A siphon draws water from a reservoir and discharges it out at atmospheric pressure. Assuming ideal fluid and the reservoir is large, the velocity at point $$P$$ in the siphon tube is:

A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at $$U = 10\,m/s.$$ The thickness of the boundary layer at section $$r$$- $$s$$ is $$10$$ $$mm,$$ the breadth of the plate is $$1$$ $$m$$ (into the paper) and the density of the gas, $$\rho = 1.0\,kg/{m^3}.$$ Assume that the boundary layer is thin, two-dimensional, and follows a linear velocity distribution, $$u = U\left( {y/\delta } \right),$$ at the section $$r$$-$$s$$, where $$y$$ is the height from plate.

The mass flow rate (in kg/s) across the section $$q$$-$$r$$ is

A $$100$$ $$W$$ electric bulb was switched on in a $$2.5 \times 3 \times 3m$$ size thermally insulated room having temperature of $${20^0}C.$$ Room temp at the end of $$24$$ hours will be

With an increase in the thickness of insulation around a circular pipe, heat loss to surroundings due to