A cube shaped casting solidifies in $$5$$ min. The solidification time in min for a cube of the same material, which is $$8$$ times heavier than the original casting, will be

Water $$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$ at $${80^ \circ }C$$ enters a counter flow heat exchanger with a mass flow rate of $$0.5kg/s.$$ Air $$\left( {{C_p} = 1\,kJ/kg.\,K} \right)$$ enters at $${80^ \circ }C$$ with a mass flow rate $$2.09$$ $$kg/s.$$ If the effectiveness of the heat exchanger is $$0.8,$$ the $$LMTD$$ (in $$^ \circ C$$) is

Two cutting tools are being compared for a machining operation. The tool life equations are:
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,Carbi{\mathop{\rm de}\nolimits} \,\,tool:\,\,\,\,\,\,\,\,\,\,\,\,V{T^{1.6}} = 3000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,HSS\,\,tool:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,V{T^{0.6}} = 200 \cr} $$

Where $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in $$min.$$ The carbide tool will provide higher tool life if the cutting speed in $$m/min$$ exceeds

Details pertaining to an orthogonal metal cutting process are given below.

Chip thickness ratio $$0.4$$
Under formed thickness $$0.6mm$$
Rake angle $$ + {10^0}$$
Cutting speed $$2.5m/s$$
Mean thickness of primary shear zone $$25microns$$

The shear strain rate in $${s^{ - 1}}$$ during the process is

Following data refers to an automat and a center lathe, which are being compared to machine a batch of parts in a manufacturing shop

Automat will be economical if the batch size exceeds

In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$mm$$ and cutting velocity of $$90$$ $$m/min,$$ it is observed that the main (tangential) cutting force is prependicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is $$1500$$ $$N.$$

The orthogonal rake angle of the cutting tool in degree is

In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$mm$$ and cutting velocity of $$90$$ $$m/min,$$ it is observed that the main (tangential) cutting force is prependicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is $$1500$$ $$N.$$

The normal force acting at the chip-tool interface in $$N$$ is

A steel bar $$200$$ $$mm$$ in diameter is turned at a feed of $$0.25$$ $$mm/rev$$ with a depth of cut of $$4$$ $$mm.$$ The rotational speed of the work piece is $$160$$ $$rpm.$$ The material removal rate in $$m{m^3}/s$$ is

A disc of $$200$$ $$mm$$ outer and $$80$$ $$mm$$ inner diameter is faced at a feed of $$0.1$$ $$mm/rev$$ with a depth of cut of $$1$$ $$mm.$$ The facing operation is undertaken at a constant cutting speed of $$90$$ $$m/min$$ in a $$CNC$$ lathe. The main (tangential) cutting force is $$200$$ $$N$$

Assuming approach and over-travel of the cutting tool to be zero, the machining time in $$min$$ is

A disc of $$200$$ $$mm$$ outer and $$80$$ $$mm$$ inner diameter is faced at a feed of $$0.1$$ $$mm/rev$$ with a depth of cut of $$1$$ $$mm.$$ The facing operation is undertaken at a constant cutting speed of $$90$$ $$m/min$$ in a $$CNC$$ lathe. The main (tangential) cutting force is $$200$$ $$N$$

Neglecting the contribution of the feed force towards cutting power, the specific cutting energy in $$J/m{m^3}$$ is

In a $$CAD$$ package, mirror image of a $$2D$$ points $$P(5, 10)$$ is to be obtained about a line which passes through the origin and makes an angle of $${45^ \circ }$$ counterclockwise with the $$X$$-axis. The coordinates of the transformed points will be

In a rolling process, the state of stress of the material undergoing deformation is

Circular blanks of $$10mm$$ diameter are punched from an aluminium sheet of $$2$$ $$mm$$ thickness. The shear strength of aluminium is $$80$$ $$MPa.$$ The minimum punching force required in $$kN$$ is

Cylindrical pins of $${25^{\matrix{ { + 0.020} \cr { + 0.010} \cr } }}\,\,mm$$ diameter are electroplated in a shop. Thickness of the plating is $$30 \pm 0.2$$ micron. Neglecting gage tolerances, the size of the $$GO$$ gage in $$mm$$ to inspect the plated components is