List of top Fluid Mechanics and Thermal Sciences Questions

The fundamental thermodynamic relation for a rubber band is given by 
\[ dU = TdS + \tau dL \] where \( T \) is the absolute temperature, \( S \) is the entropy, \( \tau \) is the tension in the rubber band, and \( L \) is the length of the rubber band.
Which one of the following relations is CORRECT: 
 

An uninsulated cylindrical wire of radius 1.0 mm produces electric heating at the rate of 5.0 W/m. The temperature of the surface of the wire is 75°C when placed in air at 25°C. When the wire is coated with PVC of thickness 1.0 mm, the temperature of the surface of the wire reduces to 55°C. Assume that the heat generation rate from the wire and the convective heat transfer coefficient are same for both uninsulated wire and the coated wire. The thermal conductivity of PVC is _________ W/m.K (round off to two decimal places).
A solid sphere of radius 10 mm is placed at the centroid of a hollow cubical enclosure of side length 30 mm. The outer surface of the sphere is denoted by 1 and the inner surface of the cube is denoted by 2. The view factor \( F_{22} \) for radiation heat transfer is _________ (rounded off to two decimal places).
Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is 20 kJ/kg. The work output from the high pressure turbine is 750 kJ/kg. The work output from the low pressure turbine is 1500 kJ/kg. The thermal efficiency of the cycle is 50%. The enthalpy of saturated liquid and saturated vapor at condenser pressure are 200 kJ/kg and 2600 kJ/kg, respectively. The quality of steam at the exit of the low pressure turbine is _________ % (round off to the nearest integer).
A rigid insulated tank is initially evacuated. It is connected through a valve to a supply line that carries air at a constant pressure and temperature of 250 kPa and 400 K respectively. Now the valve is opened and air is allowed to flow into the tank until the pressure inside the tank reaches 250 kPa at which point the valve is closed. Assume that the air behaves as a perfect gas with constant properties (cp = 1.005 kJ/kg.K, cv = 0.718 kJ/kg.K, R = 0.287 kJ/kg.K). Final temperature of the air inside the tank is _________ K (round off to one decimal place).
Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top plate moves with a constant velocity of U = 4 m/s. Separation between the plates is 5 mm. There is no pressure gradient in the direction of flow. The density of fluid is 800 kg/m$^3$, and the kinematic viscosity is \(1.25 \times 10^{-4}\) m$^2$/s. The average shear stress in the fluid is _________ Pa (round off to the nearest integer).
A pressure measurement device fitted on the surface of a submarine, located at a depth H below the surface of an ocean, reads an absolute pressure of 4.2 MPa. The density of sea water is 1050 kg/m$^3$, the atmospheric pressure is 101 kPa, and the acceleration due to gravity is 9.8 m/s$^2$. The depth H is _________ m (round off to the nearest integer).
In which of the following pairs of cycles, both cycles have at least one isothermal process?
Superheated steam at 1500 kPa, has a specific volume of 2.75 m\(^3\)/kmol and compressibility factor (Z) of 0.95. The temperature of steam is________°C (round off to the nearest integer).
A hot steel spherical ball is suddenly dipped into a low temperature oil bath. Which of the following dimensionless parameters are required to determine the instantaneous center temperature of the ball using a Heisler chart?
An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of \( \dot{Q}_1 \) to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes \( \dot{Q}_2 \). The ratio \( \dot{Q}_2 / \dot{Q}_1 \) is
The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapor equal to \( p_v \). The saturation pressure of water at 300 K is \( p_{sat} \). The correct relation for the air-water mixture is
A linear spring mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitude of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping in (N.s/m) is
Tmin=300 K,Tmax=1200K,Q=1200 KJ.Find work done.

 find total heat (Gate) find total heat