Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from $$20cm$$ to $$10cm.$$ The pressure in the $$20cm$$ pipe just upstream of the reducer is $$150kPa.$$ The fluid has a vapour pressure of $$50kPa$$ and a specific weight of $$5\,\,kN/{m^3}.$$ Neglecting frictional effects, the maximum discharge (in $${m^3}/s$$) that can pass through the reducer without causing cavitation is

A venturimeter of $$20$$ $$mm$$ throat diameter is used to measure the velocity of water in a horizontal pipe of $$40$$ $$mm$$ diameter. If the pressure difference between the pipe and throat sections is found to be $$30$$ $$kPa$$ then, neglecting frictional losses, the flow velocity is

A $$U$$-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two locations $$A$$ and $$B$$ in a conical section through which an incompressible fluid flows. At a particular flow rate, the mercury column appears as shown in the figure. The density of mercury is $$13600$$ $$kg/{m^3}$$ and $$g = 9.81$$ $$m/{s^2}.$$ Which of the following is correct?

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