A smooth pipe of diameter $$200$$ $$mm$$ carries water. The pressure in the pipe at section
$${S_1}\,\,$$ (elevation : $$10$$ $$m$$ ) is the $$50$$ $$kPa.$$ At section
$${S_2}\,\,$$ (elevation : $$12$$ $$m$$ ) the pressure is $$20$$ $$kPa$$ and velocity is $$2$$ $$m/s.$$
Density of water is $$1000$$ $$kg/{m^3}$$ and acceleration due to gravity is $$9.8$$ $$m{s^{ - 2}}.$$ Which of the following is TRUE?

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 $$U$$-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?

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