Air flows through a venture and into atmosphere. Air density is $$\rho $$; atmospheric pressure is $$'\,{P_a}';$$ throat diameter is exit diameter is $$'{D_t}';$$ and exit velocity is $$U.$$ the throat is connected to a cylinder containing a frictionless piston attached to a spring. The spring constant is $$'k'.$$ the bottom surface of the piston is exposed to atmosphere. Due to the flow, the piston moves by distance $$x.$$ assuming incompressible frictionless flow, $$x$$ is

A water container is kept on a weighing balance. Water from a tap is falling vertically into the container with a volume flow rate of $$'Q'$$; the velocity of the water when it hits the water surface is $$'U'$$. At a particular instant of time the total mass of the container and water is $$'m'.$$ The force registered by the weighing balance at this instant of time is

Water flows through a vertical contraction from a pipe of diameter $$d$$ to another of diameter $$d/2$$ (see Figure). The flow velocity at the inlet to the contraction is $$2m/s$$ and pressure $$200$$ $$kN/{m^2}.$$ If the height of the contraction measures $$2m$$, then pressure at the exit of the contraction will be very nearly

A jet of water issues from a Nozzle with a velocity $$20$$ $$m/s$$ and it impinges normally on a flat plate moving away from it at $$10\,m/s.$$ The cross-sectional area of the jet is $$0.01$$ $${m^2},$$ and the density of water $$ =1000\,\,kg/{m^3}.$$ The force developed on the plate is: