A $$2m \times 2m$$ square operating in a vertical wall is covered with a metalic plate of the same dimensions as shown in the figure below. Consider the acceleration due to gravity to be $$10.0\,\,m/{s^2}.$$ The force (in kN) exerted by water on the plate is _____________.

A vertical cylindrical tank of $$1$$ $$m$$ diameter is filled with water up to a height of $$5$$ $$m$$ from its bottom. Top surface of water is exposed to atmosphere. A hole of $$5$$ $$m{m^2}$$ area forms at the bottom of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due to gravity to be $$10\,\,m/{s^2}$$, the rate of leakage of water (in litre/min) through the hole from the tank to the atmosphere, under the given conditions, is ______________

In a fully developed turbulent flow through a circular pipe, a head loss of ݄$${{h_1}}$$ is observed. The diameter of the pipe is increased by $$10\% $$ for the same flow rate and a head loss of ݄$${{h_2}}$$ is noted. Assume friction factor for both the cases of pipe flow is the same. The ratio of $${{{h_2}} \over {{h_1}}}$$is closest to

A long slender metallic rod of length $$L$$ is used as a fin. As shown in the figure below, the left end of the fin is kept at a constant temperature $${t_b}.$$ The fin loses heat by convection to the atmosphere which is at a temperature ta $${t_a}\,\,\left( {{t_a} < {t_b}} \right).$$ Four options of temperature profiles are shown. Identify the correct option.