List of top Fluid Mechanics and Thermal Sciences Questions

Consider steady one-dimensional heat conduction in a slab of thickness $2L$ (with $L=1$ m). Thermal conductivity varies as $k = C T$, with $C = 2$ W·m$^{-1}$·K$^{-2}$, and the slab generates heat at $1280$ kW/m$^3$. Both faces are held at 600 K. The temperature at $x=0$ is __________ K (in integer).
Saturated vapor at 200°C condenses to saturated liquid at 150 kg/s on the shell side of a heat exchanger (latent heat $h_{fg} = 2400$ kJ/kg). A fluid with $c_p = 4$ kJ·kg$^{-1}$·K$^{-1}$ enters the tube side at 100°C. Effectiveness = 0.9. The required tube-side mass flow rate is __________ kg/s (in integer).
A hydrodynamically and thermally fully-developed fluid of 1 kg/s flows in a uniformly heated pipe (diameter 0.1 m, length 40 m). A constant heat flux of 15000 W/m$^2$ is applied. The fluid enters at 200$^\circ$C. Given: Re = 85000, Pr = 5, $k = 0.08$ W/m·K, $c_p = 2600$ J/kg·K. Correlation: \[ \text{Nu} = 0.023\, \text{Re}^{0.8} \text{Pr}^{0.4} \] Find the pipe surface temperature at the exit (nearest integer).
A rigid tank (8 m$^3$) is filled with air from a pipeline at 600 kPa and 306 K. Heat loss during filling = 1000 kJ. Final tank pressure equals pipeline pressure. Final temperature is __________ K (rounded to nearest integer).
A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm, length = 8 m) is hinged at A at waterline. A lead sphere (specific gravity = 11.4) is attached at the free end to keep the rod submerged horizontally. Find the radius of the lead ball (in cm, round to 2 decimals).
A project consists of five activities (A, B, C, D, E). Each activity duration follows beta distribution. Three-time estimates are given and expected completion time is __________ weeks (in integer).
A cylindrical billet of diameter 100 mm and length 100 mm is directly extruded into an L-section. The extrusion pressure is given by \[ p = K_s\, \sigma_m \left[0.8 + 1.5\ln(r) + \frac{2l}{d_0}\right] \] where \( \sigma_m = 50\ \text{MPa} \), \( K_s = 1.05 \), \( d_0 = 100\ \text{mm} \). Find the maximum force at the start of extrusion (in kN).
The steady velocity field in an inviscid fluid of density 1.5 is given to be $\vec{V} = (y^{2} - x^{2})\hat{i} + (2xy)\hat{j}.$ Neglecting body forces, the pressure gradient at $(x = 1, y = 1)$ is ________________.
In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure with enthalpy 250 kJ/kg. The exit of the compressor is at 300 kJ/kg. COP of the cycle is 3. The refrigerant after condensation is throttled to evaporator pressure. If the enthalpy of saturated liquid at evaporator pressure is 50 kJ/kg, the dryness fraction at entry to evaporator is ________________.
A tube of uniform diameter $D$ is immersed in a steady flowing inviscid liquid stream of velocity $V$, as shown in the figure. Gravitational acceleration is $g$. The volume flow rate through the tube is ________________.
Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat at constant volume is \( c_v = 750\ \text{J kg}^{-1}\text{K}^{-1} \). A stirrer performs 225 kJ of work on the gas. Assume no heat interaction. The final pressure of the gas will be ________________ bar (integer).
The velocity field in a fluid is given to be \[ \vec{V} = (4xy)\,\hat{i} + 2(x^{2} - y^{2})\,\hat{j}. \] Which of the following statement(s) is/are correct?
Which one of the following is an intensive property of a thermodynamic system?
Which of the following non-dimensional terms is an estimate of Nusselt number?
Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right. Pressure at location B is observed to be higher than that at an upstream location A. Which among the following options can be the reason?

An adiabatic vortex tube, shown in the figure given below is supplied with 5 kg/s of air (inlet 1) at 500 kPa and 300 K. Two separate streams of air are leaving the device from outlets 2 and 3. Hot air leaves the device at a rate of 3 kg/s from outlet 2 at 100 kPa and 340 K, and 2 kg/s of cold air stream is leaving the device from outlet 3 at 100 kPa and 240 K. 

 

Assume constant specific heat of air is 1005 J/kg.K and gas constant is 287 J/kg.K. There is no work transfer across the boundary of this device. The rate of entropy generation is \(\underline{\hspace{2cm}}\) kW/K (round off to one decimal place). 
 

