I with its corresponding quantitative value in Column II for this shaft–hole assembly.

$F(t)$ is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of $F(t)$?

Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral \[ \int_A \vec{F} \cdot d\vec{A} \] of the vector field \[ \vec{F} = 3x\,\hat{i} + 5y\,\hat{j} + 6z\,\hat{k} \] over the entire surface A of the cube is ________________.

Consider the definite integral \[ \int_{1}^{2} (4x^2 + 2x + 6)\, dx. \] Let I_e be the exact value. Using Simpson’s rule with 10 equal subintervals, the estimate is I_s.
The percentage error \[ e = 100 \times \frac{(I_e - I_s)}{I_e} \] is ________________.

The figure shows the relationship between fatigue strength (S) and fatigue life (N) of a material. The fatigue strength of the material for a life of 1000 cycles is 450 MPa, while its fatigue strength for a life of $ 10^6 $ cycles is 150 MPa. The life of a cylindrical shaft made of this material subjected to an alternating stress of 200 MPa will then be $\underline{\hspace{1cm}}$ cycles (round off to the nearest integer).

A cantilever beam with a uniform flexural rigidity $ EI = 200 \times 10^6 \, \text{N.m}^2 $ is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is 10000 N.m². The magnitude of the slope of the beam at its free end is $\underline{\hspace{1cm}}$ micro-radian (round off to nearest integer).

The wheels and axle system lying on a rough surface is shown in the figure.

Each wheel has diameter 0.8 m and mass 1 kg. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The diameter of axle is 0.2 m and its mass is 1.5 kg. Neglect the moment of inertia of the axle and assume $ g = 9.8 \, \text{m/s}^2 $. An effort of 10 N is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel axle system in horizontal direction is $\underline{\hspace{1cm}}$ m/s² (round off to one decimal place).

A block of negligible mass rests on a surface that is inclined at 30° to the horizontal plane as shown in the figure. When a vertical force of 900 N and a horizontal force of 750 N are applied, the block is just about to slide.

The coefficient of static friction between the block and surface is $\underline{\hspace{2cm}}$ (round off to two decimal places).

An adiabatic vortex tube, shown in the figure given below is supplied with 5 kg/s of air (inlet 1) at 500 kPa and 300 K. Two separate streams of air are leaving the device from outlets 2 and 3. Hot air leaves the device at a rate of 3 kg/s from outlet 2 at 100 kPa and 340 K, and 2 kg/s of cold air stream is leaving the device from outlet 3 at 100 kPa and 240 K.

Assume constant specific heat of air is 1005 J/kg.K and gas constant is 287 J/kg.K. There is no work transfer across the boundary of this device. The rate of entropy generation is $\underline{\hspace{2cm}}$ kW/K (round off to one decimal place).

A vertical shaft Francis turbine rotates at 300 rpm. The available head at the inlet to the turbine is 200 m. The tip speed of the rotor is 40 m/s. Water leaves the runner of the turbine without whirl. Velocity at the exit of the draft tube is 3.5 m/s. The head losses in different components of the turbine are: (i) stator and guide vanes: 5.0 m, (ii) rotor: 10 m, and (iii) draft tube: 2 m. Flow rate through the turbine is 20 m³/s. Take $ g = 9.8 \, \text{m/s}^2 $. The hydraulic efficiency of the turbine is $\underline{\hspace{1cm}}$ % (round off to one decimal place).

A high velocity water jet of cross section area = 0.01 m² and velocity = 35 m/s enters a pipe filled with stagnant water. The diameter of the pipe is 0.32 m. This high velocity water jet entrains additional water from the pipe and the total water leaves the pipe with a velocity 6 m/s as shown in the figure.

The flow rate of entrained water is $\underline{\hspace{1cm}}$ litres/s (round off to two decimal places).

Water flows out from a large tank of cross-sectional area $ A_t = 1 \ \text{m}^2 $ through a small rounded orifice of cross-sectional area $ A_o = 1 \ \text{cm}^2 $, located at $ y = 0 $. Initially the water level, measured from $ y = 0 $, is $ H = 1 \ \text{m} $. The acceleration due to gravity is $ 9.8 \ \text{m/s}^2 $.

Neglecting any losses, the time taken by water in the tank to reach a level of $ y = H/4 $ is $\underline{\hspace{2cm}}$ seconds (round off to one decimal place).

Ambient air flows over a heated slab having flat, top surface at $ y = 0 $. The local temperature (in Kelvin) profile within the thermal boundary layer is given by $ T(y) = 300 + 200 \exp(-5y) $, where $ y $ is the distance measured from the slab surface in meter. If the thermal conductivity of air is 1.0 W/m.K and that of the slab is 100 W/m.K, then the magnitude of temperature gradient $ \left| \frac{dT}{dy} \right| $ within the slab at $ y = 0 $ is $\underline{\hspace{1cm}}$ K/m (round off to the nearest integer).

A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at 300 K at a rate of 100 kg/s. The overall heat transfer coefficient is 1500 W/m².K, and total heat transfer area is 400 m². Steam condenses at a saturation temperature of 350 K. Assume that the specific heat of coolant water is 4000 J/kg.K. The temperature of the coolant water coming out of the condenser is $\underline{\hspace{1cm}}$ K (round off to the nearest integer).

A 76.2 mm gauge block is used under one end of a 254 mm sine bar with roll diameter of 25.4 mm. The height of gauge blocks required at the other end of the sine bar to measure an angle of 30° is $\underline{\hspace{2cm}}$ mm (round off to two decimal places).

The thickness, width and length of a metal slab are 50 mm, 250 mm and 3600 mm, respectively. A rolling operation on this slab reduces the thickness by 10% and increases the width by 3%. The length of the rolled slab is $\underline{\hspace{2cm}}$ mm (round off to one decimal place).

In pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be 400 N. The cutting velocity, $ V_c = 100 \ \text{m/min} $, depth of cut, $ t = 2.0 \ \text{mm} $, feed, $ s_0 = 0.1 \ \text{mm/revolution} $ and chip velocity, $ V_f = 20 \ \text{m/min} $, the shear strength $ \tau_s $ of the material will be $\underline{\hspace{2cm}}$ MPa (round off to two decimal places).

A surface grinding operation has been performed on a Cast Iron plate having dimensions 300 mm (length) $ \times $ 10 mm (width) $ \times $ 50 mm (height). The grinding was performed using an alumina wheel having a wheel diameter of 150 mm and wheel width of 12 mm. The grinding velocity used is 40 m/s, table speed is 5 m/min, depth of cut per pass is 50 μm and the number of grinding passes is 20. The average tangential and average normal force for each pass is found to be 40 N and 60 N respectively. The value of the specific grinding energy under the aforesaid grinding conditions is $\underline{\hspace{2cm}}$ J/mm³ (round off to one decimal place).