Water flows steadily through a horizontal pipe that narrows from a cross-sectional…

PHYSICS · Single correct · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

Water flows steadily through a horizontal pipe that narrows from a cross-sectional area of

4.0\times10^{-3}\,\text{m}^2

1.0\times10^{-3}\,\text{m}^2

. Just downstream of the narrow section, a small, flush-mounted piston of area

2.0\times10^{-4}\,\text{m}^2

forms part of the pipe wall and is exposed to the water inside; the outer face of the piston is open to the atmosphere at pressure

1.0\times10^{5}\,\text{Pa}

. Upstream of the narrowing, the water speed is

1.2\,\text{m}\,\text{s}^{-1}

and the absolute pressure is

2.0\times10^{5}\,\text{Pa}

. Taking

\rho_{\text{water}} = 1.0\times10^{3}\,\text{kg}\,\text{m}^{-3}

, what is the magnitude of the net force exerted by the water on the piston? (a)

3.6\times10^{1}\;\text{N}

(b)

1.8\times10^{1}\;\text{N}

(c)

2.2\times10^{1}\;\text{N}

(d)

9.0\;\text{N}