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.

Consider the saline drip bottle shown. If $$\rho $$ is the density of saline, find
(a) Pressure at $$A,$$
(b) The velocity of flow of saline through the tube. (Neglect viscous losses in tube). Atmospheric pressure $${P_{atm}}.$$

A jet of water (area $${A_j},$$ velocity $${V_j},$$ density $$\rho $$ ) impinges horizontally on a curved vane which deflects the jet through $${60^0}$$ upwards. If the vane travels horizontally at a speed $$'u'$$ find
(a) the force experienced by the vane, and
(b) the power developed by the vane.