A solid cylinder of diameter $$D$$ and height equal to $$D,$$ and a solid cube of side $$L$$ are being sand cast by using the same material. Assuming there is no super-heat in both the cases, the ratio of solidification times of the cylinder to the solidification time of the cube is

Hot chamber die casting is NOT suited for

The value of the determinant $$\left| {\matrix{ 1 & 3 & 2 \cr 4 & 1 & 1 \cr 2 & 1 & 3 \cr } } \right|$$ is

During the numerical solution of a first order differential equation using the Euler (also known as Euler Cauchy) method with step size $$h,$$ the local truncation error is of the order of

The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions
(i) $${{dy} \over {dx}} = 1$$ at $$x=0$$
(ii) $${{dy} \over {dx}} = 1$$ at $$x=1$$

The homogeneous part of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + qy = r\,\,$$ ( $$p, q, r$$ are constants) has real distinct roots if

The line integral of the vector function $$\overrightarrow F = 2x\widehat i + {x^2}\widehat j\,\,$$ along the $$x$$ - axis from $$x=1$$ to $$x=2$$ is

The total derivative of the function $$'xy'$$ is

The value of $${x_3}$$ obtained by solving the following system of linear equations is $$${x_1} + 2{x_2} - 2{x_3} = 4$$$ $$$2{x_1} + {x_2} + {x_3} = - 2$$$ $$$ - {x_1} + {x_2} - {x_3} = 2$$$

The pressure drop for laminar flow of a liquid in a smooth pipe at normal temperature and pressure is

Consider steady flow of water in a situation where two pipe lines (pipe $$1$$ and pipe $$2$$) combine into a single pipe line $$(pipe-3)$$ as shown in the figure. The cross-sectional areas of all three pipelines are constant. The following data is given :

Assuming the water properties and the velocities to be uniform across the cross section of the inlets and the outlet, the exit velocity (in $$m/s$$) in pipe $$3$$ is

Heat is being transferred convectively from a cylindrical nuclear reactor fuel rod of $$50mm$$ diameter to water at $${70^ \circ }C$$, under steady state condition, the rate of heat generation within the fuel element is $$50 \times {10^6}\,\,W/{m^3}$$ and the convective heat transfer coefficient is $$1$$ $$kW/{m^2}K.$$ The outer surface temperature of the fuel element would be

Resistance spot welding of two steel sheets is carried out in lap joint configuration by using a welding current of $$3$$ $$KA$$ and a weld time of $$0.2s.$$ A molten weld nugget of volume $$20m{m^3}$$ is obtained. The effective contact resistance is $$200\mu \Omega .$$ The material properties of steel are given as (i) latent heat of melting $$1400$$ $$kJ/kg,$$ (ii) density $$8000$$ $$kg/{m^3},$$ (iii) melting temp $${1520^ \circ }C$$, (iv) specific heat $$0.5$$ $$kJ/kgC.$$ The ambient temp is $$20C.$$

Heat (Joules) dissipated to the base metal will be (neglecting all other heat losses)

Resistance spot welding of two steel sheets is carried out in lap joint configuration by using a welding current of $$3$$ $$KA$$ and a weld time of $$0.2s.$$ A molten weld nugget of volume $$20m{m^3}$$ is obtained. The effective contact resistance is $$200\mu \Omega .$$ The material properties of steel are given as (i) latent heat of melting $$1400$$ $$kJ/kg,$$ (ii) density $$8000$$ $$kg/{m^3},$$ (iii) melting temp $${1520^ \circ }C$$, (iv) specific heat $$0.5$$ $$kJ/kgC.$$ The ambient temp is $$20C.$$

Heat (in Joules) used for producing weld nugget will be (assuming $$100\% $$ heat transfer efficiency

Autogeneous gas tungsten arc welding of a steel plate is carried out with welding current of $$500A,$$ voltage of $$20V,$$ and weld speed of $$20mm/min.$$ Consider the heat transfer efficiency from the arc to the weld pool as $$90\% $$. The heat input per unit length (in $$kJ/mm$$) is

A titanium sheet of $$5.0mm$$ thickness is cut by wire cut $$EDM$$ process using a wire of $$1.0mm$$ diameter. A uniform spark gap of $$0.5mm$$ on both sides of the wire is maintained during cutting operation. If the feed rate of the wire into the sheet is $$20mm/min,$$ the material removal rate (in $$m{m^3}/\min $$) will be

The total angular movement (in degrees) of a lead screw with a pitch of $$5.0mm$$ to drive the work table by a distance of $$200mm$$ in a $$NC$$ machine is

An orthogonal operation is carried out at $$20m/min$$ cutting speed, using a cutting tool of rake angle $$15deg$$. The chip thickness is $$0.4mm$$ and uncut chip thickness is $$0.2mm.$$

The chip velocity (in $$m/min$$) is

An orthogonal operation is carried out at $$20m/min$$ cutting speed, using a cutting tool of rake angle $$15deg$$. The chip thickness is $$0.4mm$$ and uncut chip thickness is $$0.2mm.$$

The shear angle (in degrees) is

In an orthogonal machining operation , the tool life obtained is $$10min$$ at a cutting speed of $$10m/min,$$ while at $$75m/min$$ cutting speed, the tool life is $$30min$$. The value of index (n) in the Taylor's tool life equation is

Diamond cutting tools are not recommended for machining of ferrous metals due to

Using direct extrusion process, a round billet of $$100$$ $$mm$$ length and $$50mm$$ diameter is extruded. Considering an ideal deformation process (no friction and no redundant work), extrusion ratio $$4$$ and average flow stress of material $$300$$ $$MPa,$$ the pressure $$(MPa)$$ on the $$ram$$ will be

A disc of $$200$$ $$mm$$ diameter is blanked from a strip of an aluminium alloy of thickness $$3.2$$ $$mm.$$ The material shear strength to fracture is $$150$$ $$MPa.$$ The blanking force (in $$kN$$) is

Anisotropy in rolled components is caused by

Match the following

An autocollimator is used to