Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is $\text{300 m/s}$, temperature is $\text{330 K}$ and pressure is $\text{180 kPa}$. 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 _______ $\text{K} (\textit{round off to two decimal places}$).
Consider an ideal vapour compression refrigeration cycle working on $\text{R-134a}$ refrigerant. The $\text{COP}$ of the cycle is $10$ and the refrigeration capacity is $\text{150 kJ/kg}$. The heat rejected by the refrigerant in the condenser is __________ $\text{kJ/kg} (\textit{round off to the nearest integer}$).
A rigid tank of volume $50 \text{ m}^{3}$ contains a pure substance as a saturated liquid vapour mixture at $\text{400 kPa}$. Of the total mass of the mixture, $20\%$ mass is liquid and $80\%$ mass is vapour. Properties at $\text{400 kPa}$ ... $/kg}$. The total mass of liquid vapour mixture in the tank is _______ $\text{kg } (\textit{round off to the nearest integer}$).
An object is moving with a Mach number of $0.6$ in an ideal gas environment, which is at a temperature of $\text{350 K}$. The gas constant is $\text{320 J/kg.K}$ and ratio of specific heats is $1.3$. The speed of object is _________ $\text{m/s} (\textit{round off to the nearest integer}$).
A column with one end fixed and one end free has a critical buckling load of $\text{100 N}$. For the same column, if the free end is replaced with a pinned end then the critical buckling load will be _______ $\text{N}\; (\textit{round off to the nearest integer}$).
A steel cubic block of side $\text{200 mm}$ is subjected to hydrostatic pressure of $\text{250 N/mm}^{2}$. The elastic modulus is $2 \times 10^{5}\:\text{N/mm}^{2}$ and Poisson ratio is $0.3$ for steel. The side of the block is reduced by _________ $\text{mm}\: (\textit{round off to two decimal places}$).
Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{2})$ is ______ ($\textit{round off to two decimal places}$).
Daily production capacity of a bearing manufacturing company is $30000$ bearings. The daily demand of the bearing is $15000$. The holding cost per year of keeping a bearing in the inventory is $₹20$. The setup cost for the production of a batch is $₹1800$. Assuming $300$ working days in a year, the economic batch quantity in number of bearings is ______ ($\textit{in integer}$).
A cast product of a particular material has dimensions $75\: \text{mm} \times 125\: \text{mm} \times 20 \:\text{mm}$. The total solidification time for the cast product is found to be $2.0$ minutes as calculated using Chvorinov's rule having the index, $n =2$. ... $\text{50 mm}$, the total solidification time will be ______ minutes ($\textit{round off to two decimal places}$).
A spot welding operation performed on two pieces of steel yielded a nugget with a diameter of $\text{5 mm}$ and a thickness of $\text{1 mm}$. The welding time was $\text{0.1 s}$. The melting energy for the steel is $\text{20 J/mm}^{3}$. Assuming ... as $10\%$, the power required for performing the spot welding operation is ________ $\text{kW} (\textit{round off to two decimal places}$).
A surface grinding operation has been performed on a Cast Iron plate having dimensions $\text{300 mm} (\textit{length}) \times \text{10 mm} (\textit{width})\times\text{50 mm}({height}$). The grinding was performed using an alumina wheel having a wheel diameter ... specific grinding energy under the aforesaid grinding conditions is ______ $\text{J/mm}^{3} (\textit{round off to one decimal place}$).
In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be $\text{400 N}$. The cutting velocity, $V_{c}=100$ $\text{m/min}$, depth of cut, $\text{t= 2.0 mm}$, feed, $s_{0}=0.1 \text{ mm}$/ ... $\text{m/min}$, the shear strength, $\tau_{s}$, of the material will be ______ $\text{MPa} (\textit{round off to two decimal places}$).
The thickness, width and length of a metal slab are $\text{50 mm}$, $\text{250 mm}$ and $\text{3600 mm}$, respectively. A rolling operation on this slab reduces the thickness by $10\%$ and increases the width by $3\%$. The length of the rolled slab is ________ $\text{mm} \:(\textit{round off to one decimal place}$).
