Instantaneous centre of a body rolling with sliding on a stationary curved surface lies.

A Venturimeter (throat diameter $$=10.5$$ $$cm$$) is fitted to a water pipe line (internal diameter $$=21.0$$ $$cm$$) in order to monitor flow rate. To improve accuracy of measurement, pressure difference across the venturimeter is measured with the help of an inclined tube manometer, the angle of inclination being $${30^0}$$ (see figure below). For manometer reading of $$9.5$$ $$cm$$ of mercury, find the flow rate.Discharge coefficient of venture is $$0.984.$$

A fluid flowing over a flat plate has the following properties: dynamic viscocity $$ = 25 \times {10^{ - 6}}\,\,kg/ms,$$ specific heat $$=2.0 $$ $$kJ/kgK,$$ thermal conductivity $$0.05W/mK.$$ The hydrodynamic boundary layer thickness is measured to be $$0.5$$ $$mm.$$ The thickness of the thermal boundary layer would be

Two rods, one of length $$L$$ and the other of length $$2L$$ are made of the same material and have the same diameter. The two ends of the longer rod are maintained at $${100^ \circ }C.$$ One end of the shorter end is maintained at $${100^ \circ }C.$$ while the other end is insulated. Both the rods are exposed to the same environment at $${40^ \circ }C.$$ The temperature at the insulated end of the shorter rod is measured to be $${55^ \circ }C.$$ The temperature at the mid-point of the longer rod would be