Computer science Problem $1$: Thermodynamics $-$ Gas Power Cycle

A gas turbine power plant operates on an ideal Brayton cycle with regeneration. The pressure ratio across the compressor is $10.$ Air enters the compressor at $300$ K and $100$ kPa and leaves at $800$ K$.$ The turbine inlet temperature is $1400$ K$,$ and the isentropic efficiencies of the compressor and turbine are $85\%$ and $90\%,$ respectively.

Determine the temperature and pressure at all points in the cycle.

Calculate the thermal efficiency of the cycle without regeneration.

If the regenerator effectiveness is $70\%,$ find the thermal efficiency of the cycle with regeneration.

Determine the back work ratio and the net work output per unit mass of air.

Problem $2$: Fluid Mechanics $-$ Pipe Flow

Water flows through a horizontal pipe with a varying diameter. The pipe diameter at section $1$ is $10$ cm and at section $2$ is $5$ cm$.$ The flow rate of water is $0\mathrm{.}02$ m$^3/$s$.$

Determine the velocity of water at sections $1$ and $2.$

Calculate the pressure difference between sections $1$ and $2$ if the head loss due to friction is $2$ m$.$

If the pipe length between sections $1$ and $2$ is $100$ m$,$ find the Darcy$-$Weisbach friction factor.

Determine the Reynolds number at both sections and state whether the flow is laminar or turbulent.

Problem $3$: Heat Transfer $-$ Conduction and Convection

A composite wall consists of three layers: a $5$ cm thick layer of brick $($k $=0\mathrm{.}7$ W$/$m$$K$),$ a $10$ cm thick layer of insulation $($k $=0\mathrm{.}04$ W$/$m$$K$),$ and a $2$ cm thick layer of plaster $($k $=0\mathrm{.}5$ W$/$m$$K$).$ The inner surface temperature is maintained at $100\backslash$deg C and the outer surface temperature is $20\backslash$deg C$.$

Determine the overall thermal resistance of the wall.

Calculate the heat flux through the wall.

If the inner surface convective heat transfer coefficient is $10$ W$/$m$^2$K and the outer surface is exposed to ambient air at $20\backslash$deg C with a convective heat transfer coefficient of $15$ W$/$m$^2$K$,$ find the overall heat transfer coefficient.

Determine the temperature at the interface between the brick and insulation layers.

Problem $4$: Mechanics of Materials $-$ Beam Deflection

A simply supported beam of length $6$ m carries a uniformly distributed load of $5$ kN$/$m over its entire length. The beam is made of steel with a modulus of elasticity of $200$ GPa and a moment of inertia of $8\backslash$times $10$ mm$^4.$

Calculate the maximum bending moment in the beam.

Determine the maximum deflection of the beam.

If a concentrated load of $10$ kN is applied at the midpoint of the beam, find the new maximum bending moment.

Calculate the maximum deflection with the concentrated load applied. what is artificial intelligence