A $\text{76.2 mm}$ gauge block is used under one end of a $\text{254 mm}$ sine bar with roll diameter of $\text{25.4 mm}$. The height of gauge blocks required at the other end of the sine bar to measure an angle of $30^{\circ}$ is ______ $\text{mm} (\textit{round off to two decimal places}$).
The demand and forecast of an item for five months are given in the table. ... $\text{(MAPE)}$ in the forecast is __________________ $\% (\textit{round off to two decimal places}$)
A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at $300 \text{ K}$ at a rate of $100 \text{ kg/s}$. The overall heat transfer coefficient is $1500 \text{ W/m}^{2}.\text{K}$, and total heat transfer area ... $\text{K} (\textit{round off to the nearest integer}$).
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 $\text{T(y)} = 300 + 200 \exp (-5y)$, where $\text{y}$ is the distance measured from the slab surface in ... $\text{|dT/dy|}$ within the slab at $y=0$ is ____________________ $\text{K/m} (\textit{round off to the nearest integer}$).
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 $y = 0$ ... time taken by water in the tank to reach a level of $\text{y = H/4}$ is __________________ seconds ($\textit{round off to one decimal places}$).
Consider the open feed water heater $\text{(FWH)}$ shown in the figure given below: Specific enthalpy of steam at location $2$ is $\text{2624 kJ/kg}$, specific enthalpy of water at location $5$ is $\text{226.7 kJ/kg}$ and specific enthalpy of saturated water at location $6$ ... $2$ will be ________ $\text{kg/s}$ (round off to one decimal place).
A high velocity water jet of cross section area = $0.01 \text{ m}^{2}$ and velocity $\text{35 m/s}$ enters a pipe filled with stagnant water. The diameter of the pipe is $\text{0.32 m}$. This high velocity water jet entrains additional water from the pipe ... as shown in the figure. The flow rate of entrained water is _______________ liters/$\text{s}\: (\textit{round off to two decimal places}$).
A vertical shaft Francis turbine rotates at $\text{300 rpm}$. The available head at the inlet to the turbine is $\text{200 m}$. The tip speed of the rotor is $\text{40 m/s}$ ... $g=9.8 \text{ m/s}^{2}$. The hydraulic efficiency of the turbine is ______ $\% (\textit{round off to one decimal place}$).
An adiabatic vortex tube, shown in the figure given below is supplied with $\text{5 kg/s}$ of air (inlet $1$) at $\text{500 kPa}$ and $\text{300 K}$. Two separate streams of air are leaving the device from outlets $2$ and $3$. Hot air leaves the ... transfer across the boundary of this device. The rate of entropy generation is _______ $\text{kW/K}\:(\textit{round off to one decimal place}$).
A block of negligible mass rests on a surface that is inclined at $30^{\circ}$ to the horizontal plane as shown in the figure. When a vertical force of $\text{900 N}$ and a horizontal force of $\text{750 N}$ are applied, the block is just about to slide. The coefficient of static friction between the block and surface is _______ ($\textit{round off to two decimal places}$).
The wheels and axle system lying on a rough surface is shown in the figure. Each wheel has diameter $\text{0.8 m}$ and mass $\text{1 kg}$ ... . The acceleration of the wheel axle system in horizontal direction is ______ $\text{m/s}^{2} (\textit{round off to one decimal place}$).
A cantilever beam with a uniform flexural rigidity ($\text{EI} = 200 \times 10^{6} \text{N.m}^{2}$ ) is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is $10000 \text{ N.m}^{2}$. The magnitude of the slope of the beam at its free end is ______ micro radian ($\textit{round off to the nearest integer}$).
The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. The mean speed of the engine is $\text{200 rpm}$ and it drives a machine that provides a ... $\text{kg.m}^{2} (\textit{round off to the nearest integer}$).
The figure shows the relationship between fatigue strength $\text{(S)}$ and fatigue life $\text{(N)}$ of a material. The fatigue strength of the material for a life of $1000$ cycles is $\text{450 MPa}$, while its fatigue strength for a life of $10^{6}$ ... this material subjected to an alternating stress of $\text{200 MPa}$ will then be _______ cycles ($\textit{round off to the nearest integer}$).
