List of top Fluid Mechanics and Thermal Sciences Questions

Heat is being removed from a refrigerator at a rate of 300 kJ/min to maintain its inside temperature at \( 2^\circ \text{C} \). If the input power to the refrigerator is 2 kW, the coefficient of performance of the refrigerator is _________.
\text{[round off to one decimal place]}
In an ideal Otto cycle, 800 kJ/kg is transferred to air during the constant volume heat addition process and 381 kJ/kg is removed during the constant volume heat rejection process. The thermal efficiency in % of the cycle is _________.
The dimensionless number defined by the ratio of inertial force to viscous force is called
A small capillary tube of 3 mm inner diameter is inserted into a fluid having density 900 kg/m\(^3\), surface tension 0.1 N/m, and contact angle 30°. The rise in the height of fluid in the capillary tube due to surface tension is

Consider the open feed water heater (FWH) shown in the figure given below: Specific enthalpy of steam at location 2 is 2624 kJ/kg, specific enthalpy of water at location 5 is 226.7 kJ/kg and specific enthalpy of saturated water at location 6 is 708.6 kJ/kg. If the mass flow rate of water entering the open feed water heater at location 5 is 100 kg/s then the mass flow rate of steam at location 2 will be \(\underline{\hspace{2cm}}\) kg/s (round off to one decimal place).

An object is moving with a Mach number of 0.6 in an ideal gas environment, which is at a temperature of 350 K. The gas constant is 320 J/kg.K and ratio of specific heats is 1.3. The speed of object is \(\underline{\hspace{1cm}}\) m/s (round off to the nearest integer).
A rigid tank of volume 50 m³ contains a pure substance as a saturated liquid-vapour mixture at 400 kPa. Of the total mass of the mixture, 20% mass is liquid and 80% mass is vapour. Properties at 400 kPa are: \( T_{\text{sat}} = 143.61 \, \text{°C}, \, v_f = 0.001084 \, \text{m³/kg}, \, v_g = 0.46242 \, \text{m³/kg} \). The total mass of liquid-vapour mixture in the tank is \(\underline{\hspace{1cm}}\) kg (round off to the nearest integer).
Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is 300 m/s, temperature is 330 K and pressure is 180 kPa. Assume that the air behaves as a perfect gas with constant \(c_p = 1.005 \, \text{kJ/kg.K}\). The stagnation temperature at this point is \(\underline{\hspace{1cm}}\) K (round off to two decimal places).
A two dimensional flow has velocities in \( x \) and \( y \) directions given by \( u = 2xyt \) and \( v = -y^2 t \), where \( t \) denotes time. The equation for the streamline passing through \( x = 1, y = 1 \) is
Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?
For a two-dimensional, incompressible flow having velocity components \(u\) and \(v\) in the x and y directions, respectively, the expression \[ \frac{\partial(u^2)}{\partial x} + \frac{\partial(uv)}{\partial y} \] can be simplified to:
In forced convective heat transfer, Stanton number (St), Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr) are related as
Ambient pressure, temperature, and relative humidity at a location are 101 kPa, 300 K, and 60%, respectively. The saturation pressure of water at 300 K is 3.6 kPa. The specific humidity of ambient air is \(\underline{\hspace{2cm}}\) g/kg of dry air.
Consider an ideal vapour compression refrigeration cycle working on R-134a refrigerant. The COP of the cycle is 10 and the refrigeration capacity is 150 kJ/kg. The heat rejected by the refrigerant in the condenser is \(\underline{\hspace{1cm}}\) kJ (round off to the nearest integer).

An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the quality of the indoor air, the intake duct supplies a mixture of fresh air with a cold air stream. The two streams are mixed in an insulated mixing chamber located upstream of the intake duct. Cold air enters the mixing chamber at 5°C, 105 kPa with a volume flow rate of 1.25 m³/s during steady state operation. Fresh air enters the mixing chamber at 34°C and 105 kPa. The mass flow rate of the fresh air is 1.6 times of the cold air stream. Air leaves the room through the exit duct at 24°C. 

Assuming the air behaves as an ideal gas with \(c_p = 1.005 \, \text{kJ/kg.K}\) and \(R = 0.287 \, \text{kJ/kg.K}\), the rate of heat gain by the air from the room is ________ kW (round off to two decimal places).

A cylindrical jet of water (density = 1000 kg/m³) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The plate is resting on a linear spring with a spring constant \( k = 1 \ \text{kN/m} \). The incoming jet diameter is \( D = 1 \ \text{cm} \). 

If the spring shows a steady deflection of 1 cm upon impingement of the jet, then the velocity of the incoming jet is ________ m/s (round off to one decimal place).
 

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).
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 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).
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).