Question

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.

Answer 1

(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