Robot $\text{Ltd}$. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the customer demand during the lead time period is $95\%$. The lead time ... achieve this demand fulfillment probability for the lead time period is _____________ units ($\textit{round off to two decimal places}$).
A pressure measurement device fitted on the surface of a submarine, located at a depth $\text{H}$ below the surface of an ocean, reads an absolute pressure of $\text{4.2 MPa}$. The density of sea water is $\text{1050 kg/m$^{3}$}$, the atmospheric pressure is $\text{101 kPa}$, ... $}$ The depth $\text{H}$ is _____________ $\text{m}$ ($\textit{round off to the nearest integer}$).
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 $\text{U= 4 m/s}$. Separation between the plates is $\text{5 mm}$. There ... $\text{Pa}$ ($\textit{round off to the nearest integer}$).
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 $\text{250 kPa}$ and $\text{400 K}$ respectively. Now the valve is opened and air is allowed to flow into the tank ... $\text{K}$ ($\textit{round off to one decimal place}$).
The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is $\text{100 kg.m}^{2}$. The propeller rotates at $\omega =12$ $\text{rad/s}$. The waves acting on the ship ... The gyroscopic moment generated on the shaft due to the motion described is ________ $\text{N.m}(\textit{round off to the nearest integer}$).
Consider a single degree of freedom system comprising a mass $\text{M}$, supported on a spring and a dashpot as shown in the figure. If the amplitude of the free vibration response reduces from $\text{8 mm}$ to $\text{1.5 mm}$ in $3$ cycles, the damping ratio of the system is ______________ ($\textit{round off to three decimal places}$).
Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are ... ________________ ($\textit{round off to two decimal places}$). ($\text{Note}$: Probability is a number between $0$ and $1$).
A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of $\text{250 mm}$ and inner diameter of $\text{230 mm}$. The value of acceleration due to gravity, $g = 10\text{ m/s}^{2}$ ... $\text{rpm}$ ($\textit{round off to the nearest integer}$).
The resistance spot welding of two $\text{1.55 mm}$ thick metal sheets is performed using welding current of $\text{10000 A}$ for $\text{0.25 s}$. The contact resistance at the interface of the metal sheets is $0.0001\; \Omega$ . The volume of weld nugget formed after ... $\%$ ($\textit{round off to one decimal place}$).
An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of $12^{\circ}$ on a lathe. During turning, the cutting force and the friction force are $\text{1000 N}$ and $\text{600 N}$, respectively. If the chip thickness and the uncut ... $\text{0.75 mm}$, respectively, then the shear force is ________$\text{N}$ ($\textit{round off to two decimal places}$).
In a grinding operation of a metal, specific energy consumption is $15 \text{ J/mm}^{3}$. If a grinding wheel with a diameter of $\text{200 mm}$ is rotating at $\text{3000 rpm}$ to obtain a material removal rate of $6000\text{ mm$^{3}$/min}$, then the tangential force on the wheel is _______ $\text{N}$ ($\textit{round off to two decimal places}$).
A $\text{200 mm}$ wide plate having a thickness of $\text{20 mm}$ is fed through a rolling mill with two rolls. The radius of each roll is $\text{300 mm}$. The plate thickness is to be reduced to $\text{18 mm}$ in one pass using a roll speed of ... friction is sufficient to permit the rolling operation then the roll force will be _________ $\text{kN}$ ($\textit{round off to the nearest integer}$).
The $\text{XY}$ table of a $\text{NC}$ machine tool is to move from $P(1,1)$ to $Q(51,1)$; all coordinates are in $\text{mm}$. The pitch of the $\text{NC}$ drive leadscrew is $\text{1 mm}$. If the backlash between the leadscrew and the nut is $1.8^{\circ}$ ... the total backlash of the table on moving from $\text{P}$ to $\text{Q}$ is ______ $\text{mm}$ ($\textit{round off to two decimal places}$)