The function $$f\left( z \right) = {{{z^2} + 1} \over {{z^2} + 4}}$$ is singular at

In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of the focusing tube, abrasive particles and water come out with equal velocity. Consider that there is no air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) of the abrasive water jet at the end of the focusing tube is _________.

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 _____________.

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