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A massless smooth piston forces water with a velocity of 8 m/s out of a tube shaped container with radii 4.0 cm and 1.0 cm respectively as shown in the figure. Assume that the water leaving the container enters air at 1 atmospheric pressure. Find (a) The velocity of the piston. (b) Force F applied to the piston.

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(a) Let F be the force applied horizontally such that v1 is the velocity of water in tube A of radius 4.0 cm and v2 equal to 8 m/s is the velocity of water out of tube B of radius 1.0 cm. Let p0 be atmospheric pressure.

∴ At A, v1 = ?, r1 = 4.0 cm, p1 = p0 +F/a

where a is area of cross-section of piston or tube A

At B, v2 = 8 m/s, r2 = 1.0 cm, p2 = p0

Bernoulli’s theorem at A and B gives,

p1 +1/2 ρv12 +hρg = p2 +1/2 ρv22 +hρg

where ρ is density of water and h is height of axis of both tubes from ground level

Equation of continuity at A and B gives

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