List of top Questions asked in GATE NM- 2024

Identify the type of flow from the time series plots of instantaneous fluid velocity (\( u \)) at a point.

A. \[ \begin{array}{l} I - \text{unsteady turbulent flow}; \\ II - \text{steady turbulent flow}; \\ III - \text{steady laminar flow}; \\ IV - \text{unsteady laminar flow}. \end{array} \]
B. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady turbulent flow}; \\ III - \text{unsteady laminar flow}; \\ IV - \text{steady laminar flow}. \end{array} \]
C. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady turbulent flow}; \\ III - \text{steady laminar flow}; \\ IV - \text{unsteady laminar flow}. \end{array} \]
D. \[ \begin{array}{l} I - \text{steady turbulent flow}; \\ II - \text{unsteady laminar flow}; \\ III - \text{unsteady turbulent flow}; \\ IV - \text{steady laminar flow}. \end{array} \]
 

A 10 m long pipe with inlet and outlet diameters of 40 cm and 20 cm respectively, is carrying an incompressible fluid with a flow rate of \( 0.04 \, \text{m}^3/\text{s} \). The ratio of the velocity at the outlet to that at the inlet is ………….. (rounded off to one decimal place).

An 80 m long barge with a rectangular cross-section of 12 m beam and 4 m draft floats at even keel. The transverse metacenter (KM) above the keel is ………. m.
 

A 100 m long ship has a cruising speed of 25 knots. A geometrically similar model of 4 m length is used for resistance prediction in a towing tank. The corresponding speed of the model is ………….. knots.

A cube-shaped pontoon with 200 tonnes of mass placed on it floats with a freeboard of 1 m in fresh water. When the mass is removed, the pontoon floats with a freeboard of 3 m. The length of the pontoon is ………. m (rounded off to two decimal places).
 

A simply supported beam is subjected to a concentrated moment \( M \) at the mid-span as shown in the figure. The magnitude of the bending moment at a distance of \( L/4 \) from the left support \( A \) is equal to: 

Consider a fluid between two horizontal parallel flat plates 5 mm apart as shown in the figure. The top plate of dimensions 0.5 m \( \times \) 2 m is towed with an applied horizontal force \( F \) of \( 0.01 \, \text{N} \), while the infinitely long bottom plate is kept fixed. The horizontal velocity profile between the plates is assumed to be linear. If the dynamic viscosity (\( \mu \)) of the fluid is \( 0.89 \times 10^{-3} \, \text{N}\text{-}\text{s}/\text{m}^2 \), then the towing velocity of the top plate is ………… \( \text{m/s} \) (rounded off to three decimal places). 

Consider a two-dimensional ship section as shown in the figure. About the point \( O \), let the sway added mass components be \( a_{22} \) and \( a_{24} \) and roll added moment of inertia be \( a_{44} \). The clockwise roll angle is considered positive. The roll added mass due to roll, about \( P \), which is at a distance \( z_p \) above \( O \), is given by: 

The open water characteristics of a propeller is shown in the figure. Match the labels in Column 1 with the corresponding descriptions in Column 2. 

Which one of the following \( p{-}h \) plots represents the ideal vapour compression cycle with intercooling? Here, \( p \) and \( h \) denote pressure and specific enthalpy respectively.

Which one of the following psychrometric processes is represented by the line 1-2 in the figure? 

A uniform flow, a point source of strength \( +\sigma \) at \( (a, 0) \) and a point sink of strength \( -\sigma \) at \( (-a, 0) \) are shown in the figure. The velocity potential \( \phi \) resulting from the superposition of these flow fields is given by 


 

Consider the \( 2\pi \)-periodic function defined by \( f(x) = \begin{cases} -1, & \text{if } -\pi < x \leq 0, \\ 1, & \text{if } 0 < x \leq \pi. \end{cases} \) 
Which of the following is/are correct about its Fourier series expansion, \( \frac{a_0}{2} + \sum_{n=1}^\infty a_n \cos nx + b_n \sin nx \)?

Consider the flow past a curved wall as shown in the figure. Which of the following statement(s) is/are correct? 

If \( X \) is a Poisson random variable with mean \( \mu = 1 \), then the conditional probability of the event \( \{ X \geq 2 \} \) given that the event \( \{ X \geq 4 \} \) has occurred, is ……… (rounded off to two decimal places).
 

The value of the triple integral \(\iiint (xy^2 + yz^3) \, dx \, dy \, dz\) over the region given by \(-1 \leq x \leq 1\), \(3 \leq y \leq 4\), \(0 \leq z \leq 2\), is .

A 4-cylinder, 4-stroke diesel engine operating at 3000 rpm has a compression ratio \(r\) of 12 and cut-off ratio \(r_c\) of 2.5. The temperature rise during the heat addition process is 2400 K. The efficiency of an air-standard diesel cycle is given by: \[ \eta = 1 - \frac{1}{r^{\gamma-1}} \left( \frac{r_c^\gamma - 1}{\gamma (r_c - 1)} \right). \] Assume the working fluid as air with a mass flow rate of 0.05 kg/s, \(\gamma = 1.4\), and \(C_p = 1.004 \, \text{kJ/kg-K}\). The power output of the engine is …… kW (rounded off to the nearest integer).
 

A single degree of freedom system has a mass, stiffness, and damping of 200 kg, 20 N/m, and 62 N-s/m respectively. For a forced oscillation system, if the excitation frequency is equal to the undamped natural frequency, then the dynamic magnification factor is  ………….(rounded off to three decimal places).
 

The wave spectrum and the ship heave Response Amplitude Operator (RAO) are shown in the figure. The variance of the heave motion is …… m\(^2\) (rounded off to three decimal places). 

Consider a thin-walled closed cylindrical steel vessel with an internal pressure of \(2 \, \text{N/mm}^2\). The inner diameter is \(1 \, \text{m}\), and the thickness of the wall is \(10 \, \text{mm}\). The hoop stress is ……….. \(\text{N/mm}^2\) (rounded off to one decimal place).

A propeller disc of diameter \(2 \, \text{m}\) produces a thrust of \(88 \, \text{kN}\) while advancing at a speed of \(5 \, \text{m/s}\) in fresh water of density \(1000 \, \text{kg/m}^3\). Based on the axial momentum theory, the propeller efficiency is ………….. % (rounded off to one decimal place).
 

Consider a rectangular plate with in-plane loads. The stress at an arbitrary angle \( \theta \) is given by \( \sigma_x \), \( \sigma_y \), and \( \tau_{xy} \) as shown in the figure. If the principal plane is at \( \theta = 45^\circ \), and the principal stresses are \( \sigma_x = 8 \, \text{N/mm}^2 \) and \( \sigma_y = 3 \, \text{N/mm}^2 \), then the corresponding \( \tau_{xy} \) is …………… \( \text{N/mm}^2. \) 

A ship of 5000 tonnes displacement has a rectangular tank 6 m long and 10 m wide, half-filled with oil of relative density 0.8. The virtual reduction in the transverse metacentric height of the ship due to the free surface effect of the oil in the tank is ……….. cm.