A vertical shaft Francis turbine rotates at 300 rpm. The available head at the inlet to the turbine is 200 m. The tip speed of the rotor is 40 m/s. Water leaves the runner of the turbine without whirl. Velocity at the exit of the draft tube is 3.5 m/s. The head losses in different components of the turbine are: (i) stator and guide vanes: 5.0 m, (ii) rotor: 10 m, and (iii) draft tube: 2 m. Flow rate through the turbine is 20 m³/s. Take \( g = 9.8 \, \text{m/s}^2 \). The hydraulic efficiency of the turbine is \(\underline{\hspace{1cm}}\) % (round off to one decimal place).

A high velocity water jet of cross section area = 0.01 m² and velocity = 35 m/s enters a pipe filled with stagnant water. The diameter of the pipe is 0.32 m. This high velocity water jet entrains additional water from the pipe and the total water leaves the pipe with a velocity 6 m/s as shown in the figure. 

The flow rate of entrained water is \(\underline{\hspace{1cm}}\) litres/s (round off to two decimal places).

Water flows out from a large tank of cross-sectional area \( A_t = 1 \ \text{m}^2 \) through a small rounded orifice of cross-sectional area \( A_o = 1 \ \text{cm}^2 \), located at \( y = 0 \). Initially the water level, measured from \( y = 0 \), is \( H = 1 \ \text{m} \). The acceleration due to gravity is \( 9.8 \ \text{m/s}^2 \). 

Neglecting any losses, the time taken by water in the tank to reach a level of \( y = H/4 \) is \(\underline{\hspace{2cm}}\) seconds (round off to one decimal place).

Ambient air flows over a heated slab having flat, top surface at \( y = 0 \). The local temperature (in Kelvin) profile within the thermal boundary layer is given by \( T(y) = 300 + 200 \exp(-5y) \), where \( y \) is the distance measured from the slab surface in meter. If the thermal conductivity of air is 1.0 W/m.K and that of the slab is 100 W/m.K, then the magnitude of temperature gradient \( \left| \frac{dT}{dy} \right| \) within the slab at \( y = 0 \) is \(\underline{\hspace{1cm}}\) K/m (round off to the nearest integer).
A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at 300 K at a rate of 100 kg/s. The overall heat transfer coefficient is 1500 W/m².K, and total heat transfer area is 400 m². Steam condenses at a saturation temperature of 350 K. Assume that the specific heat of coolant water is 4000 J/kg.K. The temperature of the coolant water coming out of the condenser is \(\underline{\hspace{1cm}}\) K (round off to the nearest integer).

Temperature field inside a sphere of radius \( R = 1 \, \text{m} \) with origin at its center is \[ T(x, y, z) = 100 - 70x + 51y - 80z - 10x^2 - 20y^2 - 20z^2. \] If thermal conductivity of the sphere material is \( K = 50 \, \text{W/m.K} \) and Fourier law of heat conduction is valid, net heat leaving the sphere per unit time in W is _________. 
[round off to one decimal place]

A fluid with dynamic viscosity \( \mu = 1 \, \text{Pa.s} \) is flowing through a circular pipe with diameter 1 cm. If the flow rate (discharge) in the pipe is 0.2 liters/s, the maximum velocity in m/s of the fluid in the pipe is (assume fully developed flow and take fluid density \( \rho = 1000 \, \text{kg/m}^3 \)) _________.
A 3 mm thick steel sheet, kept at room temperature of 30ºC, is cut by a fiber laser beam. The laser spot diameter on the top surface of the sheet is 0.2 mm. The laser absorptivity of the sheet is 50%. The properties of steel are density = 8000 kg/m\(^3\), specific heat = 500 J/kg.°C, melting temperature = 1530ºC, and latent heat of fusion = \( 3 \times 10^5 \) J/kg. Assume that melting efficiency is 100% and that the kerf width is equal to the laser spot diameter. The maximum speed (in m/s) at which the sheet can be fully cut at 2 kW laser power is _________.
A circular tank of 4 m diameter is filled up to a height of 3 m. Assuming almost steady flow and neglecting losses, the time taken in seconds to empty the tank through a 5 cm diameter hole located at the center of the tank bottom (take acceleration due to gravity \( g = 9.81 \, \text{m/s}^2 \)) is [round off to the nearest integer].