computer Science Question $1$: Heat Exchanger Design

Part A: Calculate the heat transfer rate required for a heat exchanger to cool $1500$ kg$/$hr of water from $85\backslash$deg C to $30\backslash$deg C$.$ Assume the specific heat capacity of water is $4\mathrm{.}18$ kJ$/$kg$\backslash$deg C$.$

Part B: Determine the logarithmic mean temperature difference $($LMTD$)$ for a counterflow heat exchanger if the hot fluid enters at $150\backslash$deg C and leaves at $90\backslash$deg C while the cold fluid enters at $30\backslash$deg C and leaves at $85\backslash$deg C$.$

Part C: Calculate the overall heat transfer coefficient if the heat exchanger has an area of $25$ m$^2.$

Part D: Using the effectiveness$-$NTU method, find the number of transfer units $($NTU$)$ for the heat exchanger.

Part E: Determine the heat exchanger effectiveness.

Question $2$: Gear Train Analysis

Part A: Design a gear train to achieve a speed reduction of $16$:$1$ using three gears. Specify the number of teeth on each gear.

Part B: Calculate the torque on the output shaft if the input shaft has a torque of $10$ Nm$.$

Part C: Determine the efficiency of the gear train if the power loss is $5\%.$

Part D: Calculate the stress on the gear teeth if the modulus of elasticity is $210$ GPa and the gear tooth form factor is $0\mathrm{.}3.$

Part E: Find the bending stress if the face width of the gears is $20$ mm$.$

Question $3$: Thermodynamic Cycle

Part A: Sketch a T$-$S diagram for an ideal Rankine cycle.

Part B: Calculate the thermal efficiency of the cycle if the steam enters the turbine at $3$ MPa and $350\backslash$deg C and is condensed at $10$ kPa.

Part C: Determine the work done by the turbine per kg of steam.

Part D: Calculate the work required by the pump per kg of water.

Part E: Find the heat added in the boiler per kg of steam.

Question $4$: Fluid Flow in Pipes

Part A: Calculate the Reynolds number for water flowing in a pipe with a diameter of $50$ mm at a velocity of $2$ m$/$s$.$ Assume the kinematic viscosity of water is $1$ x $10$ m$^2/$s$.$

Part B: Determine the friction factor using the Moody chart if the pipe is smooth.

Part C: Calculate the head loss due to friction for a $100$ m long pipe.

Part D: Find the power required to pump the water through the pipe.

Part E: Determine the pressure drop across the pipe.

Question $5$: Composite Beam Analysis

Part A: Design a composite beam made of steel and aluminum layers with a total depth of $200$ mm$.$ The steel layer is $100$ mm and the aluminum layer is $100$ mm$.$

Part B: Calculate the neutral axis position of the composite beam.

Part C: Determine the moment of inertia of the composite section.

Part D: Calculate the maximum stress in both steel and aluminum layers if a moment of $5000$ Nm is applied.

Part E: Find the deflection of the beam over a span of $4$ m$.$

Question $6$: Dynamic Analysis of a Rotating Shaft

Part A: Calculate the critical speed of a rotating shaft of length $2$ m with a diameter of $50$ mm$.$ Assume the modulus of elasticity is $200$ GPa.

Part B: Determine the natural frequency of the shaft if it is simply supported at both ends.

Part C: Find the deflection at the center of the shaft due to a load of $100$ N applied at the midpoint.

Part D: Calculate the torsional stiffness of the shaft.

Part E: Determine the maximum shear stress in the shaft if it is subjected to a torque of $150$ Nm$.$

Question $7$: Combustion Analysis

Part A: Calculate the stoichiometric air$-$fuel ratio for the complete combustion of octane $($C$8$H$18).$

Part B: Determine the amount of air required for the complete combustion of $1$ kg of octane.

Part C: Find the lower heating value $($LHV$)$ of octane if the higher heating value $($HHV$)$ is $44\mathrm{.}4$ MJ$/$kg and the latent heat of vaporization of water is $2\mathrm{.}45$ MJ$/$kg$.$

Part D: Calculate the flame temperature if the combustion takes place adiabatically and all the heat is used to raise the temperature of the products.

Part E: Determine the volume of exhaust gases produced at standard conditions.

Question $8$: Stress and Strain in a Cylinder

Part A: Calculate the hoop stress in a thin$-$walled cylinder with an internal pressure of $2$ MPa, an internal radius of $0\mathrm{.}5$ m$,$ and a wall thickness of $10$ mm$.$

Part B: Determine the longitudinal stress in the cylinder.

