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.
An ocean wave of period 8 s and height 2 m is propagating in the Indian Ocean from south to north. According to linear wave theory, for the wave to be considered as a deep-water wave, the minimum water depth should be …………. (rounded off to the nearest integer).
Consider a gas turbine combustor with air as the working fluid. The flow enters the device at 500 K and leaves at 1400 K with a mass flow rate of 0.1 kg/s. The changes in kinetic energy and potential energy of the flow are neglected. Assuming \( C_p = 0.717 \, \text{kJ/kg-K} \) and \( R = 0.287 \, \text{kJ/kg-K} \), the rate of heat addition is kW (rounded off to the nearest integer).
Consider a circular cylinder of diameter 0.5 m and length 2 m, rotating in clockwise direction at a speed of 100 rpm in a flow of velocity 2 m/s. Assume the density of the fluid as 1.225 kg/m\(^3\) and \( \pi = 3.14 \). By Kutta-Joukowski theorem, the lift force on the cylinder is \(\_\_\_\_\_\) N (rounded off to the nearest integer).
A fully filled water tank OABCD has a circular arc (AB) of radius 10 m at the bottom as shown in the following figure. The height BC is 10 m. The length OA and CD are 5 m and 15 m, respectively. The density of the water is \(\rho\) kg/m³ and the acceleration due to gravity is \(g\) m/s². The magnitude of the resultant hydrostatic force per unit width acting on AB in N/m lies between
Consider a truss as shown in the following figure. The length of each member is 2 m. The area of cross section of each member is 100 \(mm^2\) and Young's modulus is \(2 x 10^5 N/mm^2\). The vertical deflection at C is .................... mm (round off to one decimal place)
A marker buoy of mass 1500 kg floating in sea water of density 1025 kg/m³, consists of a cylinder and cone as shown in the following figure. The buoy is suitably ballasted to make it stable in the floating condition. The buoy is subjected to an external periodic excitation force in Newton, \(F_e(t) = 2000 \sin (1.25 t)\). Ignore damping effects and assume g = 9.81 m/s², added mass = 25% of the mass of the buoy. The maximum heave response amplitude of the buoy is .................... m (round off to one decimal place)
An air-standard diesel cycle, as shown in the following figure with a compression ratio of 16, has an initial pressure 0.9 bar and temperature 300 K. Assume \(\gamma = 1.4\) and \(C_p = 1.004\) kJ/kg-K. If the heat added during the constant pressure process is 900 kJ/kg, then the peak temperature during the cycle is .................... K (round off to the nearest integer)
A simple vapor compression refrigeration cycle with ammonia as the working fluid operates between 30°C and -10 °C as shown in the following figure. The saturated liquid and vapor enthalpies at 30 °C and -10 °C are provided in the table below. If the COP of the cycle is 5.6, the specific enthalpy at the inlet to the condenser is .................... kJ/kg (round off to the nearest integer)
A vessel of 100 m length has a constant triangular cross-section with a depth of 12 m and breadth of 15 m as shown in following figure. The vessel has a vertical center of gravity (KG) = 6.675 m. The minimum draft (d), at which the vessel will become stable is .................... m (round off to one decimal place)
