Water $$\left( {\rho = 1000\,\,kg/{m^3}} \right)$$ flows horizontally through a nozzle into the atmosphere under the conditions given below. (assume steady state flow).

At inlet: $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$ At outlet:
$${A_1} = {10^{ - 3}}{m^2};\,$$ $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$ $${A_2} = {10^{ - 4}}{m^2};$$
$${V_1} = 2\,m/\sec ;$$ $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,$$ $${P_2} = {P_{atm}}$$
$${P_1} = 3 \times {10^5}\,Pa\,(gauge)$$

Determine the external horizontal force needed to keep the nozzle

A Venturimeter (throat diameter $$=10.5$$ $$cm$$) is fitted to a water pipe line (internal diameter $$=21.0$$ $$cm$$) in order to monitor flow rate. To improve accuracy of measurement, pressure difference across the venturimeter is measured with the help of an inclined tube manometer, the angle of inclination being $${30^0}$$ (see figure below). For manometer reading of $$9.5$$ $$cm$$ of mercury, find the flow rate.Discharge coefficient of venture is $$0.984.$$

A jet of water with a velocity $${V_1}$$ (Figure shown below) and area of cross-section $${A_1}$$ enters a stream of slow moving water in a pipe of area $${A_2}$$ and velocity $${V_2}$$. The two streams enter with the same pressure $${P_1}$$. After thoroughly mixing in the pipe the stream emerges as a single stream with velocity $${V_3}$$ and pressure $${p_2}$$. If there are no losses in the flow, determine $$\left( {{p_2} - {p_1}} \right)$$ for
$${V_1} = 20\,\,m/s,\,\,$$
$${V_2} = 10\,\,m/s,\,\,$$
$${A_1} = 0.01\,\,{m^2},\,$$
$$\,{A_2} = 0.02\,{m^2},$$
density of water $$\rho = 1000kg/{m^3}.$$

In a syringe as shown in the figure, a piston of $$1\,\,c{m^2}$$ cross section is pushed at a constant speed of $$10\,\,cm/s$$ to eject water through an outlet of $$1\,\,m{m^2}.$$ Determine the force required to move the piston. Neglecting losses.