Part C: Find the maximum shear stress in the cylinder.

Part D: Calculate the volumetric strain if the material's modulus of elasticity is $200$ GPa and Poisson's ratio is $0\mathrm{.}3.$

Part E: Determine the change in diameter of the cylinder due to internal pressure.

Question $9$: Heat Transfer in Fins

Part A: Calculate the heat transfer rate from a fin with a length of $100$ mm$,$ a diameter of $10$ mm$,$ and a thermal conductivity of $200$ W$/$m$$K$.$ The base temperature is $150\backslash$deg C$,$ and the ambient temperature is $25\backslash$deg C$.$ Assume convective heat transfer coefficient is $50$ W$/$m$^2$K$.$

Part B: Determine the fin efficiency.

Part C: Find the fin effectiveness.

Part D: Calculate the temperature distribution along the fin length.

Part E: Determine the total heat loss from an array of $10$ such fins.

Question $10$: Power Transmission by Belt

Part A: Calculate the power transmitted by a belt drive if the tension in the tight side is $1000$ N$,$ the tension in the slack side is $400$ N$,$ and the belt speed is $15$ m$/$s$.$

Part B: Determine the belt tension ratio.

Part C: Find the coefficient of friction between the belt and the pulley if the angle of contact is $180\backslash$deg $.$

Part D: Calculate the torque on the driving pulley.

Part E: Determine the initial tension in the belt.

Question $11$: Vibration Analysis of a Mass$-$Spring System

Part A: Calculate the natural frequency of a mass$-$spring system with a mass of $5$ kg and a spring constant of $2000$ N$/$m$.$

Part B: Determine the damping coefficient if the system has a damping ratio of $0\mathrm{.}05.$

Part C: Find the damped natural frequency of the system.

Part D: Calculate the logarithmic decrement for the system.

Part E: Determine the amplitude of vibration if the system is subjected to a harmonic force of $100$ N at the resonance frequency.

Question $12$: Internal Combustion Engine Performance

Part A: Calculate the indicated power of a $4-$cylinder engine with a bore of $80$ mm$,$ a stroke of $100$ mm$,$ an indicated mean effective pressure of $1\mathrm{.}2$ MPa, and an engine speed of $3000$ rpm$.$

Part B: Determine the brake power if the mechanical efficiency is $85\%.$

Part C: Find the brake specific fuel consumption if the fuel consumption is $0\mathrm{.}1$ kg$/$min and the calorific value of the fuel is $42$ MJ$/$kg$.$

Part D: Calculate the thermal efficiency of the engine.

Part E: Determine the volumetric efficiency if the air intake volume is $0\mathrm{.}85$ m$^3/$min and the engine displacement volume is $1\mathrm{.}6$ liters per cycle.

Question $13$: Bending of Beams

Part A: Calculate the bending moment at the midpoint of a simply supported beam with a span of $6$ m and a uniformly distributed load of $2$ kN$/$m$.$

Part B: Determine the maximum bending stress if the beam has a rectangular cross$-$section with a width of $100$ mm and a height of $200$ mm$.$

Part C: Find the shear force at a section $2$ m from one end.

Part D: Calculate the deflection at the midpoint using the double integration method. Assume the modulus of elasticity is $200$ GPa.

Part E: Determine the slope at the ends of the beam.

Question $14$: Thermodynamic Properties of Gases

Part A: Calculate the specific volume of air at $500$ K and $1$ MPa using the ideal gas law. Assume R $=287$ J$/$kg$$K$.$

Part B: Determine the change in internal energy if the temperature of $1$ kg of air increases from $300$ K to $600$ K$.$ Assume Cv $=718$ J$/$kg$$K$.$

Part C: Find the change in enthalpy for the same temperature change. Assume Cp $=1005$ J$/$kg$$K$.$

Part D: Calculate the entropy change if the pressure remains constant during the temperature change.

Part E: Determine the final pressure if the air undergoes an isentropic expansion to double its initial volume.

Question $15$: Stress Analysis in a Beam

Part A: Calculate the maximum bending moment in a cantilever beam with a length of $3$ m and a point load of $500$ N at the free end.

Part B: Determine the bending stress at the fixed end if the beam has an I$-$section with a moment of inertia of $80$ x $10$ mm$^4$ and a depth of $300$ mm$.$

Part C: Find the shear stress at the fixed end if the beam has a width of $100$ mm what is network security $?$